# Glicko2 (Rust Edition)
Glicko2 is an iterative algorithm for ranking opponents or teams in 1v1 games. This is a zero-dependency Rust library implementing this algorithm.
## Installation
Add the following to your `Cargo.toml`:
```toml
[dependencies]
glicko_2 = "1.1.0"
```
## Sample Usage
The most common usage is to update a series of matches for each team, but this library provides many other convenience methods.
### To update a series of matchups
```rust
use glicko_2::{Rating, Tuning, game::Outcome, algorithm};
/// Tune the rating values, here we use the default
let tuning = Tuning::default();
/// Create a Rating struct for each team
let mut team_to_update = Rating::new(&tuning);
let mut opponent_1 = Rating::new(&tuning);
let mut opponent_2 = Rating::new(&tuning);
let mut opponent_3 = Rating::new(&tuning);
let mut opponent_4 = Rating::new(&tuning);
/// Rate our team against a vector of matchup results
algorithm::rate(
&mut team_to_update,
&mut [(Outcome::Win, &mut opponent_1),
(Outcome::Loss, &mut opponent_2),
(Outcome::Draw, &mut opponent_3),
]
);
/// Opponent 4 did not play, so their rating must be decayed
opponent_4.decay();
/// Print our updated rating
println!("{:?}", team_to_update); // Rating(μ=1500.0, φ=255.40, σ=0.0059)0059 }
```
### To get the odds one team will beat another
```rust
use glicko_2::{Rating, Tuning, game};
/// Tune the rating values, here we use the default
let tuning = Tuning::default();
/// Create a Rating struct for each team
let mut rating_1 = Rating::new(&tuning);
let mut rating_2 = Rating::new(&tuning);
/// Get odds (percent chance team_1 beats team_2)
let odds = game::odds(&mut rating_1, &mut rating_2);
println!("{odds}"); // 0.5, perfect odds since both teams have the same rating
```
### To determine the quality of a matchup
```rust
use glicko_2::{Rating, Tuning, game};
/// Tune the rating values, here we use the defaults
let tuning = Tuning::default();
/// Create a Rating struct for each team
let mut rating_1 = Rating::new(&tuning);
let mut rating_2 = Rating::new(&tuning);
/// Get odds (the advantage team 1 has over team 2)
let quality = game::quality(&mut rating_1, &mut rating_2);
println!("{quality}"); // 1.0, perfect matchup since both teams have the same rating
```
### To update both team's ratings for a single matchup
```rust
use glicko_2::{Rating, Tuning, game};
/// Tune the rating values, here we use the defaults
let tuning = Tuning::default();
/// Create a Rating struct for each team
let mut rating_1 = Rating::new(&tuning);
let mut rating_2 = Rating::new(&tuning);
/// Update ratings for team_1 beating team_2
game::compete(&mut rating_1, &mut rating_2, false);
/// Print our updated ratings
println!("{rating_1}"); // Rating(μ=1646.47, φ=307.84, σ=0.0059)
println!("{rating_2}"); // Rating(μ=1383.42, φ=306.83, σ=0.0059)
```
## Rating
Each side of a 1v1 competition is assigned a rating and a rating deviation. The rating represents the skill of a player or team, and the rating deviation measures confidence in the rating value.
### Rating Deviation
A team or player's rating deviation decreases with results and increases during periods of inactivity. Rating deviation also depends on volatility, or how consistent a player or team's performance is.
Thus, a confidence interval represents a team's or player's skill: a player with a rating of `1300` and a rating deviation of `25` means the player's real strength lies between `1350` and `1250` with 95% confidence.
### Match Timing Caveat
Since time is a factor in rating deviation, the algorithm assumes all matches within a rating period were played concurrently and use the same values for uncertainty.
## Tuning Parameters
- Rating period length and quantity impact decay in rating deviation
- Should generally be `{10..15}` matches per team per period
- Initial mu and phi values affect how much teams or players can change
- Defaults are `1500` and `350` respectively
- Sigma is the base volatility
- Default to `0.06`
- Tau is the base change constraint; higher means increased weight given to upsets
- Should be `{0.3..1.2}`
## Problems
- Difficult to determine the impact of an individual match
- No ratings available in the middle of a rating period
- Ratings are only valid at compute time
## Paper
Mark Glickman developed the Glicko2 algorithm. His paper is available [here](http://www.glicko.net/glicko/glicko2.pdf).