Glicko rating system
The Glicko rating system and Glicko-2 rating system are methods for assessing a player's strength in games of skill, such as chess and go. It was invented by Mark Glickman as an improvement of the Elo rating system, and initially intended for the primary use as a chess rating system. Glickman's principal contribution to measurement is "ratings reliability", called RD, for ratings deviation.
Both Glicko and Glicko-2 rating systems are under public domain and found implemented on game servers online (like Lichess, Free Internet Chess Server, Chess.com, Counter Strike: Global Offensive, Guild Wars 2). The formulas used for the systems can be found on the Glicko website.
The RD measures the accuracy of a player's rating, with one RD being equal to one standard deviation. For example, a player with a rating of 1500 and an RD of 50 has a real strength between 1400 and 1600 (two standard deviations from 1500) with 95% confidence. Twice the RD is added and subtracted from their rating to calculate this range. After a game, the amount the rating changes depends on the RD: the change is smaller when the player's RD is low (since their rating is already considered accurate), and also when their opponent's RD is high (since the opponent's true rating is not well known, so little information is being gained). The RD itself decreases after playing a game, but it will increase slowly over time of inactivity.
The Glicko-2 rating system improves upon the Glicko rating system and further introduces the rating volatility σ. A very slightly modified version of the Glicko-2 rating system is implemented by the Australian Chess Federation.
These steps only apply to the original Glicko system, and not its successor, Glicko-2.
If the player is unrated, the rating is usually set to 1500 and the RD to 350.
The new Ratings Deviation () is found using the old Ratings Deviation ():
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