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blitzkit/docs/technical/kitscore.html
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2024-10-22 23:47:52 -05:00

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<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<title>KitScore</title>
<style>
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/*---------------------------------------------------------------------------------------------
* Copyright (c) Microsoft Corporation. All rights reserved.
* Licensed under the MIT License. See License.txt in the project root for license information.
*--------------------------------------------------------------------------------------------*/
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border-top: 1px solid var(--color-border-default);
}
.github-markdown-body .footnotes ol {
padding-left: 16px;
}
.github-markdown-body .footnotes ol ul {
display: inline-block;
padding-left: 16px;
margin-top: 16px;
}
.github-markdown-body .footnotes li {
position: relative;
}
.github-markdown-body .footnotes li:target::before {
position: absolute;
top: -8px;
right: -8px;
bottom: -8px;
left: -24px;
pointer-events: none;
content: "";
border: 2px solid var(--color-accent-emphasis);
border-radius: 6px;
}
.github-markdown-body .footnotes li:target {
color: var(--color-fg-default);
}
.github-markdown-body .footnotes .data-footnote-backref g-emoji {
font-family: monospace;
}
.github-markdown-body .pl-c {
color: var(--color-prettylights-syntax-comment);
}
.github-markdown-body .pl-c1,
.github-markdown-body .pl-s .pl-v {
color: var(--color-prettylights-syntax-constant);
}
.github-markdown-body .pl-e,
.github-markdown-body .pl-en {
color: var(--color-prettylights-syntax-entity);
}
.github-markdown-body .pl-smi,
.github-markdown-body .pl-s .pl-s1 {
color: var(--color-prettylights-syntax-storage-modifier-import);
}
.github-markdown-body .pl-ent {
color: var(--color-prettylights-syntax-entity-tag);
}
.github-markdown-body .pl-k {
color: var(--color-prettylights-syntax-keyword);
}
.github-markdown-body .pl-s,
.github-markdown-body .pl-pds,
.github-markdown-body .pl-s .pl-pse .pl-s1,
.github-markdown-body .pl-sr,
.github-markdown-body .pl-sr .pl-cce,
.github-markdown-body .pl-sr .pl-sre,
.github-markdown-body .pl-sr .pl-sra {
color: var(--color-prettylights-syntax-string);
}
.github-markdown-body .pl-v,
.github-markdown-body .pl-smw {
color: var(--color-prettylights-syntax-variable);
}
.github-markdown-body .pl-bu {
color: var(--color-prettylights-syntax-brackethighlighter-unmatched);
}
.github-markdown-body .pl-ii {
color: var(--color-prettylights-syntax-invalid-illegal-text);
background-color: var(--color-prettylights-syntax-invalid-illegal-bg);
}
.github-markdown-body .pl-c2 {
color: var(--color-prettylights-syntax-carriage-return-text);
background-color: var(--color-prettylights-syntax-carriage-return-bg);
}
.github-markdown-body .pl-sr .pl-cce {
font-weight: bold;
color: var(--color-prettylights-syntax-string-regexp);
}
.github-markdown-body .pl-ml {
color: var(--color-prettylights-syntax-markup-list);
}
.github-markdown-body .pl-mh,
.github-markdown-body .pl-mh .pl-en,
.github-markdown-body .pl-ms {
font-weight: bold;
color: var(--color-prettylights-syntax-markup-heading);
}
.github-markdown-body .pl-mi {
font-style: italic;
color: var(--color-prettylights-syntax-markup-italic);
}
.github-markdown-body .pl-mb {
font-weight: bold;
color: var(--color-prettylights-syntax-markup-bold);
}
.github-markdown-body .pl-md {
color: var(--color-prettylights-syntax-markup-deleted-text);
background-color: var(--color-prettylights-syntax-markup-deleted-bg);
}
.github-markdown-body .pl-mi1 {
color: var(--color-prettylights-syntax-markup-inserted-text);
background-color: var(--color-prettylights-syntax-markup-inserted-bg);
}
.github-markdown-body .pl-mc {
color: var(--color-prettylights-syntax-markup-changed-text);
background-color: var(--color-prettylights-syntax-markup-changed-bg);
}
.github-markdown-body .pl-mi2 {
color: var(--color-prettylights-syntax-markup-ignored-text);
background-color: var(--color-prettylights-syntax-markup-ignored-bg);
}
.github-markdown-body .pl-mdr {
font-weight: bold;
color: var(--color-prettylights-syntax-meta-diff-range);
}
.github-markdown-body .pl-ba {
color: var(--color-prettylights-syntax-brackethighlighter-angle);
}
.github-markdown-body .pl-sg {
color: var(--color-prettylights-syntax-sublimelinter-gutter-mark);
}
.github-markdown-body .pl-corl {
text-decoration: underline;
color: var(--color-prettylights-syntax-constant-other-reference-link);
}
.github-markdown-body g-emoji {
display: inline-block;
min-width: 1ch;
font-family: "Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";
font-size: 1em;
font-style: normal !important;
font-weight: var(--base-text-weight-normal, 400);
line-height: 1;
vertical-align: -0.075em;
}
.github-markdown-body g-emoji img {
width: 1em;
height: 1em;
}
.github-markdown-body .task-list-item {
list-style-type: none;
}
.github-markdown-body .task-list-item label {
font-weight: var(--base-text-weight-normal, 400);
}
.github-markdown-body .task-list-item.enabled label {
cursor: pointer;
}
.github-markdown-body .task-list-item+.task-list-item {
margin-top: 4px;
}
.github-markdown-body .task-list-item .handle {
display: none;
}
.github-markdown-body .task-list-item-checkbox {
margin: 0 .2em .25em -1.4em;
vertical-align: middle;
}
.github-markdown-body .contains-task-list:dir(rtl) .task-list-item-checkbox {
margin: 0 -1.6em .25em .2em;
}
.github-markdown-body .contains-task-list {
position: relative;
}
.github-markdown-body .contains-task-list:hover .task-list-item-convert-container,
.github-markdown-body .contains-task-list:focus-within .task-list-item-convert-container {
display: block;
width: auto;
height: 24px;
overflow: visible;
clip: auto;
}
.github-markdown-body ::-webkit-calendar-picker-indicator {
filter: invert(50%);
}
.github-markdown-body .markdown-alert {
padding: var(--base-size-8) var(--base-size-16);
margin-bottom: 16px;
color: inherit;
border-left: .25em solid var(--color-border-default);
}
.github-markdown-body .markdown-alert>:first-child {
margin-top: 0;
}
.github-markdown-body .markdown-alert>:last-child {
margin-bottom: 0;
}
.github-markdown-body .markdown-alert .markdown-alert-title {
display: flex;
font-weight: var(--base-text-weight-medium, 500);
align-items: center;
line-height: 1;
}
.github-markdown-body .markdown-alert.markdown-alert-note {
border-left-color: var(--color-accent-emphasis);
}
.github-markdown-body .markdown-alert.markdown-alert-note .markdown-alert-title {
color: var(--color-accent-fg);
}
.github-markdown-body .markdown-alert.markdown-alert-important {
border-left-color: var(--color-done-emphasis);
}
.github-markdown-body .markdown-alert.markdown-alert-important .markdown-alert-title {
color: var(--color-done-fg);
}
.github-markdown-body .markdown-alert.markdown-alert-warning {
border-left-color: var(--color-attention-emphasis);
}
.github-markdown-body .markdown-alert.markdown-alert-warning .markdown-alert-title {
color: var(--color-attention-fg);
}
.github-markdown-body .markdown-alert.markdown-alert-tip {
border-left-color: var(--color-success-emphasis);
}
.github-markdown-body .markdown-alert.markdown-alert-tip .markdown-alert-title {
color: var(--color-success-fg);
}
.github-markdown-body .markdown-alert.markdown-alert-caution {
border-left-color: var(--color-danger-emphasis);
}
.github-markdown-body .markdown-alert.markdown-alert-caution .markdown-alert-title {
color: var(--color-danger-fg);
}
.github-markdown-body>*:first-child>.heading-element:first-child {
margin-top: 0 !important;
}
[data-color-mode=light][data-light-theme=light],
[data-color-mode=dark][data-dark-theme=light],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=light],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=light] {
/*light*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #116329;
--color-prettylights-syntax-keyword: #cf222e;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #953800;
--color-prettylights-syntax-brackethighlighter-unmatched: #82071e;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #82071e;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #cf222e;
--color-prettylights-syntax-string-regexp: #116329;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #82071e;
--color-prettylights-syntax-markup-deleted-bg: #ffebe9;
--color-prettylights-syntax-markup-inserted-text: #116329;
--color-prettylights-syntax-markup-inserted-bg: #dafbe1;
--color-prettylights-syntax-markup-changed-text: #953800;
--color-prettylights-syntax-markup-changed-bg: #ffd8b5;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #1F2328;
--color-fg-muted: #656d76;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #1a7f37;
--color-success-emphasis: #1f883d;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #d1242f;
--color-danger-emphasis: #cf222e;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=light] {
/*light*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #116329;
--color-prettylights-syntax-keyword: #cf222e;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #953800;
--color-prettylights-syntax-brackethighlighter-unmatched: #82071e;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #82071e;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #cf222e;
--color-prettylights-syntax-string-regexp: #116329;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #82071e;
--color-prettylights-syntax-markup-deleted-bg: #ffebe9;
--color-prettylights-syntax-markup-inserted-text: #116329;
--color-prettylights-syntax-markup-inserted-bg: #dafbe1;
--color-prettylights-syntax-markup-changed-text: #953800;
--color-prettylights-syntax-markup-changed-bg: #ffd8b5;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #1F2328;
--color-fg-muted: #656d76;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #1a7f37;
--color-success-emphasis: #1f883d;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #d1242f;
--color-danger-emphasis: #cf222e;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=light] {
/*light*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #116329;
--color-prettylights-syntax-keyword: #cf222e;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #953800;
--color-prettylights-syntax-brackethighlighter-unmatched: #82071e;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #82071e;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #cf222e;
--color-prettylights-syntax-string-regexp: #116329;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #82071e;
--color-prettylights-syntax-markup-deleted-bg: #ffebe9;
--color-prettylights-syntax-markup-inserted-text: #116329;
--color-prettylights-syntax-markup-inserted-bg: #dafbe1;
--color-prettylights-syntax-markup-changed-text: #953800;
--color-prettylights-syntax-markup-changed-bg: #ffd8b5;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #1F2328;
--color-fg-muted: #656d76;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #1a7f37;
--color-success-emphasis: #1f883d;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #d1242f;
--color-danger-emphasis: #cf222e;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
}
[data-color-mode=light][data-light-theme=light_colorblind],
[data-color-mode=dark][data-dark-theme=light_colorblind],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=light_colorblind],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=light_colorblind] {
/*light_colorblind*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #0550ae;
--color-prettylights-syntax-keyword: #b35900;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #8a4600;
--color-prettylights-syntax-brackethighlighter-unmatched: #6f3800;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #6f3800;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #b35900;
--color-prettylights-syntax-string-regexp: #0550ae;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #6f3800;
--color-prettylights-syntax-markup-deleted-bg: #fff5e8;
--color-prettylights-syntax-markup-inserted-text: #0550ae;
--color-prettylights-syntax-markup-inserted-bg: #ddf4ff;
--color-prettylights-syntax-markup-changed-text: #8a4600;
--color-prettylights-syntax-markup-changed-bg: #ffddb0;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #24292f;
--color-fg-muted: #57606a;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #0969da;
--color-success-emphasis: #0969da;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #b35900;
--color-danger-emphasis: #b35900;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=light_colorblind] {
/*light_colorblind*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #0550ae;
--color-prettylights-syntax-keyword: #b35900;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #8a4600;
--color-prettylights-syntax-brackethighlighter-unmatched: #6f3800;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #6f3800;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #b35900;
--color-prettylights-syntax-string-regexp: #0550ae;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #6f3800;
--color-prettylights-syntax-markup-deleted-bg: #fff5e8;
--color-prettylights-syntax-markup-inserted-text: #0550ae;
--color-prettylights-syntax-markup-inserted-bg: #ddf4ff;
--color-prettylights-syntax-markup-changed-text: #8a4600;
--color-prettylights-syntax-markup-changed-bg: #ffddb0;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #24292f;
--color-fg-muted: #57606a;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #0969da;
--color-success-emphasis: #0969da;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #b35900;
--color-danger-emphasis: #b35900;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=light_colorblind] {
/*light_colorblind*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #0550ae;
--color-prettylights-syntax-keyword: #b35900;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #8a4600;
--color-prettylights-syntax-brackethighlighter-unmatched: #6f3800;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #6f3800;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #b35900;
--color-prettylights-syntax-string-regexp: #0550ae;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #6f3800;
--color-prettylights-syntax-markup-deleted-bg: #fff5e8;
--color-prettylights-syntax-markup-inserted-text: #0550ae;
--color-prettylights-syntax-markup-inserted-bg: #ddf4ff;
--color-prettylights-syntax-markup-changed-text: #8a4600;
--color-prettylights-syntax-markup-changed-bg: #ffddb0;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #24292f;
--color-fg-muted: #57606a;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #0969da;
--color-success-emphasis: #0969da;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #b35900;
--color-danger-emphasis: #b35900;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
}
[data-color-mode=light][data-light-theme=light_tritanopia],
[data-color-mode=dark][data-dark-theme=light_tritanopia],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=light_tritanopia],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=light_tritanopia] {
/*light_tritanopia*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #0550ae;
--color-prettylights-syntax-keyword: #cf222e;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #a40e26;
--color-prettylights-syntax-brackethighlighter-unmatched: #82071e;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #82071e;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #cf222e;
--color-prettylights-syntax-string-regexp: #0550ae;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #82071e;
--color-prettylights-syntax-markup-deleted-bg: #ffebe9;
--color-prettylights-syntax-markup-inserted-text: #0550ae;
--color-prettylights-syntax-markup-inserted-bg: #ddf4ff;
--color-prettylights-syntax-markup-changed-text: #a40e26;
--color-prettylights-syntax-markup-changed-bg: #ffcecb;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #24292f;
--color-fg-muted: #57606a;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #0969da;
--color-success-emphasis: #0969da;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #cf222e;
--color-danger-emphasis: #cf222e;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=light_tritanopia] {
/*light_tritanopia*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #0550ae;
--color-prettylights-syntax-keyword: #cf222e;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #a40e26;
--color-prettylights-syntax-brackethighlighter-unmatched: #82071e;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #82071e;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #cf222e;
--color-prettylights-syntax-string-regexp: #0550ae;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #82071e;
--color-prettylights-syntax-markup-deleted-bg: #ffebe9;
--color-prettylights-syntax-markup-inserted-text: #0550ae;
--color-prettylights-syntax-markup-inserted-bg: #ddf4ff;
--color-prettylights-syntax-markup-changed-text: #a40e26;
--color-prettylights-syntax-markup-changed-bg: #ffcecb;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #24292f;
--color-fg-muted: #57606a;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #0969da;
--color-success-emphasis: #0969da;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #cf222e;
--color-danger-emphasis: #cf222e;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=light_tritanopia] {
/*light_tritanopia*/
color-scheme: light;
--color-prettylights-syntax-comment: #57606a;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #6639ba;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #0550ae;
--color-prettylights-syntax-keyword: #cf222e;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #a40e26;
--color-prettylights-syntax-brackethighlighter-unmatched: #82071e;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #82071e;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #cf222e;
--color-prettylights-syntax-string-regexp: #0550ae;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #82071e;
--color-prettylights-syntax-markup-deleted-bg: #ffebe9;
--color-prettylights-syntax-markup-inserted-text: #0550ae;
--color-prettylights-syntax-markup-inserted-bg: #ddf4ff;
--color-prettylights-syntax-markup-changed-text: #a40e26;
--color-prettylights-syntax-markup-changed-bg: #ffcecb;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #24292f;
--color-fg-muted: #57606a;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-success-fg: #0969da;
--color-success-emphasis: #0969da;
--color-attention-fg: #9a6700;
--color-attention-emphasis: #9a6700;
--color-attention-subtle: #fff8c5;
--color-danger-fg: #cf222e;
--color-danger-emphasis: #cf222e;
--color-done-fg: #8250df;
--color-done-emphasis: #8250df;
}
}
[data-color-mode=light][data-light-theme=light_high_contrast],
[data-color-mode=dark][data-dark-theme=light_high_contrast],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=light_high_contrast],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=light_high_contrast] {
/*light_high_contrast*/
color-scheme: light;
--color-prettylights-syntax-comment: #4b535d;
--color-prettylights-syntax-constant: #023b95;
--color-prettylights-syntax-entity: #512598;
--color-prettylights-syntax-storage-modifier-import: #0e1116;
--color-prettylights-syntax-entity-tag: #024c1a;
--color-prettylights-syntax-keyword: #a0111f;
--color-prettylights-syntax-string: #032563;
--color-prettylights-syntax-variable: #702c00;
--color-prettylights-syntax-brackethighlighter-unmatched: #6e011a;
--color-prettylights-syntax-invalid-illegal-text: #ffffff;
--color-prettylights-syntax-invalid-illegal-bg: #6e011a;
--color-prettylights-syntax-carriage-return-text: #ffffff;
--color-prettylights-syntax-carriage-return-bg: #a0111f;
--color-prettylights-syntax-string-regexp: #024c1a;
--color-prettylights-syntax-markup-list: #2e1800;
--color-prettylights-syntax-markup-heading: #023b95;
--color-prettylights-syntax-markup-italic: #0e1116;
--color-prettylights-syntax-markup-bold: #0e1116;
--color-prettylights-syntax-markup-deleted-text: #6e011a;
--color-prettylights-syntax-markup-deleted-bg: #fff0ee;
--color-prettylights-syntax-markup-inserted-text: #024c1a;
--color-prettylights-syntax-markup-inserted-bg: #d2fedb;
--color-prettylights-syntax-markup-changed-text: #702c00;
--color-prettylights-syntax-markup-changed-bg: #ffc67b;
--color-prettylights-syntax-markup-ignored-text: #e7ecf0;
--color-prettylights-syntax-markup-ignored-bg: #023b95;
--color-prettylights-syntax-meta-diff-range: #622cbc;
--color-prettylights-syntax-brackethighlighter-angle: #4b535d;
--color-prettylights-syntax-sublimelinter-gutter-mark: #88929d;
--color-prettylights-syntax-constant-other-reference-link: #032563;
--color-fg-default: #0e1116;
--color-fg-muted: #0e1116;
--color-fg-subtle: #66707b;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #e7ecf0;
--color-border-default: #20252c;
--color-border-muted: #88929d;
--color-neutral-muted: rgba(172,182,192,0.2);
--color-accent-fg: #0349b4;
--color-accent-emphasis: #0349b4;
--color-success-fg: #055d20;
--color-success-emphasis: #055d20;
--color-attention-fg: #744500;
--color-attention-emphasis: #744500;
--color-attention-subtle: #fcf7be;
--color-danger-fg: #d1242f;
--color-danger-emphasis: #a0111f;
--color-done-fg: #622cbc;
--color-done-emphasis: #622cbc;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=light_high_contrast] {
/*light_high_contrast*/
color-scheme: light;
--color-prettylights-syntax-comment: #4b535d;
--color-prettylights-syntax-constant: #023b95;
--color-prettylights-syntax-entity: #512598;
--color-prettylights-syntax-storage-modifier-import: #0e1116;
--color-prettylights-syntax-entity-tag: #024c1a;
--color-prettylights-syntax-keyword: #a0111f;
--color-prettylights-syntax-string: #032563;
--color-prettylights-syntax-variable: #702c00;
--color-prettylights-syntax-brackethighlighter-unmatched: #6e011a;
--color-prettylights-syntax-invalid-illegal-text: #ffffff;
--color-prettylights-syntax-invalid-illegal-bg: #6e011a;
--color-prettylights-syntax-carriage-return-text: #ffffff;
--color-prettylights-syntax-carriage-return-bg: #a0111f;
--color-prettylights-syntax-string-regexp: #024c1a;
--color-prettylights-syntax-markup-list: #2e1800;
--color-prettylights-syntax-markup-heading: #023b95;
--color-prettylights-syntax-markup-italic: #0e1116;
--color-prettylights-syntax-markup-bold: #0e1116;
--color-prettylights-syntax-markup-deleted-text: #6e011a;
--color-prettylights-syntax-markup-deleted-bg: #fff0ee;
--color-prettylights-syntax-markup-inserted-text: #024c1a;
--color-prettylights-syntax-markup-inserted-bg: #d2fedb;
--color-prettylights-syntax-markup-changed-text: #702c00;
--color-prettylights-syntax-markup-changed-bg: #ffc67b;
--color-prettylights-syntax-markup-ignored-text: #e7ecf0;
--color-prettylights-syntax-markup-ignored-bg: #023b95;
--color-prettylights-syntax-meta-diff-range: #622cbc;
--color-prettylights-syntax-brackethighlighter-angle: #4b535d;
--color-prettylights-syntax-sublimelinter-gutter-mark: #88929d;
--color-prettylights-syntax-constant-other-reference-link: #032563;
--color-fg-default: #0e1116;
--color-fg-muted: #0e1116;
--color-fg-subtle: #66707b;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #e7ecf0;
--color-border-default: #20252c;
--color-border-muted: #88929d;
--color-neutral-muted: rgba(172,182,192,0.2);
--color-accent-fg: #0349b4;
--color-accent-emphasis: #0349b4;
--color-success-fg: #055d20;
--color-success-emphasis: #055d20;
--color-attention-fg: #744500;
--color-attention-emphasis: #744500;
--color-attention-subtle: #fcf7be;
--color-danger-fg: #d1242f;
--color-danger-emphasis: #a0111f;
--color-done-fg: #622cbc;
--color-done-emphasis: #622cbc;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=light_high_contrast] {
/*light_high_contrast*/
color-scheme: light;
--color-prettylights-syntax-comment: #4b535d;
--color-prettylights-syntax-constant: #023b95;
--color-prettylights-syntax-entity: #512598;
--color-prettylights-syntax-storage-modifier-import: #0e1116;
--color-prettylights-syntax-entity-tag: #024c1a;
--color-prettylights-syntax-keyword: #a0111f;
--color-prettylights-syntax-string: #032563;
--color-prettylights-syntax-variable: #702c00;
--color-prettylights-syntax-brackethighlighter-unmatched: #6e011a;
--color-prettylights-syntax-invalid-illegal-text: #ffffff;
--color-prettylights-syntax-invalid-illegal-bg: #6e011a;
--color-prettylights-syntax-carriage-return-text: #ffffff;
--color-prettylights-syntax-carriage-return-bg: #a0111f;
--color-prettylights-syntax-string-regexp: #024c1a;
--color-prettylights-syntax-markup-list: #2e1800;
--color-prettylights-syntax-markup-heading: #023b95;
--color-prettylights-syntax-markup-italic: #0e1116;
--color-prettylights-syntax-markup-bold: #0e1116;
--color-prettylights-syntax-markup-deleted-text: #6e011a;
--color-prettylights-syntax-markup-deleted-bg: #fff0ee;
--color-prettylights-syntax-markup-inserted-text: #024c1a;
--color-prettylights-syntax-markup-inserted-bg: #d2fedb;
--color-prettylights-syntax-markup-changed-text: #702c00;
--color-prettylights-syntax-markup-changed-bg: #ffc67b;
--color-prettylights-syntax-markup-ignored-text: #e7ecf0;
--color-prettylights-syntax-markup-ignored-bg: #023b95;
--color-prettylights-syntax-meta-diff-range: #622cbc;
--color-prettylights-syntax-brackethighlighter-angle: #4b535d;
--color-prettylights-syntax-sublimelinter-gutter-mark: #88929d;
--color-prettylights-syntax-constant-other-reference-link: #032563;
--color-fg-default: #0e1116;
--color-fg-muted: #0e1116;
--color-fg-subtle: #66707b;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #e7ecf0;
--color-border-default: #20252c;
--color-border-muted: #88929d;
--color-neutral-muted: rgba(172,182,192,0.2);
--color-accent-fg: #0349b4;
--color-accent-emphasis: #0349b4;
--color-success-fg: #055d20;
--color-success-emphasis: #055d20;
--color-attention-fg: #744500;
--color-attention-emphasis: #744500;
--color-attention-subtle: #fcf7be;
--color-danger-fg: #d1242f;
--color-danger-emphasis: #a0111f;
--color-done-fg: #622cbc;
--color-done-emphasis: #622cbc;
}
}
[data-color-mode=light][data-light-theme=dark],
[data-color-mode=dark][data-dark-theme=dark],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=dark],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=dark] {
/*dark*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #7ee787;
--color-prettylights-syntax-keyword: #ff7b72;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #ffa657;
--color-prettylights-syntax-brackethighlighter-unmatched: #f85149;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #8e1519;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #b62324;
--color-prettylights-syntax-string-regexp: #7ee787;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffdcd7;
--color-prettylights-syntax-markup-deleted-bg: #67060c;
--color-prettylights-syntax-markup-inserted-text: #aff5b4;
--color-prettylights-syntax-markup-inserted-bg: #033a16;
--color-prettylights-syntax-markup-changed-text: #ffdfb6;
--color-prettylights-syntax-markup-changed-bg: #5a1e02;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #e6edf3;
--color-fg-muted: #848d97;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #2f81f7;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #3fb950;
--color-success-emphasis: #238636;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #f85149;
--color-danger-emphasis: #da3633;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=dark] {
/*dark*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #7ee787;
--color-prettylights-syntax-keyword: #ff7b72;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #ffa657;
--color-prettylights-syntax-brackethighlighter-unmatched: #f85149;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #8e1519;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #b62324;
--color-prettylights-syntax-string-regexp: #7ee787;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffdcd7;
--color-prettylights-syntax-markup-deleted-bg: #67060c;
--color-prettylights-syntax-markup-inserted-text: #aff5b4;
--color-prettylights-syntax-markup-inserted-bg: #033a16;
--color-prettylights-syntax-markup-changed-text: #ffdfb6;
--color-prettylights-syntax-markup-changed-bg: #5a1e02;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #e6edf3;
--color-fg-muted: #848d97;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #2f81f7;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #3fb950;
--color-success-emphasis: #238636;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #f85149;
--color-danger-emphasis: #da3633;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=dark] {
/*dark*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #7ee787;
--color-prettylights-syntax-keyword: #ff7b72;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #ffa657;
--color-prettylights-syntax-brackethighlighter-unmatched: #f85149;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #8e1519;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #b62324;
--color-prettylights-syntax-string-regexp: #7ee787;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffdcd7;
--color-prettylights-syntax-markup-deleted-bg: #67060c;
--color-prettylights-syntax-markup-inserted-text: #aff5b4;
--color-prettylights-syntax-markup-inserted-bg: #033a16;
--color-prettylights-syntax-markup-changed-text: #ffdfb6;
--color-prettylights-syntax-markup-changed-bg: #5a1e02;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #e6edf3;
--color-fg-muted: #848d97;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #2f81f7;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #3fb950;
--color-success-emphasis: #238636;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #f85149;
--color-danger-emphasis: #da3633;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
}
[data-color-mode=light][data-light-theme=dark_dimmed],
[data-color-mode=dark][data-dark-theme=dark_dimmed],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=dark_dimmed],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=dark_dimmed] {
/*dark_dimmed*/
color-scheme: dark;
--color-prettylights-syntax-comment: #768390;
--color-prettylights-syntax-constant: #6cb6ff;
--color-prettylights-syntax-entity: #dcbdfb;
--color-prettylights-syntax-storage-modifier-import: #adbac7;
--color-prettylights-syntax-entity-tag: #8ddb8c;
--color-prettylights-syntax-keyword: #f47067;
--color-prettylights-syntax-string: #96d0ff;
--color-prettylights-syntax-variable: #f69d50;
--color-prettylights-syntax-brackethighlighter-unmatched: #e5534b;
--color-prettylights-syntax-invalid-illegal-text: #cdd9e5;
--color-prettylights-syntax-invalid-illegal-bg: #922323;
--color-prettylights-syntax-carriage-return-text: #cdd9e5;
--color-prettylights-syntax-carriage-return-bg: #ad2e2c;
--color-prettylights-syntax-string-regexp: #8ddb8c;
--color-prettylights-syntax-markup-list: #eac55f;
--color-prettylights-syntax-markup-heading: #316dca;
--color-prettylights-syntax-markup-italic: #adbac7;
--color-prettylights-syntax-markup-bold: #adbac7;
--color-prettylights-syntax-markup-deleted-text: #ffd8d3;
--color-prettylights-syntax-markup-deleted-bg: #78191b;
--color-prettylights-syntax-markup-inserted-text: #b4f1b4;
--color-prettylights-syntax-markup-inserted-bg: #1b4721;
--color-prettylights-syntax-markup-changed-text: #ffddb0;
--color-prettylights-syntax-markup-changed-bg: #682d0f;
--color-prettylights-syntax-markup-ignored-text: #adbac7;
--color-prettylights-syntax-markup-ignored-bg: #255ab2;
--color-prettylights-syntax-meta-diff-range: #dcbdfb;
--color-prettylights-syntax-brackethighlighter-angle: #768390;
--color-prettylights-syntax-sublimelinter-gutter-mark: #545d68;
--color-prettylights-syntax-constant-other-reference-link: #96d0ff;
--color-fg-default: #adbac7;
--color-fg-muted: #768390;
--color-fg-subtle: #636e7b;
--color-canvas-default: #22272e;
--color-canvas-subtle: #2d333b;
--color-border-default: #444c56;
--color-border-muted: #373e47;
--color-neutral-muted: rgba(99,110,123,0.4);
--color-accent-fg: #539bf5;
--color-accent-emphasis: #316dca;
--color-success-fg: #57ab5a;
--color-success-emphasis: #347d39;
--color-attention-fg: #c69026;
--color-attention-emphasis: #966600;
--color-attention-subtle: rgba(174,124,20,0.15);
--color-danger-fg: #e5534b;
--color-danger-emphasis: #c93c37;
--color-done-fg: #986ee2;
--color-done-emphasis: #8256d0;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=dark_dimmed] {
/*dark_dimmed*/
color-scheme: dark;
--color-prettylights-syntax-comment: #768390;
--color-prettylights-syntax-constant: #6cb6ff;
--color-prettylights-syntax-entity: #dcbdfb;
--color-prettylights-syntax-storage-modifier-import: #adbac7;
--color-prettylights-syntax-entity-tag: #8ddb8c;
--color-prettylights-syntax-keyword: #f47067;
--color-prettylights-syntax-string: #96d0ff;
--color-prettylights-syntax-variable: #f69d50;
--color-prettylights-syntax-brackethighlighter-unmatched: #e5534b;
--color-prettylights-syntax-invalid-illegal-text: #cdd9e5;
--color-prettylights-syntax-invalid-illegal-bg: #922323;
--color-prettylights-syntax-carriage-return-text: #cdd9e5;
--color-prettylights-syntax-carriage-return-bg: #ad2e2c;
--color-prettylights-syntax-string-regexp: #8ddb8c;
--color-prettylights-syntax-markup-list: #eac55f;
--color-prettylights-syntax-markup-heading: #316dca;
--color-prettylights-syntax-markup-italic: #adbac7;
--color-prettylights-syntax-markup-bold: #adbac7;
--color-prettylights-syntax-markup-deleted-text: #ffd8d3;
--color-prettylights-syntax-markup-deleted-bg: #78191b;
--color-prettylights-syntax-markup-inserted-text: #b4f1b4;
--color-prettylights-syntax-markup-inserted-bg: #1b4721;
--color-prettylights-syntax-markup-changed-text: #ffddb0;
--color-prettylights-syntax-markup-changed-bg: #682d0f;
--color-prettylights-syntax-markup-ignored-text: #adbac7;
--color-prettylights-syntax-markup-ignored-bg: #255ab2;
--color-prettylights-syntax-meta-diff-range: #dcbdfb;
--color-prettylights-syntax-brackethighlighter-angle: #768390;
--color-prettylights-syntax-sublimelinter-gutter-mark: #545d68;
--color-prettylights-syntax-constant-other-reference-link: #96d0ff;
--color-fg-default: #adbac7;
--color-fg-muted: #768390;
--color-fg-subtle: #636e7b;
--color-canvas-default: #22272e;
--color-canvas-subtle: #2d333b;
--color-border-default: #444c56;
--color-border-muted: #373e47;
--color-neutral-muted: rgba(99,110,123,0.4);
--color-accent-fg: #539bf5;
--color-accent-emphasis: #316dca;
--color-success-fg: #57ab5a;
--color-success-emphasis: #347d39;
--color-attention-fg: #c69026;
--color-attention-emphasis: #966600;
--color-attention-subtle: rgba(174,124,20,0.15);
--color-danger-fg: #e5534b;
--color-danger-emphasis: #c93c37;
--color-done-fg: #986ee2;
--color-done-emphasis: #8256d0;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=dark_dimmed] {
/*dark_dimmed*/
color-scheme: dark;
--color-prettylights-syntax-comment: #768390;
--color-prettylights-syntax-constant: #6cb6ff;
--color-prettylights-syntax-entity: #dcbdfb;
--color-prettylights-syntax-storage-modifier-import: #adbac7;
--color-prettylights-syntax-entity-tag: #8ddb8c;
--color-prettylights-syntax-keyword: #f47067;
--color-prettylights-syntax-string: #96d0ff;
--color-prettylights-syntax-variable: #f69d50;
--color-prettylights-syntax-brackethighlighter-unmatched: #e5534b;
--color-prettylights-syntax-invalid-illegal-text: #cdd9e5;
--color-prettylights-syntax-invalid-illegal-bg: #922323;
--color-prettylights-syntax-carriage-return-text: #cdd9e5;
--color-prettylights-syntax-carriage-return-bg: #ad2e2c;
--color-prettylights-syntax-string-regexp: #8ddb8c;
--color-prettylights-syntax-markup-list: #eac55f;
--color-prettylights-syntax-markup-heading: #316dca;
--color-prettylights-syntax-markup-italic: #adbac7;
--color-prettylights-syntax-markup-bold: #adbac7;
--color-prettylights-syntax-markup-deleted-text: #ffd8d3;
--color-prettylights-syntax-markup-deleted-bg: #78191b;
--color-prettylights-syntax-markup-inserted-text: #b4f1b4;
--color-prettylights-syntax-markup-inserted-bg: #1b4721;
--color-prettylights-syntax-markup-changed-text: #ffddb0;
--color-prettylights-syntax-markup-changed-bg: #682d0f;
--color-prettylights-syntax-markup-ignored-text: #adbac7;
--color-prettylights-syntax-markup-ignored-bg: #255ab2;
--color-prettylights-syntax-meta-diff-range: #dcbdfb;
--color-prettylights-syntax-brackethighlighter-angle: #768390;
--color-prettylights-syntax-sublimelinter-gutter-mark: #545d68;
--color-prettylights-syntax-constant-other-reference-link: #96d0ff;
--color-fg-default: #adbac7;
--color-fg-muted: #768390;
--color-fg-subtle: #636e7b;
--color-canvas-default: #22272e;
--color-canvas-subtle: #2d333b;
--color-border-default: #444c56;
--color-border-muted: #373e47;
--color-neutral-muted: rgba(99,110,123,0.4);
--color-accent-fg: #539bf5;
--color-accent-emphasis: #316dca;
--color-success-fg: #57ab5a;
--color-success-emphasis: #347d39;
--color-attention-fg: #c69026;
--color-attention-emphasis: #966600;
--color-attention-subtle: rgba(174,124,20,0.15);
--color-danger-fg: #e5534b;
--color-danger-emphasis: #c93c37;
--color-done-fg: #986ee2;
--color-done-emphasis: #8256d0;
}
}
[data-color-mode=light][data-light-theme=dark_colorblind],
[data-color-mode=dark][data-dark-theme=dark_colorblind],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=dark_colorblind],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=dark_colorblind] {
/*dark_colorblind*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #a5d6ff;
--color-prettylights-syntax-keyword: #ec8e2c;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #fdac54;
--color-prettylights-syntax-brackethighlighter-unmatched: #d47616;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #6c3906;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #914d04;
--color-prettylights-syntax-string-regexp: #a5d6ff;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffe2bb;
--color-prettylights-syntax-markup-deleted-bg: #4e2906;
--color-prettylights-syntax-markup-inserted-text: #cae8ff;
--color-prettylights-syntax-markup-inserted-bg: #0c2d6b;
--color-prettylights-syntax-markup-changed-text: #ffe2bb;
--color-prettylights-syntax-markup-changed-bg: #4e2906;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #c9d1d9;
--color-fg-muted: #8b949e;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #58a6ff;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #58a6ff;
--color-success-emphasis: #1f6feb;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #d47616;
--color-danger-emphasis: #b76100;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=dark_colorblind] {
/*dark_colorblind*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #a5d6ff;
--color-prettylights-syntax-keyword: #ec8e2c;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #fdac54;
--color-prettylights-syntax-brackethighlighter-unmatched: #d47616;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #6c3906;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #914d04;
--color-prettylights-syntax-string-regexp: #a5d6ff;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffe2bb;
--color-prettylights-syntax-markup-deleted-bg: #4e2906;
--color-prettylights-syntax-markup-inserted-text: #cae8ff;
--color-prettylights-syntax-markup-inserted-bg: #0c2d6b;
--color-prettylights-syntax-markup-changed-text: #ffe2bb;
--color-prettylights-syntax-markup-changed-bg: #4e2906;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #c9d1d9;
--color-fg-muted: #8b949e;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #58a6ff;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #58a6ff;
--color-success-emphasis: #1f6feb;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #d47616;
--color-danger-emphasis: #b76100;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=dark_colorblind] {
/*dark_colorblind*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #a5d6ff;
--color-prettylights-syntax-keyword: #ec8e2c;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #fdac54;
--color-prettylights-syntax-brackethighlighter-unmatched: #d47616;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #6c3906;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #914d04;
--color-prettylights-syntax-string-regexp: #a5d6ff;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffe2bb;
--color-prettylights-syntax-markup-deleted-bg: #4e2906;
--color-prettylights-syntax-markup-inserted-text: #cae8ff;
--color-prettylights-syntax-markup-inserted-bg: #0c2d6b;
--color-prettylights-syntax-markup-changed-text: #ffe2bb;
--color-prettylights-syntax-markup-changed-bg: #4e2906;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #c9d1d9;
--color-fg-muted: #8b949e;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #58a6ff;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #58a6ff;
--color-success-emphasis: #1f6feb;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #d47616;
--color-danger-emphasis: #b76100;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
}
[data-color-mode=light][data-light-theme=dark_tritanopia],
[data-color-mode=dark][data-dark-theme=dark_tritanopia],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=dark_tritanopia],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=dark_tritanopia] {
/*dark_tritanopia*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #a5d6ff;
--color-prettylights-syntax-keyword: #ff7b72;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #ffa198;
--color-prettylights-syntax-brackethighlighter-unmatched: #f85149;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #8e1519;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #b62324;
--color-prettylights-syntax-string-regexp: #a5d6ff;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffdcd7;
--color-prettylights-syntax-markup-deleted-bg: #67060c;
--color-prettylights-syntax-markup-inserted-text: #cae8ff;
--color-prettylights-syntax-markup-inserted-bg: #0c2d6b;
--color-prettylights-syntax-markup-changed-text: #ffdcd7;
--color-prettylights-syntax-markup-changed-bg: #67060c;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #c9d1d9;
--color-fg-muted: #8b949e;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #58a6ff;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #58a6ff;
--color-success-emphasis: #1f6feb;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #f85149;
--color-danger-emphasis: #da3633;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=dark_tritanopia] {
/*dark_tritanopia*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #a5d6ff;
--color-prettylights-syntax-keyword: #ff7b72;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #ffa198;
--color-prettylights-syntax-brackethighlighter-unmatched: #f85149;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #8e1519;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #b62324;
--color-prettylights-syntax-string-regexp: #a5d6ff;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffdcd7;
--color-prettylights-syntax-markup-deleted-bg: #67060c;
--color-prettylights-syntax-markup-inserted-text: #cae8ff;
--color-prettylights-syntax-markup-inserted-bg: #0c2d6b;
--color-prettylights-syntax-markup-changed-text: #ffdcd7;
--color-prettylights-syntax-markup-changed-bg: #67060c;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #c9d1d9;
--color-fg-muted: #8b949e;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #58a6ff;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #58a6ff;
--color-success-emphasis: #1f6feb;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #f85149;
--color-danger-emphasis: #da3633;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=dark_tritanopia] {
/*dark_tritanopia*/
color-scheme: dark;
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #a5d6ff;
--color-prettylights-syntax-keyword: #ff7b72;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #ffa198;
--color-prettylights-syntax-brackethighlighter-unmatched: #f85149;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #8e1519;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #b62324;
--color-prettylights-syntax-string-regexp: #a5d6ff;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffdcd7;
--color-prettylights-syntax-markup-deleted-bg: #67060c;
--color-prettylights-syntax-markup-inserted-text: #cae8ff;
--color-prettylights-syntax-markup-inserted-bg: #0c2d6b;
--color-prettylights-syntax-markup-changed-text: #ffdcd7;
--color-prettylights-syntax-markup-changed-bg: #67060c;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #c9d1d9;
--color-fg-muted: #8b949e;
--color-fg-subtle: #6e7681;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #58a6ff;
--color-accent-emphasis: #1f6feb;
--color-success-fg: #58a6ff;
--color-success-emphasis: #1f6feb;
--color-attention-fg: #d29922;
--color-attention-emphasis: #9e6a03;
--color-attention-subtle: rgba(187,128,9,0.15);
--color-danger-fg: #f85149;
--color-danger-emphasis: #da3633;
--color-done-fg: #a371f7;
--color-done-emphasis: #8957e5;
}
}
[data-color-mode=light][data-light-theme=dark_high_contrast],
[data-color-mode=dark][data-dark-theme=dark_high_contrast],
.vscode-body.vscode-light [data-color-mode=auto][data-light-theme=dark_high_contrast],
.vscode-body.vscode-dark [data-color-mode=auto][data-dark-theme=dark_high_contrast] {
/*dark_high_contrast*/
color-scheme: dark;
--color-prettylights-syntax-comment: #bdc4cc;
--color-prettylights-syntax-constant: #91cbff;
--color-prettylights-syntax-entity: #dbb7ff;
--color-prettylights-syntax-storage-modifier-import: #f0f3f6;
--color-prettylights-syntax-entity-tag: #72f088;
--color-prettylights-syntax-keyword: #ff9492;
--color-prettylights-syntax-string: #addcff;
--color-prettylights-syntax-variable: #ffb757;
--color-prettylights-syntax-brackethighlighter-unmatched: #ff6a69;
--color-prettylights-syntax-invalid-illegal-text: #ffffff;
--color-prettylights-syntax-invalid-illegal-bg: #e82a2f;
--color-prettylights-syntax-carriage-return-text: #ffffff;
--color-prettylights-syntax-carriage-return-bg: #ff4445;
--color-prettylights-syntax-string-regexp: #72f088;
--color-prettylights-syntax-markup-list: #fbd669;
--color-prettylights-syntax-markup-heading: #409eff;
--color-prettylights-syntax-markup-italic: #f0f3f6;
--color-prettylights-syntax-markup-bold: #f0f3f6;
--color-prettylights-syntax-markup-deleted-text: #ffdedb;
--color-prettylights-syntax-markup-deleted-bg: #cc1421;
--color-prettylights-syntax-markup-inserted-text: #acf7b6;
--color-prettylights-syntax-markup-inserted-bg: #007728;
--color-prettylights-syntax-markup-changed-text: #ffe1b4;
--color-prettylights-syntax-markup-changed-bg: #a74c00;
--color-prettylights-syntax-markup-ignored-text: #f0f3f6;
--color-prettylights-syntax-markup-ignored-bg: #318bf8;
--color-prettylights-syntax-meta-diff-range: #dbb7ff;
--color-prettylights-syntax-brackethighlighter-angle: #bdc4cc;
--color-prettylights-syntax-sublimelinter-gutter-mark: #7a828e;
--color-prettylights-syntax-constant-other-reference-link: #addcff;
--color-fg-default: #f0f3f6;
--color-fg-muted: #f0f3f6;
--color-fg-subtle: #9ea7b3;
--color-canvas-default: #0a0c10;
--color-canvas-subtle: #272b33;
--color-border-default: #7a828e;
--color-border-muted: #7a828e;
--color-neutral-muted: rgba(158,167,179,0.4);
--color-accent-fg: #71b7ff;
--color-accent-emphasis: #409eff;
--color-success-fg: #26cd4d;
--color-success-emphasis: #09b43a;
--color-attention-fg: #f0b72f;
--color-attention-emphasis: #e09b13;
--color-attention-subtle: rgba(224,155,19,0.15);
--color-danger-fg: #ff6a69;
--color-danger-emphasis: #ff6a69;
--color-done-fg: #b780ff;
--color-done-emphasis: #b87fff;
}
@media (prefers-color-scheme: light) {
[data-color-mode='system'][data-light-theme=dark_high_contrast] {
/*dark_high_contrast*/
color-scheme: dark;
--color-prettylights-syntax-comment: #bdc4cc;
--color-prettylights-syntax-constant: #91cbff;
--color-prettylights-syntax-entity: #dbb7ff;
--color-prettylights-syntax-storage-modifier-import: #f0f3f6;
--color-prettylights-syntax-entity-tag: #72f088;
--color-prettylights-syntax-keyword: #ff9492;
--color-prettylights-syntax-string: #addcff;
--color-prettylights-syntax-variable: #ffb757;
--color-prettylights-syntax-brackethighlighter-unmatched: #ff6a69;
--color-prettylights-syntax-invalid-illegal-text: #ffffff;
--color-prettylights-syntax-invalid-illegal-bg: #e82a2f;
--color-prettylights-syntax-carriage-return-text: #ffffff;
--color-prettylights-syntax-carriage-return-bg: #ff4445;
--color-prettylights-syntax-string-regexp: #72f088;
--color-prettylights-syntax-markup-list: #fbd669;
--color-prettylights-syntax-markup-heading: #409eff;
--color-prettylights-syntax-markup-italic: #f0f3f6;
--color-prettylights-syntax-markup-bold: #f0f3f6;
--color-prettylights-syntax-markup-deleted-text: #ffdedb;
--color-prettylights-syntax-markup-deleted-bg: #cc1421;
--color-prettylights-syntax-markup-inserted-text: #acf7b6;
--color-prettylights-syntax-markup-inserted-bg: #007728;
--color-prettylights-syntax-markup-changed-text: #ffe1b4;
--color-prettylights-syntax-markup-changed-bg: #a74c00;
--color-prettylights-syntax-markup-ignored-text: #f0f3f6;
--color-prettylights-syntax-markup-ignored-bg: #318bf8;
--color-prettylights-syntax-meta-diff-range: #dbb7ff;
--color-prettylights-syntax-brackethighlighter-angle: #bdc4cc;
--color-prettylights-syntax-sublimelinter-gutter-mark: #7a828e;
--color-prettylights-syntax-constant-other-reference-link: #addcff;
--color-fg-default: #f0f3f6;
--color-fg-muted: #f0f3f6;
--color-fg-subtle: #9ea7b3;
--color-canvas-default: #0a0c10;
--color-canvas-subtle: #272b33;
--color-border-default: #7a828e;
--color-border-muted: #7a828e;
--color-neutral-muted: rgba(158,167,179,0.4);
--color-accent-fg: #71b7ff;
--color-accent-emphasis: #409eff;
--color-success-fg: #26cd4d;
--color-success-emphasis: #09b43a;
--color-attention-fg: #f0b72f;
--color-attention-emphasis: #e09b13;
--color-attention-subtle: rgba(224,155,19,0.15);
--color-danger-fg: #ff6a69;
--color-danger-emphasis: #ff6a69;
--color-done-fg: #b780ff;
--color-done-emphasis: #b87fff;
}
}
@media (prefers-color-scheme: dark) {
[data-color-mode='system'][data-dark-theme=dark_high_contrast] {
/*dark_high_contrast*/
color-scheme: dark;
--color-prettylights-syntax-comment: #bdc4cc;
--color-prettylights-syntax-constant: #91cbff;
--color-prettylights-syntax-entity: #dbb7ff;
--color-prettylights-syntax-storage-modifier-import: #f0f3f6;
--color-prettylights-syntax-entity-tag: #72f088;
--color-prettylights-syntax-keyword: #ff9492;
--color-prettylights-syntax-string: #addcff;
--color-prettylights-syntax-variable: #ffb757;
--color-prettylights-syntax-brackethighlighter-unmatched: #ff6a69;
--color-prettylights-syntax-invalid-illegal-text: #ffffff;
--color-prettylights-syntax-invalid-illegal-bg: #e82a2f;
--color-prettylights-syntax-carriage-return-text: #ffffff;
--color-prettylights-syntax-carriage-return-bg: #ff4445;
--color-prettylights-syntax-string-regexp: #72f088;
--color-prettylights-syntax-markup-list: #fbd669;
--color-prettylights-syntax-markup-heading: #409eff;
--color-prettylights-syntax-markup-italic: #f0f3f6;
--color-prettylights-syntax-markup-bold: #f0f3f6;
--color-prettylights-syntax-markup-deleted-text: #ffdedb;
--color-prettylights-syntax-markup-deleted-bg: #cc1421;
--color-prettylights-syntax-markup-inserted-text: #acf7b6;
--color-prettylights-syntax-markup-inserted-bg: #007728;
--color-prettylights-syntax-markup-changed-text: #ffe1b4;
--color-prettylights-syntax-markup-changed-bg: #a74c00;
--color-prettylights-syntax-markup-ignored-text: #f0f3f6;
--color-prettylights-syntax-markup-ignored-bg: #318bf8;
--color-prettylights-syntax-meta-diff-range: #dbb7ff;
--color-prettylights-syntax-brackethighlighter-angle: #bdc4cc;
--color-prettylights-syntax-sublimelinter-gutter-mark: #7a828e;
--color-prettylights-syntax-constant-other-reference-link: #addcff;
--color-fg-default: #f0f3f6;
--color-fg-muted: #f0f3f6;
--color-fg-subtle: #9ea7b3;
--color-canvas-default: #0a0c10;
--color-canvas-subtle: #272b33;
--color-border-default: #7a828e;
--color-border-muted: #7a828e;
--color-neutral-muted: rgba(158,167,179,0.4);
--color-accent-fg: #71b7ff;
--color-accent-emphasis: #409eff;
--color-success-fg: #26cd4d;
--color-success-emphasis: #09b43a;
--color-attention-fg: #f0b72f;
--color-attention-emphasis: #e09b13;
--color-attention-subtle: rgba(224,155,19,0.15);
--color-danger-fg: #ff6a69;
--color-danger-emphasis: #ff6a69;
--color-done-fg: #b780ff;
--color-done-emphasis: #b87fff;
}
}
/*!
Theme: GitHub
Description: Highlight-js port of github.com theme
Author: github.com
Maintainer: @SNDST00M, @mjbvz
Updated: 2021-12-08
*/
.markdown-body pre code.hljs {
display: block;
overflow-x: auto;
padding: 16px;
}
.markdown-body code.hljs {
padding: 3px 5px;
}
/*!
Theme: GitHub
Description: Theme as seen on github.com
Author: github.com
Maintainer: @Hirse
Updated: 2021-05-15
Outdated base version: https://github.com/primer/github-syntax-dark
Current colors taken from GitHub's CSS
*/
.markdown-body .hljs,
.markdown-body pre > code {
color: var(--color-fg-default);
background: var(--color-canvas-subtle);
}
.markdown-body .hljs-function,
.markdown-body .hljs-params {
color: var(--color-fg-default);
}
.markdown-body .hljs-doctag,
.markdown-body .hljs-keyword,
.markdown-body .hljs-meta .hljs-keyword,
.markdown-body .hljs-template-tag,
.markdown-body .hljs-template-variable,
.markdown-body .hljs-type,
.markdown-body .hljs-variable.language_ {
color: var(--color-prettylights-syntax-keyword);
}
.markdown-body .hljs-title,
.markdown-body .hljs-title.class_,
.markdown-body .hljs-title.class_.inherited__,
.markdown-body .hljs-title.function_ {
color: var(--color-prettylights-syntax-entity);
}
.markdown-body .hljs-attr,
.markdown-body .hljs-attribute,
.markdown-body .hljs-literal,
.markdown-body .hljs-meta,
.markdown-body .hljs-number,
.markdown-body .hljs-operator,
.markdown-body .hljs-selector-attr,
.markdown-body .hljs-selector-class,
.markdown-body .hljs-selector-id,
.markdown-body .hljs-variable {
color: var(--color-prettylights-syntax-constant);
}
.markdown-body .hljs-meta .hljs-string,
.markdown-body .hljs-regexp,
.markdown-body .hljs-string {
color: var(--color-prettylights-syntax-string);
}
.markdown-body .hljs-built_in,
.markdown-body .hljs-symbol {
color: var(--color-prettylights-syntax-variable);
}
.markdown-body .hljs-code,
.markdown-body .hljs-comment,
.markdown-body .hljs-formula {
color: var(--color-prettylights-syntax-comment);
}
.markdown-body .hljs-name,
.markdown-body .hljs-quote,
.markdown-body .hljs-selector-pseudo,
.markdown-body .hljs-selector-tag {
color: var(--color-prettylights-syntax-entity-tag);
}
.markdown-body .hljs-subst {
color: var(--color-prettylights-syntax-constant);
}
.markdown-body .hljs-section {
color: var(--color-prettylights-syntax-markup-heading);
font-weight: bold;
}
.markdown-body .hljs-bullet {
color: var(--color-prettylights-syntax-markup-list);
}
.markdown-body .hljs-emphasis {
color: var(--color-prettylights-syntax-constant);
font-style: italic;
}
.markdown-body .hljs-strong {
color: var(--color-prettylights-syntax-constant);
font-weight: bold;
}
.markdown-body .hljs-addition {
color: var(--color-prettylights-syntax-markup-inserted-text);
background-color: var(--color-prettylights-syntax-markup-inserted-bg);
}
.markdown-body .hljs-deletion {
color: var(--color-prettylights-syntax-markup-deleted-text);
background-color: var(--color-prettylights-syntax-markup-deleted-bg);
}
</style>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex/dist/katex.min.css">
<link href="https://cdn.jsdelivr.net/npm/katex-copytex@latest/dist/katex-copytex.min.css" rel="stylesheet" type="text/css">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/gh/Microsoft/vscode/extensions/markdown-language-features/media/markdown.css">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/gh/Microsoft/vscode/extensions/markdown-language-features/media/highlight.css">
<style>
body {
font-family: -apple-system, BlinkMacSystemFont, 'Segoe WPC', 'Segoe UI', system-ui, 'Ubuntu', 'Droid Sans', sans-serif;
font-size: 14px;
line-height: 1.6;
}
</style>
<style>
.task-list-item {
list-style-type: none;
}
.task-list-item-checkbox {
margin-left: -20px;
vertical-align: middle;
pointer-events: none;
}
</style>
<style>
:root {
--color-note: #0969da;
--color-tip: #1a7f37;
--color-warning: #9a6700;
--color-severe: #bc4c00;
--color-caution: #d1242f;
--color-important: #8250df;
}
</style>
<style>
@media (prefers-color-scheme: dark) {
:root {
--color-note: #2f81f7;
--color-tip: #3fb950;
--color-warning: #d29922;
--color-severe: #db6d28;
--color-caution: #f85149;
--color-important: #a371f7;
}
}
</style>
<style>
.markdown-alert {
padding: 0.5rem 1rem;
margin-bottom: 16px;
color: inherit;
border-left: .25em solid #888;
}
.markdown-alert>:first-child {
margin-top: 0
}
.markdown-alert>:last-child {
margin-bottom: 0
}
.markdown-alert .markdown-alert-title {
display: flex;
font-weight: 500;
align-items: center;
line-height: 1
}
.markdown-alert .markdown-alert-title .octicon {
margin-right: 0.5rem;
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<div class="github-markdown-content"><h1 id="kitscore">KitScore</h1>
<h2 id="memo">Memo</h2>
<p>A performance metric that makes sense. This metric can be applied to any game, virtual or real. Specific pieces of information relating directly to World of Tanks Blitz will be provided within parentheses and with a &quot;WoTB:&quot; prefix.</p>
<h2 id="consumption-of-observations">Consumption of Observations</h2>
<p>KitScore is driven solely by the behavior of other players and finding meaning of a new observation within a pool of condensed data based on previously observed data. Generally, we will be provided with a number of statistics (the <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> of an observation) per player (WoTB: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mtext>frags</mtext></msub></mrow><annotation encoding="application/x-tex">x_\text{frags}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">frags</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mtext>damage_dealt</mtext></msub></mrow><annotation encoding="application/x-tex">x_\text{damage\_dealt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7976em;vertical-align:-0.367em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">damage_dealt</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.367em;"><span></span></span></span></span></span></span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mtext>spots</mtext></msub></mrow><annotation encoding="application/x-tex">x_\text{spots}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">spots</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span>, etc.) including a target statistic (the <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span> of an observation) that all other statistics try to maximize (WoTB: &quot;winrate&quot; which we will defined later as <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span>).</p>
<p>If the statistics are cumulative, they will have to be normalized (WoTB: statistics fetched from Wargaming are indeed cumulative even for a single player; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mtext>frags</mtext></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Σ</mi><msub><mi>x</mi><mtext>frags</mtext></msub></mrow><mrow><mi mathvariant="normal">Σ</mi><msub><mi>x</mi><mtext>battles</mtext></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_\text{frags}=\frac{\Sigma x_\text{frags}}{\Sigma x_\text{battles}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">frags</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4423em;vertical-align:-0.4509em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9914em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Σ</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord text mtight"><span class="mord mtight">battles</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1512em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5131em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Σ</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord text mtight"><span class="mord mtight">frags</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2901em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4509em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mtext>spots</mtext></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Σ</mi><msub><mi>x</mi><mtext>spots</mtext></msub></mrow><mrow><mi mathvariant="normal">Σ</mi><msub><mi>x</mi><mtext>battles</mtext></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_\text{spots}=\frac{\Sigma x_\text{spots}}{\Sigma x_\text{battles}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">spots</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4365em;vertical-align:-0.4509em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9857em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Σ</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord text mtight"><span class="mord mtight">battles</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1512em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5073em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Σ</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2963em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord text mtight"><span class="mord mtight">spots</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2819em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4509em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Σ</mi><msub><mi>x</mi><mtext>wins</mtext></msub></mrow><mrow><mi mathvariant="normal">Σ</mi><msub><mi>x</mi><mtext>battles</mtext></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_j=\frac{\Sigma x_\text{wins}}{\Sigma x_\text{battles}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3393em;vertical-align:-0.4509em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8884em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Σ</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord text mtight"><span class="mord mtight">battles</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1512em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4101em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Σ</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.334em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord text mtight"><span class="mord mtight">wins</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4509em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>, etc.). Each player will have such average statistics, giving us many points of data to work with. If the statistics are not cumulative, then you will be dealing with multiple observations per player which will only help improve accuracy.</p>
<h2 id="its-impossible-to-find-what-makes-the-metric-tick">It’s Impossible to &quot;Find What Makes the Metric Tick&quot;</h2>
<p>WN8, a widely adopted metric in the World of Tanks and World of Tanks Blitz communities is plagued with problems. One of them being that people often &quot;what makes the metric tick.&quot; In other words, people easily exploit the rudimentary nature of WN8 to score undeservedly high.</p>
<p>In WN8, the gains of some rewarding categories overshadow the losses of others. KitScore makes this nearly impossible as it punishes a player for scoring well solely high in a certain category. You will never exploit KitScore. Period.</p>
<h2 id="generating-reasonable-values">Generating Reasonable Values</h2>
<p>TODO: there's like no runaway cases</p>
<h2 id="symbol-interpretation">Symbol Interpretation</h2>
<table>
<thead>
<tr>
<th>Symbol</th>
<th>Interpretation</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mtext>human</mtext></msub></mrow><annotation encoding="application/x-tex">A_\text{human}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">human</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td>The human readable version of the raw score <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span>.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span></td>
<td>The raw KitScore.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span></td>
<td>An arbitrary coefficient.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi></mrow><annotation encoding="application/x-tex">I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span></span></span></span></td>
<td>The number of statistics including the target statistic. This means that there are <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">I-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> entries for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> entry for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> for each observation.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span></span></span></span></td>
<td>The statistic index of where there are <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi></mrow><annotation encoding="application/x-tex">I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span></span></span></span> entries.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.854em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span></span></span></span></td>
<td>A discriminator for the target statistic. There may never be more than <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> entries for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.854em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span></span></span></span>.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span></td>
<td>The degree of the polynomial regression.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span></td>
<td>The number of observations.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span></td>
<td>An &quot;atomic&quot; score which is a function of the $i$th statistic.</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi></mrow><annotation encoding="application/x-tex">w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span></span></span></span></td>
<td>The weight of the $i$th atomic statistic.</td>
</tr>
</tbody>
</table>
<h2 id="computing-the-score">Computing the Score</h2>
<p>The final metric <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mtext>human</mtext></msub></mrow><annotation encoding="application/x-tex">A_\text{human}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">human</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> is an arbitrarily scaled value of the raw score <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span> where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span> is any coefficient of your liking. BlitzKit uses <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mo>=</mo><mn>1</mn><msup><mn>0</mn><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">C=10^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span>.</p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>A</mi><mtext>human</mtext></msub><mo>=</mo><mi>C</mi><mi>A</mi></mrow><annotation encoding="application/x-tex">A_\text{human}=CA
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mtight">human</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">A</span></span></span></span></span></p>
<p>The final metric <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span> is the weighted average of individual scores <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> which are functions of the $i$th statistic.</p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>A</mi><mo>=</mo><mfrac><mrow><mo>∑</mo><msub><mi>w</mi><mi>i</mi></msub><msub><mi>a</mi><mi>i</mi></msub></mrow><mrow><mo>∑</mo><msub><mi>w</mi><mi>i</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">A=\frac{\sum w_{i}a_{i}}{\sum w_{i}}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p>The &quot;atomic&quot; score <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> is the difference between the predicted target statistic <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>i</mi><mo>↔</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P_{i \leftrightarrow j}(x_i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">↔</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> acquired using a polynomial regression of degree <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span> and the actual newly observed <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span>.</p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>=</mo><msub><mi>x</mi><mi>j</mi></msub><mo>−</mo><msub><mi>P</mi><mrow><mi>i</mi><mo>↔</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">a_i=x_j-P_{i \leftrightarrow j}(x_i)
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">↔</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p>
<p>The polynomial regression of $m$th degree can be written as follows:</p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>P</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>β</mi><mn>0</mn></msub><msup><mi>x</mi><mn>0</mn></msup><mo>+</mo><msub><mi>β</mi><mn>1</mn></msub><msup><mi>x</mi><mn>1</mn></msup><mo>+</mo><msub><mi>β</mi><mn>2</mn></msub><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>β</mi><mi>m</mi></msub><msup><mi>x</mi><mi>m</mi></msup></mrow><annotation encoding="application/x-tex">P_i(x)=\beta_0x^0+\beta_1x^1+\beta_2x^2+\dots+\beta_mx^m
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0585em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0585em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0585em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.9088em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7144em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span></span></span></span></span></span></span></span></span></p>
<p>Polynomial regression coefficients <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span> can be acquired through basic linear algebra where an <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mo>×</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">m \times m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span> of constants is multiplied with <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mo>×</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">m \times 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> of unknowns which equals another <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mo>×</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">m \times 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> of constants.</p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center center center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>0</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>1</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mi>m</mi></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>1</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>3</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>3</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mn>4</mn></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mrow><mi>m</mi><mo>+</mo><mn>2</mn></mrow></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mi>m</mi></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msubsup><mi>x</mi><mi>i</mi><mrow><mn>2</mn><mi>m</mi></mrow></msubsup></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>β</mi><mn>0</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>β</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>β</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>β</mi><mi>m</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>x</mi><mi>j</mi></msub><msubsup><mi>x</mi><mi>i</mi><mn>0</mn></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>x</mi><mi>j</mi></msub><msubsup><mi>x</mi><mi>i</mi><mn>1</mn></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>x</mi><mi>j</mi></msub><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>x</mi><mi>j</mi></msub><msubsup><mi>x</mi><mi>i</mi><mi>m</mi></msubsup></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix}
\sum_{k=1}^n x_i^0 &amp; \sum_{k=1}^n x_i^1 &amp; \sum_{k=1}^n x_i^2 &amp; \dots &amp; \sum_{k=1}^n x_i^m \\
\sum_{k=1}^n x_i^1 &amp; \sum_{k=1}^n x_i^2 &amp; \sum_{k=1}^n x_i^3 &amp; \dots &amp; \sum_{k=1}^n x_i^{m+1} \\
\sum_{k=1}^n x_i^2 &amp; \sum_{k=1}^n x_i^3 &amp; \sum_{k=1}^n x_i^4 &amp; \dots &amp; \sum_{k=1}^n x_i^{m+2} \\
\vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots \\
\sum_{k=1}^n x_i^m &amp; \sum_{k=1}^n x_i^{m+1} &amp; \sum_{k=1}^n x_i^{m+1} &amp; \dots &amp; \sum_{k=1}^n x_i^{2m} \\
\end{bmatrix}
\begin{bmatrix}
\beta_0 \\
\beta_1 \\
\beta_2 \\
\vdots \\
\beta_m
\end{bmatrix}
=
\begin{bmatrix}
\sum_{k=1}^n x_jx_i^0 \\
\sum_{k=1}^n x_jx_i^1 \\
\sum_{k=1}^n x_jx_i^2 \\
\vdots \\
\sum_{k=1}^n x_jx_i^m
\end{bmatrix}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.7027em;vertical-align:-3.1014em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.55em;"><span style="top:-5.55em;"><span class="pstrut" style="height:8.6em;"></span><span style="width:0.667em;height:6.600em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.667em" height="6.600em" viewBox="0 0 667 6600"><path d="M403 1759 V84 H666 V0 H319 V1759 v3000 v1759 h347 v-84
H403z M403 1759 V0 H319 V1759 v3000 v1759 h84z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.6014em;"><span style="top:-6.4489em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-5.2346em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-4.0204em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.1604em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em;"></span></span></span></span><span style="top:-0.9461em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.1014em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.6014em;"><span style="top:-6.4489em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-5.2346em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-4.0204em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.1604em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em;"></span></span></span></span><span style="top:-0.9461em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8542em;"><span style="top:-2.4231em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2769em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.1014em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.6014em;"><span style="top:-6.4489em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-5.2346em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-4.0204em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.1604em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em;"></span></span></span></span><span style="top:-0.9461em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8542em;"><span style="top:-2.4231em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2769em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.1014em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.6014em;"><span style="top:-6.2614em;"><span class="pstrut" style="height:3.5em;"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-5.0471em;"><span class="pstrut" style="height:3.5em;"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-3.8329em;"><span class="pstrut" style="height:3.5em;"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-1.9729em;"><span class="pstrut" style="height:3.5em;"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:-0.7586em;"><span class="pstrut" style="height:3.5em;"></span><span class="mord"><span class="minner">…</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.1014em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.6014em;"><span style="top:-6.4489em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-5.2346em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8542em;"><span style="top:-2.4231em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2769em;"><span></span></span></span></span></span></span></span></span><span style="top:-4.0204em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8542em;"><span style="top:-2.4231em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mbin mtight">+</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2769em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.1604em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em;"></span></span></span></span><span style="top:-0.9461em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight">m</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.1014em;"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.55em;"><span style="top:-5.55em;"><span class="pstrut" style="height:8.6em;"></span><span style="width:0.667em;height:6.600em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.667em" height="6.600em" viewBox="0 0 667 6600"><path d="M347 1759 V0 H0 V84 H263 V1759 v3000 v1759 H0 v84 H347z
M347 1759 V0 H263 V1759 v3000 v1759 h84z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.55em;"><span style="top:-5.55em;"><span class="pstrut" style="height:8.6em;"></span><span style="width:0.667em;height:6.600em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.667em" height="6.600em" viewBox="0 0 667 6600"><path d="M403 1759 V84 H666 V0 H319 V1759 v3000 v1759 h347 v-84
H403z M403 1759 V0 H319 V1759 v3000 v1759 h84z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.58em;"><span style="top:-6.4275em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-4.0275em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.1675em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em;"></span></span></span></span><span style="top:-0.9675em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.08em;"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.55em;"><span style="top:-5.55em;"><span class="pstrut" style="height:8.6em;"></span><span style="width:0.667em;height:6.600em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.667em" height="6.600em" viewBox="0 0 667 6600"><path d="M347 1759 V0 H0 V84 H263 V1759 v3000 v1759 H0 v84 H347z
M347 1759 V0 H263 V1759 v3000 v1759 h84z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.08em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.55em;"><span style="top:-5.55em;"><span class="pstrut" style="height:8.6em;"></span><span style="width:0.667em;height:6.600em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.667em" height="6.600em" viewBox="0 0 667 6600"><path d="M403 1759 V84 H666 V0 H319 V1759 v3000 v1759 h347 v-84
H403z M403 1759 V0 H319 V1759 v3000 v1759 h84z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.58em;"><span style="top:-6.4275em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-4.0275em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.1675em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em;"></span></span></span></span><span style="top:-0.9675em;"><span class="pstrut" style="height:3.6875em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.08em;"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.55em;"><span style="top:-5.55em;"><span class="pstrut" style="height:8.6em;"></span><span style="width:0.667em;height:6.600em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.667em" height="6.600em" viewBox="0 0 667 6600"><path d="M347 1759 V0 H0 V84 H263 V1759 v3000 v1759 H0 v84 H347z
M347 1759 V0 H263 V1759 v3000 v1759 h84z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
<p>The weight <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi></mrow><annotation encoding="application/x-tex">w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span></span></span></span> is a slice of the Pearson corelation matrix. The numerator is the corelation between the $i$th statistic and the target statistic <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.854em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span></span></span></span> while the denominator the sum of the corelations between the $i$th statistic and all statistics but the target statistic <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.854em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span></span></span></span> (including itself which will always result in <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">r=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span>).</p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>w</mi><mi>i</mi></msub><mo>=</mo><mfrac><msubsup><mi>r</mi><mrow><mi>i</mi><mo>↔</mo><mi>j</mi></mrow><mn>2</mn></msubsup><mrow><munder><mo>∑</mo><mrow><msub><mi>i</mi><mi>k</mi></msub><mo mathvariant="normal">≠</mo><mi>j</mi></mrow></munder><msubsup><mi>r</mi><mrow><mi>i</mi><mo>↔</mo><msub><mi>i</mi><mi>k</mi></msub></mrow><mn>2</mn></msubsup></mrow></mfrac></mrow><annotation encoding="application/x-tex">w_{i}=\frac{r_{i\leftrightarrow j}^2}{\sum_{i_{k}\neq j}r_{i\leftrightarrow i_{k}}^2}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.7207em;vertical-align:-1.1218em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5989em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1864em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1512em;"><span></span></span></span></span></span></span><span class="mrel mtight"><span class="mrel mtight"><span class="mord vbox mtight"><span class="thinbox mtight"><span class="rlap mtight"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="inner"><span class="mord mtight"><span class="mrel mtight"></span></span></span><span class="fix"></span></span></span></span></span><span class="mrel mtight">=</span></span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4358em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7959em;"><span style="top:-2.4231em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">↔</span><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1512em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.0448em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3827em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.7848em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">↔</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3948em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1218em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h2 id="understanding-the-weights">Understanding the Weights</h2>
<p>Some may find the weight equation arbitrary; it evidently isn't. The goal of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi></mrow><annotation encoding="application/x-tex">w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span></span></span></span> is to eliminate over-rewarding the same behavior represented in multiple statistics. It makes all atomic statistics concurrent by leveraging the Pearson corelation matrix.</p>
<p>A simplified example will clarify the idea. First, we compute a Pearson corelation matrix for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>=</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">I=3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span></span></span></span> statistics. We have <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>, the statistics that are trying to maximize <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span>. Reminder: a Pearson corelation matrix finds the <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> value not only between <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span> but also between all combinations of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> and themselves. Here, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>r</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">r^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> is calculated using polynomial regression corelation analysis to the $m$th degree.</p>
<table>
<thead>
<tr>
<th></th>
<th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th>
<th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th>
<th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">x_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th>
<th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span></th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mn>0</mn></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3244em;vertical-align:-0.34em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9844em;"><span style="top:-3.3244em;"><span class="pstrut" style="height:3.3244em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mord">0</span></span></span></span></span><span style="top:-2.9844em;"><span class="pstrut" style="height:3.3244em;"></span><span class="stretchy fbox" style="height:1.3244em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.34em;"><span></span></span></span></span></span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">x_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td></td>
<td></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span></td>
<td></td>
<td></td>
<td></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
</tr>
</tbody>
</table>
<p>In the case above, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>r</mi><mrow><mn>1</mn><mo>↔</mo><mn>2</mn></mrow><mn>2</mn></msubsup><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">r^2_{1 \leftrightarrow 2}=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0622em;vertical-align:-0.2481em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4519em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mrel mtight">↔</span><span class="mord mtight">2</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span> meaning that both statistics have absolutely nothing to do with each other. Hence, the player will be awarded for optimizing both individually. And since <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>r</mi><mrow><mn>1</mn><mo>↔</mo><mi>j</mi></mrow><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>r</mi><mrow><mn>2</mn><mo>↔</mo><mi>j</mi></mrow><mn>2</mn></msubsup></mrow><annotation encoding="application/x-tex">r^2_{1 \leftrightarrow j}=r^2_{2 \leftrightarrow j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2089em;vertical-align:-0.3948em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mrel mtight">↔</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3948em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2089em;vertical-align:-0.3948em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mrel mtight">↔</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3948em;"><span></span></span></span></span></span></span></span></span></span>, they should both be rewarded equally; in other words, they should have equal weights.</p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>w</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><mn>0</mn><mo>+</mo><mn>0</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">w_{1}=\frac{1}{1 + 0 + 0}=1
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0908em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>w</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>0</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>0</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">w_{2}=\frac{1}{0 + 1 + 0}=1
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0908em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>w</mi><mn>3</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>0</mn><mo>+</mo><mn>0</mn><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">w_{3}=\frac{1}{0 + 0 + 1}=1
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0908em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p>
<p>Now consider a case where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> are fully correlated. It would be a bad idea to reward them equally; hence, their weights suffer.</p>
<table>
<thead>
<tr>
<th></th>
<th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th>
<th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th>
<th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">x_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th>
<th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span></th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mn>1</mn></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3244em;vertical-align:-0.34em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9844em;"><span style="top:-3.3244em;"><span class="pstrut" style="height:3.3244em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mord">1</span></span></span></span></span><span style="top:-2.9844em;"><span class="pstrut" style="height:3.3244em;"></span><span class="stretchy fbox" style="height:1.3244em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.34em;"><span></span></span></span></span></span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">x_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td></td>
<td></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">x_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span></td>
<td></td>
<td></td>
<td></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></td>
</tr>
</tbody>
</table>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>w</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>0</mn></mrow></mfrac><mo>=</mo><mn>0.5</mn></mrow><annotation encoding="application/x-tex">w_{1}=\frac{1}{1 + 1 + 0}=0.5
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0908em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.5</span></span></span></span></span></p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>w</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>0</mn></mrow></mfrac><mo>=</mo><mn>0.5</mn></mrow><annotation encoding="application/x-tex">w_{2}=\frac{1}{1 + 1 + 0}=0.5
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0908em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.5</span></span></span></span></span></p>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>w</mi><mn>3</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>0</mn><mo>+</mo><mn>0</mn><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">w_{3}=\frac{1}{0 + 0 + 1}=1
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0908em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p>
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