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docs/guides/timezones.md
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# Timezones
What is considered a "day's worth of games" is determined by the reset time. The reset time is generally at midnight everyday after which newer games are counted towards the next day. Reset times vary from region to region:
- North America: `UTC-5:00` (Central North American Time midnight)
- Europe: `UTC+1:00` (Central European Time midnight)
- Asia: `UTC+7:00` (Central Asia Standard Time midnight)
**Reset times are different from Blitz Stars** (Blitz Stars resets at 5:00 am locally relative to the user opening their website). Inconsistencies with Blitz Stars only occur with sleep-deprived players and players who play in the wrong region.
docs/technical/bkrl.md
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# Blitzkit Rating Leaderboard
A straightforward way of storing the entire World of Tanks Blitz rating leaderboard to disk.
```cpp
primary BlitzkitRatingLeaderboard {
utf8"BKRL" magic;
Header header;
primary Body<header> body;
}
Header {
uint16 version; // always 1
Format format;
uint32 count;
}
Format enum<uint8> {
Base,
Superset1,
}
Body<Header header> match<header.format> {
Base {
primary {
uint32 id;
uint16 score;
}[header.count] entries;
};
Superset1 {
primary {
uint32 id;
uint16 score;
uint32 battles;
uint32 wins;
uint32 survived;
uint32 damage;
uint32 kills;
}[header.count] entries;
};
}
```
docs/technical/dids.md
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# Discovered Ids
```c
primary DiscoveredIds {
utf8"DIDS" magic;
Header header;
primary Body body;
}
Header {
uint16 version; // always 1
}
Body {
uint32 count;
uint32[count] ids;
}
```
docs/technical/kitscore.md
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# KitScore
## Memo
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.
## Generating Reasonable Values
TODO: there's like no runaway cases
## Symbol Interpretation
| Symbol | Interpretation |
| ---------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------ |
| $A_\text{human}$ | 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.
$$
A=\frac{\sum_{i \neq j} w_{i}a_{i}}{\sum_{i \neq j} w_{i}}
$$
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:
$$
P(x)=\beta_0x^0+\beta_1x^1+\beta_2x^2+\dots+\beta_mx^m
$$
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.
```math
\begin{bmatrix}
\sum_{k=1}^n x_i^0 & \sum_{k=1}^n x_i^1 & \sum_{k=1}^n x_i^2 & \dots & \sum_{k=1}^n x_i^m \\
\sum_{k=1}^n x_i^1 & \sum_{k=1}^n x_i^2 & \sum_{k=1}^n x_i^3 & \dots & \sum_{k=1}^n x_i^{m+1} \\
\sum_{k=1}^n x_i^2 & \sum_{k=1}^n x_i^3 & \sum_{k=1}^n x_i^4 & \dots & \sum_{k=1}^n x_i^{m+2} \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
\sum_{k=1}^n x_i^m & \sum_{k=1}^n x_i^{m+1} & \sum_{k=1}^n x_i^{m+1} & \dots & \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}
```
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 $j$.
$$
w_{i}=\frac{r_{i\leftrightarrow j}^2}{\sum_{i_{k}\neq j}r_{i\leftrightarrow i_{k}}^2}
$$
## Understanding the Corelation Matrix
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.
| | $x_1$ | $x_2$ | $x_3$ | $x_j$ |
| ----- | --------------------------- | --------------------------- | --------------------------- | --------------------------- |
| $x_1$ | $1$ | $r_{1 \leftrightarrow 2}^2$ | $r_{1 \leftrightarrow 3}^2$ | $r_{1 \leftrightarrow j}^2$ |
| $x_2$ | $r_{1 \leftrightarrow 2}^2$ | $1$ | $r_{2 \leftrightarrow 3}^2$ | $r_{2 \leftrightarrow j}^2$ |
| $x_3$ | $r_{1 \leftrightarrow 3}^2$ | $r_{2 \leftrightarrow 3}^2$ | $1$ | $r_{3 \leftrightarrow j}^2$ |
| $x_j$ | $r_{1 \leftrightarrow j}^2$ | $r_{2 \leftrightarrow j}^2$ | $r_{3 \leftrightarrow j}^2$ | $1$ |
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.
| | $x_1$ | $x_2$ | $x_3$ | $x_j$ |
| ----- | ----- | --------------------------- | --------------------------- | --------------------------- |
| $x_1$ | $1$ | $r_{1 \leftrightarrow 2}^2$ | $r_{1 \leftrightarrow 3}^2$ | $r_{1 \leftrightarrow j}^2$ |
| $x_2$ | | $1$ | $r_{2 \leftrightarrow 3}^2$ | $r_{2 \leftrightarrow j}^2$ |
| $x_3$ | | | $1$ | $r_{3 \leftrightarrow j}^2$ |
| $x_j$ | | | | $1$ |
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, $j=4$).
$$
[r_{1 \leftrightarrow 2}^2, r_{1 \leftrightarrow 3}^2, r_{1 \leftrightarrow 4}^2, r_{2 \leftrightarrow 3}^2, r_{2 \leftrightarrow 4}^2, r_{3 \leftrightarrow 4}^2]
$$
## Understanding the Weights
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.
| | $x_1$ | $x_2$ | $x_3$ | $x_j$ |
| ----- | ----- | ----------- | ----- | ----- |
| $x_1$ | $1$ | $\boxed{1}$ | $0$ | $1$ |
| $x_2$ | | $1$ | $0$ | $1$ |
| $x_3$ | | | $1$ | $1$ |
| $x_j$ | | | | $1$ |
$$
w_{1}=\frac{1}{1 + 1 + 0}=0.5
$$
$$
w_{2}=\frac{1}{1 + 1 + 0}=0.5
$$
$$
w_{3}=\frac{1}{0 + 0 + 1}=1
$$
Remind me to write out the linearized model!
docs/technical/rts.md
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# BlitzKit Regular Tank Stats
A straightforward way of storing the entire World of Tanks Blitz tank statistics for players to disk.
## Manifest `manifest.rtsm`
```cpp
primary RegularTankStatisticsManifest {
utf8"RTSM" magic;
Header header;
primary Body body;
}
Header {
uint16 version; // always 1
}
Body {
uint32 time;
uint8 base;
}
```
## Chunk `*.rtsc`
```cpp
primary RegularTankStatisticsChunk {
utf8"RTSC" magic;
Header header;
primary Body body<header.playerCount>;
}
Header {
uint16 version; // always 1
uint32 playerCount;
}
Body<uint32 playerCount> {
Player[playerCount] players;
}
Player {
uint32 id;
uint16 tankCount;
Tank[tankCount] tanks;
}
Tank {
uint32 id;
uint32 battleLifeTime;
uint32 lastBattleTime;
uint8 markOfMastery;
uint32 battles;
uint32 capturePoints;
uint32 damageDealt;
uint32 damageReceived;
uint32 droppedCapturePoints;
uint32 frags;
uint32 frags8p;
uint32 hits;
uint32 losses;
uint8 maxFrags;
uint16 maxXp;
uint32 shots;
uint32 spotted;
uint32 survivedBattles;
uint32 winAndSurvived;
uint32 wins;
uint32 xp;
}
```