Version 1.1, August 5th, 2025. Copyright (c) TrèsAbhi.
Permission is hereby granted to anyone to:
- Fork, clone, and download the contents of this repository.
- Modify the code locally in private.
- Use and run the code **only for personal, non-public testing, or educational purposes**.
The following restrictions apply:
- You may **not** deploy, host, or make this project or any derivative publicly accessible.
- You may **not** share screenshots, recordings, or any form of media from this project unless you intend to merge your changes back into BlitzKit.
- You may **not** use this project or its contents in any public or commercial product.
- You may **not** redistribute modified or unmodified versions of this project.
Contributions:
- You are encouraged to propose changes or improvements via pull requests to the original BlitzKit repository.
- Any such contributions will be considered under the same license terms unless explicitly stated otherwise.
Violations of this license may result in revocation of usage rights and takedown requests.
For questions or licensing inquiries, contact support@blitzkit.app.
## Notes on Existing Forks
All forks fall under these categories:
- If your fork was made from commit `8462901` (Apr 17, 2023) or between commits `2958124` (Jul 3, 2023) and `85e483e` (Jul 13, 2024), your fork falls under the **MIT license**.
- If your fork was made from commits between `5646093` (Jul 13, 2024) and `e3f131c` (Aug 5, 2025), your fork falls under the **AGPL-3.0 license**.
- If your fork was made between commit `f7c356d` (Apr 17, 2023) and `2958124` (Jul 3, 2023), your fork falls under **a default exclusive copyright**.
- If your fork was made from commits between `e3f131c` (Aug 5, 2025) and today, your fork falls under **this license**.
MIT and AGPL-3.0 licensed fork owners:
- You may continue to use your fork of BlitzKit under the corresponding license.
- You may upgrade your fork up to commit `5cab394` (Aug 4, 2025) and keep the AGPL-3.0 license.
- You may upgrade to commit `e3f131c` (Aug 5, 2025) or beyond but have to **switch to this license** where all rules apply.
- If you upgrade to commit `e3f131c` (Aug 5, 2025) or beyond, you must retract all public deployments of BlitzKit.
- Existing screenshots, recordings, or any form of media can remain.
Default exclusive copyright fork owners:
- You may continue to use their forks under the AGPL-3.0 license as no license was applied to BlitzKit at the time of forking.
BlitzKit licensed fork owners:
- You may continue to upgrade to the latest commits only under the conditions of this license.
[](https://codeium.com)
Tools for everything and anything, World of Tanks Blitz.
Tools for everything World of Tanks Blitz
This GitHub repository contains the code for BlitzKit and all its services. If you are here, looking to use BlitzKit, go to https://blitzkit.app/.
## Invite the bot
If you intend to contribute to the code, note that you may need to check out sensitive, closed-source submodules to locally develop certain aspects of BlitzKit. Communicate with `@tresabhi` on Discord to get started or discuss sensitive content, such as environment variables or submodules.
Go to [application directory for BlitzKit](https://discord.com/application-directory/1097673957865443370) and click "Add to Server." Voila! You're ready to go.
| [packages/app](packages/app) | BlitzKit | [Play Store](https://play.google.com/store/apps/details?id=com.tresabhi.blitzkit), [App Store](https://apps.apple.com/app/4321), [Microsoft Store](https://apps.microsoft.com/detail/zyxw) | The native app of BlitzKit for all platforms. Unavailable from stores at this time. |
| [packages/bot](packages/bot) | BlitzKit Discord Bot | [Discord Application Directory](https://discord.com/discovery/applications/1097673957865443370) | The one-in-all Discord bot for statistics. |
| [packages/core](packages/core) | | | Mutual internal code shared between all other packages. |
| [packages/i18n](packages/i18n) | | [Crowdin](https://crowdin.com/project/blitzkrieg) | Translations served as JSON shared across all other packages, including some utility code. |
| [packages/scripts](packages/scripts) | | | CLI utilities for the development and deployment of BlitzKit services. |
| [packages/varuna](packages/varuna) | Varuna | [NPM](https://www.npmjs.com/package/varuna) | React and Astro-oriented state management library, awaiting separation from BlitzKit. Unavailable from NPM at this time. |
| [packages/website](packages/website) | BlitzKit | https://blitzkit.app | The BlitzKit website provides a wide range of tools, APIs, and interconnects all other services. |
| [submodules/blitzkit-closed](submodules/blitzkit-closed) | ClosedKit | [blitzkit/closed](https://github.com/blitzkit/closed) | Closed source, sensitive code hidden from the public to prevent bad actors from abusing the game. Discuss with `@tresabhi` on Discord for **special permission** to access. |
| [submodules/blitzkit-internal](submodules/blitzkit-internal) | InternalKit | [blitzkit/internal](https://github.com/blitzkit/internal) | Closed source, sensitive internal documentation hidden from the public to prevent bad actors from abusing the game. Access to this submodule is **not negotiable**. |
| [submodules/CUE4Parse](submodules/CUE4Parse) | CUE4Parse | [FabianFG/CUE4Parse](https://github.com/FabianFG/CUE4Parse) | An Unreal Engine archives and packages parsing library in C#. |
| `PUBLIC_WARGAMING_APPLICATION_ID` | [Wargaming Developer's Room](https://developers.wargaming.net/) | | Application ID needed to communicate with Wargaming APIs. |
| `PUBLIC_PROMOTE_OPENTEST` | | `false` | Optional boolean dictating whether the website advertises [the opentest subdomain of BlitzKit](https://opentest.blitzkit.app/). |
| `ALLOW_ROBOTS` | | `true` | Toggles between `Allow: /` and `Disallow: /` in the website's `/robots.txt`. This is usually `false` for all BlitzKit's subdomains. |
| `PUBLIC_GOOGLE_TAG_MANAGER_ID` | [Google Tag Manager](https://tagmanager.google.com/) | `G-GL2JVHCGPQ` | Google Tag Manager's unique identifier for analytical purposes. |
| `PUBLIC_GOOGLE_ANALYTICS_PROPERTY_ID` | [Google Analytics](https://analytics.google.com/) | `430711767` | Google Analytics' unique property ID for [BlitzKit's apex domain](https://blitzkit.app/) and subdomains. |
| `GOOGLE_APPLICATION_CREDENTIALS` | [Google Cloud](https://cloud.google.com/) | | Google Cloud's API key, primarily used for ranking popular tanks and finding relevant tank review videos in Tankopedia. |
| `PUBLIC_ASSET_BASE` | [blitzkit/assets](https://github.com/blitzkit/assets) | `https://blitzkit.github.io/assets` | The root domain and path that serves the external assets like tank models and icons. |
| `PUBLIC_BRANCH` | | `main` | The branch that the website is operating on. This is completely nominal. |
| `PUBLIC_GUIDE_WEBSITE` | [GuidesBlitz](https://guidesblitz.com/) | `https://guidesblitz.com` | The website that serves the encyclopedia-like content in BlitzKit. |
| `SERVICING` | | `false` | Wether the website is down for servicing. |
| `DISCORD_CLIENT_ID` | [Discord Developer Portal](https://discord.com/developers/applications) | `1097673957865443370` | The BlitzKit Discord Bot's user ID. |
| `GH_TOKEN` | [GitHub Fine-Grained Tokens](https://github.com/settings/personal-access-tokens) | | The GitHub API key used for checking out private submodules and pushing content to the asset repository. |
| `DISCORD_TOKEN` | [Discord Developer Portal](https://discord.com/developers/applications) | | The Discord API Key for the BlitzKit Discord Bot. |
| `DATABASE_URL` | [CockroachDB](https://www.cockroachlabs.com/) | | The CockroachDB-SQL database URL used to link Wargaming and Discord users. |
@@ -6,6 +6,6 @@ A minor-major fix to the armor sandbox. This update only affects the website.
- Guns are now clipped properly allowing some tanks like the 252U and T34's mantlets to be penetrable (usually with premium shells) as they are in-game
- Added "Game mode abilities" section to the tankopedia pages
- Shows the game mode provisions and consumables underneath the corresponding mode's banner
- Reworked the tech tree section
- Now shows the whole line and if multiple paths exist, they are can be selected
- The selected tank is now highlighted with the flag of the corresponding country
- This section now also shows the total required XP and credits required
- Added a battle count which indicates the number of games required to reach the next tank (not including module upgrades) based on average xp earnings of players
- XP multipliers can also be applied to get a sense of how many battles you will really have to play
- Reworked the "Review videos" section
- Removed all previews videos; we will be starting from scratch
- Added names of content creators under their corresponding videos
- Added a way for YouTubers to apply to be a part of the review videos section
- Reworked the navbar
- This are a lot more compact and contrastive
- Tool names are now separated with vertical lines now
- The hamburger menu now looks more like the homepage cards
- Added a warning for test tanks
- Switched to on-demand rendering
- This makes it so that the canvas only renders upon interaction and not the continuously synced with the screen's refresh rate
- Added the meta information section to the tankopedia pages
- Lists the full name, nation, tier, class, type, restoration, purchase, and sale prices
- Added tooltips to a lot of places
- Reduced ads on the tankopedia pages
- Added a screenshot button to take screenshots of the tank
- Added crew training slider to the compare tool
## Fixes
- Invalid Wargaming logins are now handled properly
- Season currencies are now displayed properly
- Tank filters are now persistent but will be reset on refresh
- The search for a tank now populates the search bar when navigating back to the search page
This update makes some technical internal changes to allow the website to switch to the opentest version of the game when it is released. The opentest variant of BlitzKit will be available on https://opentest.blitzkit.app/ in the future (currently, it just redirects to https://blitzkit.app).
I rewrote the whole website for performance and lower bandwidth. This update does not affect the bot. If I did my job right, you should not notice a difference.
## Changes
- Removed documentation website, all the docs are now available within https://blitzkit.app/
- Removed the Rating tool
- Removed the ability to log in with Patreon
- Removed all ads
## Technical Changes
- Converted BlitzKit to a monorepo
- The whole website is now static with no server-side rendering
- Gotta go fast ⚡
- All structural data is now stored in protocol buffers
Two updates in a day! Why? Well, these two updates were being cooked separately in parallel and happened to have matured on the same day. Merry early Christmas!
## Features
- Highly optimized the component rerenders of the Tank Sandbox
- Implemented Google Analytics into the homepage to more accurately show the most popular tanks
- Optimized page load speeds and memory consumption by loading all data in parallel instead of sequentially
## Fixes
- Dynamic armor is now loaded in React Suspense to avoid race conditions
- Re-ordered cards on the home page so that it makes a little bit more sense
- The warnings section of the Tankopedia pages are now padded on the sides
- The calibers in the antagonist gun selector are now rounded correctly
- Tank class icons are now colored and sized properly again in the header
## Technical Changes
- Removed the extreme JPEG compression for the tank textures
- Buffers of the same length are now assumed to be identical when diffing lmao I hope this doesn't go wrong
¡Ahora en 6 idiomas! This version of BlitzKit adds support for 4 new languages totalling up to 6! [Please help translate on Crowdin](https://crowdin.com/project/blitzkrieg).
## Features
- Added Croatian, Russian, Ukrainian, and Chinese
- Pre-existing languages: English, Spanish
- Added better lighting making tanks a little less yellow and a bit more realistic
- Added custom tank icons (some may be missing when the update drops; just give them an hour or so to update)
- Increased the maximum recently viewed tanks list size to 14
- Tweaked the tank name in the hero section of the Tankopedia to allow the tank to be in the center of the page
- The headers in the Performance tool are now sticky just like the Compare tool
## Fixes
- Removed unnecessary third party script that did absolutely nothing
- Localizations are now stricter in what they allow, reducing errors in the Discord bot
- Added 50 gallons of tomato soup to the bot in an attempt to keep it alive
It's all technical updates! The HD tanks will be rolled out over the span of few days.
## Technical Changes
- Shadows are disabled if your framerate drops below 30fps
- Pages that redirect to other pages (like the old /tools/tankopedia) now load a few hundred times faster
- Replaced Zustand with a custom state manager called Varuna with the goal to rewrite a significant portion of the website to not require any React for rendering increasing performance
- The transition wireframe in the Tankopedia sandbox now uses a lower quality model for performance reasons
- Tanks with PBR now use the correct maximum resolution textures
- This is a significant update as you can now literally see individual splats of dust on tanks and scratches haha
- Baked the ambient occlusion maps into the textures, hence reducing the overall model load times even with higher resolution textures
- Added a new foggy-wireframe transition between tabs to smooth out the jarring jumps
- Added animations pop-in and out animations on a few elements
- The tank name title now shrinks in size as soon as a disturbance is caused
- The shell selector, antagonist switcher, and thicknesses range now ease into frame
- The Tankopedia search page now loads as a skeleton by default before populating with tanks, allowing for the recently viewed tanks to load without cumulative shift
- Something similar was done to the Gallery tool
- Gave the meta section of the website some zest with nation-based backdrops
- The compare tabs in the Tankopedia are now centered
## Fixes
- The camera no longer snaps to the initial position when switching between tabs
## Technical Changes
- Backported some technologies from BlitzKit Reforged; you will not notice any differences in usage
- The popular tanks and gallery indexings have been moved to the asynchronous cron job
This release of Blitzkrieg focuses mainly on **performance**. Blitzkrieg now uses **Satori** and **resvg** under the hood to render images resulting in a solid **2x to 8x performance boost** depending on the situation.
This only applies to `/today` and /stats` as they're the only commands that render an image currently.
This only applies to `/today` and `/stats` as they're the only commands that render an image currently.
We're working further on **performance optimizations**. Our goal is to deliver a message within **3 seconds or less**. We're close and we'll get there!
@@ -130,6 +130,23 @@ Your consent to this Privacy Policy followed by Your submission of such informat
The Company will take all steps reasonably necessary to ensure that Your data is treated securely and in accordance with this Privacy Policy and no transfer of Your Personal Data will take place to an organization or a country unless there are adequate controls in place including the security of Your data and other personal information.
### California Consumer Privacy Act (CCPA)
If you are a California resident, you have specific rights regarding your personal information under the California Consumer Privacy Act (CCPA). This section describes your CCPA rights and explains how to exercise those rights.
#### Rights under CCPA
Under CCPA, California residents have the following rights:
1. Right to Know: You have the right to request that we disclose certain information to you about our collection and use of your personal information over the past 12 months.
2. Right to Delete: You have the right to request that we delete any of your personal information that we collected from you and retained, subject to certain exceptions.
3. Right to Opt-Out of Sale: You have the right to opt-out of the sale of your personal information. Note that we do not sell personal information as defined by the CCPA.
4. Right to Non-Discrimination: You have the right not to be discriminated against for exercising any of your CCPA rights.
#### Exercising Your CCPA Rights
To exercise your rights under CCPA and to opt-out of the sale of your personal information, you can click on the "Do not sell my personal information" link in the footer of any page on our website.
### Delete Your Personal Data
You have the right to delete or request that We assist in deleting the Personal Data that We have collected about You.
@@ -188,4 +205,4 @@ You are advised to review this Privacy Policy periodically for any changes. Chan
If you have any questions about this Privacy Policy, You can contact us:
- By visiting this page on our website: [https://discord.gg/nDt7AjGJQH](https://discord.gg/nDt7AjGJQH)
1. JSON compressed as CDON, written directly to disk (a direct 50% reduction).
2. CDON further compressed with LZ4 (a clean 90% reduction).
3. The raw JSON file as fetched from a random data source.
4. CDON decompressed once again to JSON. Note that this file is a little larger than the original JSON file as it contains a lot more decimal places due to float precision (this shouldn't affect the size in memory).

KitScore is 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 "WoTB:" prefix.
## Consumption of Observations
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 $x_i$ of an observation) per player (WoTB: $x_\text{frags}$, $x_\text{xp}$, $x_\text{spots}$, etc.) including a target statistic (the $x_j$ of an observation) that all other statistics try to maximize (WoTB: "winrate" which we will defined later as $x_j$).
If the statistics are cumulative, they will have to be normalized (WoTB: statistics fetched from Wargaming are indeed cumulative even for a single player; $x_\text{frags}=\frac{\Sigma x_\text{frags}}{\Sigma x_\text{battles}}$, $x_\text{spots}=\frac{\Sigma x_\text{spots}}{\Sigma x_\text{battles}}$, $x_j=\frac{\Sigma x_\text{wins}}{\Sigma x_\text{battles}}$, 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.
## It's Impossible to "Find What Makes the Metric Tick"
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 find and exploit "what makes the metric tick." In other words, people easily exploit the rudimentary nature of WN8 to score undeservedly high.
In WN8, the gains of some rewarding categories overshadow the losses of others though that may not necessarily be in the best interest in maximizing winrate. 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.
| $A_\text{human}$ | The human readable version of the raw score $A$. |
| $A$ | The raw KitScore. |
| $C$ | An arbitrary coefficient. |
| $I$ | The number of statistics including the target statistic. This means that there are $I-1$ entries for $x_i$ and $1$ entry for $y$ for each observation. |
| $i$ | The statistic index of where there are $I$ entries. |
| $j$ | A discriminator for the target statistic. There may never be more than $1$ entries for $j$. |
| $m$ | The degree of the polynomial regression. |
| $n$ | The number of observations. |
| $a$ | An "atomic" score which is a function of the $i$th statistic. |
| $w$ | The weight of the $i$th atomic statistic. |
## Computing the Score
The final metric $A_\text{human}$ is an arbitrarily scaled value of the raw score $A$ where $C$ is any coefficient of your liking. BlitzKit uses $C=10^3$.
$$
A_\text{human}=CA
$$
The final metric $A$ is the weighted average of individual scores $a$ which are functions of the $i$th statistic excluding the target statistic $j$ itself.
The "atomic" score $a$ is the difference between the predicted target statistic $P_{i \leftrightarrow j}(x_i)$ acquired using a polynomial regression of degree $m$ and the actual newly observed $x_j$.
$$
a_i=x_j-P_{i \leftrightarrow j}(x_i)
$$
The polynomial regression of $m$th degree can be written as follows:
Polynomial regression coefficients $\beta$ can be acquired through basic linear algebra where an $m \times m$ of constants is multiplied with $m \times 1$ of unknowns which equals another $m \times 1$ of constants.
The weight $w$ is a slice of the Pearson corelation matrix. The numerator is the corelation between the $i$th statistic and the target statistic $j$ while the denominator the sum of the corelations between the $i$th statistic and all statistics but the target statistic $j$.
Forming the corelation matrix will create an $I \times I$ matrix where. This matrix is best represented as a table. The example below illustrates a matrix/table for $I=4$ which includes $3$ entries for $i$ statistics and $1$ entry for the $j$ target statistic.
It should not be a surprise to find $r_{i \leftrightarrow i}^2=1$ which forms a neat diagonal across the table. Note that there are many duplicates within the $I^2$ entries. The "bottom-right triangle" can be eliminated to remove redundancies leaving us with only $\frac{I(I+1)}{2}$ fields occupied.
When programming this matrix into an array, $r_{i \leftrightarrow i}^2=1$ will be redundant. I recommend condensing the matrix into an array of size $\frac{I(I+1)}{2}+I=\frac{I(I-1)}{2}$ to avoid all redundant entries. For $I=4$, the array will look something like the one illustrated below (here, $j=4$).
Some may find the weight equation arbitrary; it evidently isn't. The goal of $w$ is to eliminate over-rewarding the same behavior represented in multiple statistics. It makes all atomic statistics concurrent by leveraging the Pearson corelation matrix.
A simplified example will clarify the idea. First, we compute a Pearson corelation matrix for $I=3$ statistics. We have $x_1$ and $x_2$, the statistics that are trying to maximize $x_j$. Reminder: a Pearson corelation matrix finds the $r$ value not only between $x_i$ and $x_j$ but also between all combinations of $x_i$ and themselves. Here, $r^2$ is calculated using polynomial regression corelation analysis to the $m$th degree.
| | $x_1$ | $x_2$ | $x_3$ | $x_j$ |
| ----- | ----- | ----------- | ----- | ----- |
| $x_1$ | $1$ | $\boxed{0}$ | $0$ | $1$ |
| $x_2$ | | $1$ | $0$ | $1$ |
| $x_3$ | | | $1$ | $1$ |
| $x_j$ | | | | $1$ |
In the case above, $r^2_{1 \leftrightarrow 2}=0$ meaning that both statistics have absolutely nothing to do with each other. Hence, the player will be awarded for optimizing both individually. And since $r^2_{1 \leftrightarrow j}=r^2_{2 \leftrightarrow j}$, they should both be rewarded equally; in other words, they should have equal weights.
$$
w_{1}=\frac{1}{1 + 0 + 0}=1
$$
$$
w_{2}=\frac{1}{0 + 1 + 0}=1
$$
$$
w_{3}=\frac{1}{0 + 0 + 1}=1
$$
Now consider a case where $x_1$ and $x_2$ are fully correlated. It would be a bad idea to reward them equally; hence, their weights suffer.
A next generation metric in judging player performance.
## Pre-requisites
This paper delves deep into mathematics and statistics which most may not be familiar with. You will need some basic understanding of normal distributions, correlation analysis, regressions, summation, set builder notation, and calculus.
## Preface
WSS delivers a single, easy to consume number that measures the performance of a player independent to their winrate so that it is easy to judge their contribution to the team regardless of the performance of the other players in the team. This allows you to judge wether the player in question is "pulling their own weight."
The mathematics behind this metric has been intentionally generalized such that it isn't limited to just World of Tanks Blitz. You will be easily able to apply this metric in any other game/sport.
## Understanding The Metric
On average, the score across all players will be $0$. This is because the metric is essentially a convolution of multiple standard scores and their corresponding weights. A standard score of $z=\pm1$ implies an offset by $\pm\sigma$ ($1$ standard deviation) from $\mu$ (the mean). And since the scalar of WSS is $C=1000$, $z=\pm1\iff M=\pm 1C=\pm1000$.
About $68.3\%$ of players lie within $\pm1\sigma\implies M=\pm1000$, about $95.4\%$ of players lie within $\pm2\sigma\implies M=\pm200$, and about $99.7\%$ of players lie within $\pm3\sigma\implies M=\pm300$.
## Computation
The final metric, $M$, is an integer where $0$ is the average score across all players, $-1000$ is $-\sigma$ away from $\mu$, and $1000$ is $\sigma$. This allows for a clear distinction between players that are hurting the team and who are actually helping since players with a negative score have a negative standard score, tied tightly with basic distributional statistics.
$M$, the human-readable metric, is a function of $Z$, the raw score where $C=1000$ is an arbitrary scaling factor.
$$
M=\text{round}\left(CZ\right)
$$
$Z$ is the weighted average of all $z$ ("standard score," which $z$ stands for, will be discussed later) with weights $w$.
$$
Z=\frac{\sum wz}{\sum w}
$$
$w$, the weight of each standard score is just $r$, the correlation coefficient. This value must be determined for each standard scores through corelation analysis. $r$ is allowed to be negative so that standard scores that actually harm the player's winrate will have a negative effect on the weighted average. We will be using the weighted variant of $r$ where $w_i$, the weight of the sample, is the number of battles, $\overline{x}$ the weighted average of the samples' $x$ components and $\overline{y}$ the weighted average of the samples' $y$ components (usually the winrate).
Note that $r$, $\sigma$, $\mu$, $\overline{x}$, and $\overline{y}$ use many of the same summations just in different places. During real computation, I would highly recommend pre-computing all the summations and deploying them to use to avoid excessive computation. This makes a world of difference when sampling hundreds of millions of players.
$z$ is the standard score which uses the precomputed values of $\mu$ and $\sigma$. The variable $x$ represents the input statistic of the player in question.
$$
z=\frac{x-\mu}{\sigma}
$$
## Human-Readability
### Bar Size and Position
> [!NOTE]
> The bar colors in the example graphics below may not be representative of the real scale. Read "Bar Color" for more details.
Presenting $M$ may not be sufficient in conveying the metric. It is convention to display a "progress bar" that directly represents the percentile of the player which can be derived directly from the raw score, $Z$, since its a weighted average of standard scores.
A standard score of $z=0.65\implies Z=650$ corresponds to the $75\%$ percentile. That is $25\%$ above the average $50\%$. This is visualized by a green bar halfway full.

$z=1.20\implies Z=1200$ is the $88\%$ percentile. The bar is now three quarters full.

Thus, by extension, negative scores are red bars originating from the right. $z=-1.20\implies Z=-1200$ is the $12\%$ percentile.

Generalizing this, for any given raw score $Z$, the percentile can be calculated as follows.
$P=\Phi\left(Z\right)$
And $\Phi$ is the cumulative distribution function. That being said, most languages will offer some library or built-in function to compute $\Phi$.
For any given value of $P$, the size of the bar is $B$.
$B=\left|2P-1\right|$
The bar originates from the left if $P>0.5=50\%\iff Z>0\implies M\ge0$ ($M$ may still be $0$ due to rounding). It originates from the right if $P<0.5=50\%\iff Z=0\implies M\le0$. And when $P=0.5=50\%\iff Z=0\implies M=0$, it is completely empty.
### Bar Color
The color of the bar is also a function of the percentile. $\Phi$ isn't a cheap function, so I would recommend computing these on-demand and memoize the results. Or, alternatively, you could precompute the associated $Z$ values for $P$ and use those to determine the colors. The colors that [BlitzKit](https://blitzkit.app/) uses are shown in the image below.

BlitzKit uses [Radix Colors](https://www.radix-ui.com/colors/docs/palette-composition/scales) and the scales used in the image above are as follows respectively.
- tomato
- orange
- amber
- yellow
- lime
- green
- teal
- cyan
- pink
- plum
- purple
## FAQ
### (WoTB specific) Why WSS over WN8?
- Lot less aggressive: the weights of WN8 are disproportionately distinct from one another allow people to easily find "what makes the metric tick" and exploit it to "farm" higher WN8 with that being the only the explicit goal. WSS, on the other hand, because of its symmetric and normal nature, will remain at a similar value even if a player choses to aggressively maximize one statistic.
- Mathematically grounded: every constant of WSS is based in data. Unlike WN8, it is recommended to recompute the constants of WSS often. In BlitzKit's implementation, an approximate 24 million players are samples every day to keep the metric relevant.
- Easy to read: WN8 provides no clear indication of where the average is. WSS, on the other hand, clearly states that negative scores cause a lower than average chances of winning, a positive score causes a higher chance of winning, and 0 being the average.
- Doesn't use winrate: WSS is strictly not a function of winrate. WN8, on the other hand, is majorly influenced by winrate and even XP. WSS is a measurement of your true performance regardless of what RNG may throw at you.
### Why doesn't the weight include the slope of the linear regression?
Doing this would make $w=\left|r\right|m$ or $w=r^{2}m$ where $\left|r\right|$ or $r^{2}$ represents the "confidence" in the standard score and $m$ is the "rate of effectiveness". Doing this was decided against because a drop in $m$ inherently implies a drop in the corelation $r$.
To rephrase, this is what real data looks like where $r$ drops with $m$; there is no need to include both (https://www.desmos.com/calculator/0p5kye1s7z).

And this is what real data **DOES NOT** look like where $r$ remains constant as $m$ drops (https://www.desmos.com/calculator/5yfl2ulemf).

## WoTB Specific Notes
Corelation analysis must be performed on a per-tank basis. If the goal is to evaluate the performance of a player instead of the player's performance in a tank, analysis should still be done on all played tanks severalty and must be averages with weights being the number of battles played by the player in each tank.
The Wargaming API provides many pieces of statistics on a per-tank basis (as listed below). These values cumulate over time as the player plays more games; hence, all of these values must be normalized by dividing each metric by `all.battles`. I will go through and list which of the statistics need to be included as standard scores and why/why not. Omitted statistics must not be included and are obvious why they aren't used.
- ✔️ `battle_life_time`: Normalization of this value results in the average time spent alive in seconds. Good players strive to stay alive for as long as possible and must be rewarded while people who "yolo" at the beginning of the game will be penalized.
- ❌ `all.battles`: Dividing this by itself will result in 1. Corelation analysis will always fail due to division by 0.
- ✔️ `all.capture_points`: Capturing points almost always have a negative corelation coefficient; hence, its inclusion is vital to punish players who waste time capturing points.
- ✔️ `all.damage_dealt`
- ✔️ `all.damage_received`
- ✔️ `all.dropped_capture_points`: Dropping capture points by dealing damage to opponents in base capture usually results in a very tiny positive corelation coefficient; nonetheless, it does have an effect on gameplay thus it is included.
- ✔️ `all.frags`
- ❌ `all.frags8p`: This value is `null` on most tanks below tier VIII because it only measures frags of and above tier VIII. Breaks math, pointless feature; do not include.
- ✔️ `all.hits`
- ❌ `all.losses`: Function of winrate.
- ❌ `all.max_frags`: Normalization with division by `all.battles` renders this metric useless. Do not include.
- ❌ `all.max_xp`: Just like `all.max_frags`, this metric does not accumulate over time. Do not include.
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