A pure, zero-dependency Elixir implementation of Mark Glickman’s Glicko-2 rating system for two-player games.
Glicko-2 improves on Elo by tracking two additional quantities per player: a rating deviation (how uncertain the rating is) and a volatility (how erratic the player’s performance is). It is used by Lichess, Counter-Strike 2, Splatoon 2, and many others.
Features
- Faithful implementation of Glickman’s published algorithm, including the Illinois variant of the regula falsi method for volatility convergence
- Accepts fractional scores in
[0.0, 1.0]— not just win/draw/loss — enabling graded outcomes (e.g. checkmate vs. stalemate) - Plain
{rating, deviation, volatility}tuples — no structs, no GenServers, no state - Pure functions, safe to call concurrently from any number of processes
- Strict input validation at the boundary with clear error messages
- Zero runtime dependencies
- 100% line coverage
- Supports Elixir 1.14+ / OTP 25+
Quick example
player = {1500.0, 200.0, 0.06}
opponent = {1400.0, 30.0, 0.06}
# Player wins
{rating, deviation, volatility} = GlickoRatingSystem.rate(player, [{opponent, 1.0}])
# rating > 1500.0, deviation < 200.0
# Predict win probability
GlickoRatingSystem.expected_score(player, opponent)
# returns a value > 0.5
Fractional scores
Unlike traditional Elo, Glicko-2 natively supports any score between 0.0 and 1.0. This is useful if your platform differentiates between types of victories. For example, a platform could use:
| Outcome | Winner | Loser |
|---|---|---|
| Decisive win | 1.0 |
0.0 |
| Partial win | 0.75 |
0.25 |
| Draw | 0.5 |
0.5 |
The algorithm is agnostic about the specific values and their meaning — it only requires that both sides sum to 1.0.
Background
I built this for Sashité, a platform for chess, shogi, xiangqi, and related variants. I needed a rating system that could handle graded outcomes without hacking the algorithm. It turned out Glicko-2 supports this natively through its score parameter, so the implementation follows Glickman’s specification with no ad-hoc modifications.
