# elo-multiplayer
[](https://crates.io/crates/elo-multiplayer)
[](https://crates.io/crates/elo-multiplayer)
Rust crate for calculating multiplayer rating based on elo ranking system
## Mentions
This multiplayer elo algorithm is heavily inspired from [this](https://towardsdatascience.com/developing-a-generalized-elo-rating-system-for-multiplayer-games-b9b495e87802) article.
It works quite similar to the normal elo ranking.
But the expected scores calculated by matching all the players against each other.
$$
E_A = {\sum_{1<i<N, i\neq A}{1\over 1+10^{(R_i-R_A)/D}}\over N(N-1)/2}
$$
where we have player $A$, number of players $N$ and the ranking of player $A$ is $R_A$.
And the score is a bit more complex then the usual two player elo rating.
Currently only a linear method of getting the scores for the players has been implemented:
$$
S_A^{linear} = {N-p_A\over N(N-1)/2}
$$
where $p_A$ is the postion of the player (1st, 2nd, etc...)
We can then calculated the new ranking of a player with:
$$
R'_A = R_A + K(N-1)(S_A-E_A)
$$
Where $K$ is the usual [K-factor](https://en.wikipedia.org/wiki/Elo_rating_system#Most_accurate_K-factor).
## Installation
If you are on Rust 1.62 or higher use `cargo add` to install the latest version:
```sh
cargo add elo-multiplayer
```
Alternatively, you can add the following to your `Cargo.toml` file manually:
```toml
[dependencies]
elo-multiplayer = "0.1.5"
```
## Example usage
```rust
use elo_multiplayer::EloRank;
fn main() {
let players: Vec<f64> = vec![1000.0, 1000.0, 1000., 1000.0];
let elo = EloRank { k: 32, players };
let expected: Vec<f64> = elo.calculate();
}
```