Lichess-flavored Glicko-2 rating system with fractional rating periods and instant rating updates.
This does not (yet) exactly match the Lichess implementation. Instead, it's a proof of concept for potential improvements and parameter tweaks.
See http://glicko.net/glicko/glicko2.pdf for a description of the original Glicko-2 rating system. The following changes have been made:
- Optimized default parameters based on Lichess data. Optimal parameters depend on the application, so this will not be ideal for all use cases.
- All rating components are clamped to specific ranges, so that even pathological scenarios cannot cause ratings to degenerate.
- Glicko-2 updates ratings in bulk in discrete rating periods. Lichess instead updates pairs of ratings, so that ratings can be immediately updated after each game.
- Lichess keeps the time decay of rating deviations, but generalizes it to work with fractional rating periods. This implementation further changes this approach to do a fractional update of both players, followed by a traditional Glicko-2 update.
- Allows considering an inherent advantage for the first player in a game.
use liglicko2::{RatingSystem, Score, Instant, Periods};
let system = RatingSystem::new();
let alice = system.new_rating();
let bob = system.new_rating();
let now = Instant::default() + Periods(2.3);
// Initial prediction is indifferent.
let expected_score = system.expected_score(&alice, &bob, now);
assert!(Score(0.49) < expected_score && expected_score < Score(0.51));
// Alice wins. Update ratings.
let (alice, bob) = system.update_ratings(&alice, &bob, Score::WIN, now).unwrap();
assert!(alice.rating > bob.rating);
let now = now + Periods(1.0);
// Alice is expected to win the next game.
let expected_score = system.expected_score(&alice, &bob, now);
assert!(Score(0.79) < expected_score);See resarch/ for utilities to evaluate rating systems on real-world data.
liglicko2 is licensed under MIT or APACHE-2.0, at your option.