The Glicko rating system and Glicko-2 rating system are methods of assessing a player's strength in games of skill, such as
chess
Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to disti ...
and
Go. The Glicko rating system was invented by Mark Glickman in 1995 as an improvement on the
Elo rating system
The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. It is named after its creator Arpad Elo, a Hungarian-American physics professor.
The Elo system was invented as an improved ch ...
, and initially intended for the primary use as a
chess rating system
A chess rating system is a system used in chess to estimate the strength of a player, based on their performance versus other players. They are used by organizations such as FIDE, the US Chess Federation (USCF or US Chess), International Correspond ...
. Glickman's principal contribution to measurement is "ratings reliability", called RD, for ''ratings
deviation''.
Overview
Mark Glickman created the Glicko rating system in 1995 as an improvement on the
Elo rating system
The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. It is named after its creator Arpad Elo, a Hungarian-American physics professor.
The Elo system was invented as an improved ch ...
.
Both the Glicko and Glicko-2 rating systems are under public domain and have been implemented on
game server
A game server (also sometimes referred to as a host) is a server (computing), server which is the authoritative source of events in a multiplayer video game. The server transmits enough data about its internal state to allow its connected Client ...
s online (like
Pokémon Showdown
(an abbreviation for in Japan) is a Japanese media franchise managed by The Pokémon Company, founded by Nintendo, Game Freak, and Creatures, the owners of the trademark and copyright of the franchise.
In terms of what each of thos ...
,
Pokémon Go
''Pokémon Go'' (stylized as ''Pokémon GO'') is a 2016 augmented reality (AR) mobile game, part of the ''Pokémon'' franchise, developed and published by Niantic in collaboration with Nintendo and The Pokémon Company for iOS and Android ...
,
Lichess
Lichess (; ) is a free and open-source Internet chess server run by a non-profit organization of the same name. Users of the site can play online chess anonymously and optionally register an account to play rated games. Lichess is ad-free and al ...
,
Free Internet Chess Server
The Free Internet Chess Server (FICS) is a volunteer-run Internet chess server. It was organised as a free alternative to the Internet Chess Club (ICC), after that site began charging for membership.
History
The first Internet chess server, ...
,
Chess.com
Chess.com is an internet chess server, news website and social networking website. The site has a freemium model in which some features are available for free, and others are available for accounts with subscriptions. Live online chess can be pla ...
, Online Go Server (OGS),
Counter Strike: Global Offensive,
Quake Live
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Team Fortress 2
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Dota Underlords
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Guild Wars 2
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Splatoon 2
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Dominion Online, TETR.IO, and competitive programming competitions.
The Reliability Deviation (RD) measures the accuracy of a player's rating, where the RD is 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 (exact: 1.96) 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
The Australian Chess Federation (ACF) is dedicated to promoting the game of chess in Australia, and is a member of FIDE, the World Chess Federation.
The ACF administers its own chess rating system for tournaments in Australia, and runs the ACF G ...
.
The algorithm of Glicko
Step 1: Determine ratings deviation
The new Ratings Deviation (
) is found using the old Ratings Deviation (
):
where
is the amount of time (rating periods) since the last competition and '350' is assumed to be the RD of an unrated player. If several games have occurred within one rating period, the method treats them as having happened simultaneously. The rating period may be as long as several months or as short as a few minutes, according to how frequently games are arranged. The constant
is based on the uncertainty of a player's skill over a certain amount of time. It can be derived from thorough data analysis, or estimated by considering the length of time that would have to pass before a player's rating deviation would grow to that of an unrated player. If it is assumed that it would take 100 rating periods for a player's rating deviation to return to an initial uncertainty of 350, and a typical player has a rating deviation of 50 then the constant can be found by solving
for
.
Or
Step 2: Determine new rating
The new ratings, after a series of m games, are determined by the following equation:
where:
represents the ratings of the individual opponents.
represents the rating deviations of the individual opponents.
represents the outcome of the individual games. A win is 1, a draw is
, and a loss is 0.
Step 3: Determine new ratings deviation
The function of the prior RD calculation was to increase the RD appropriately to account for the increasing uncertainty in a player's skill level during a period of non-observation by the model. Now, the RD is updated (decreased) after the series of games:
Glicko-2 algorithm
Glicko-2 works in a similar way to the original Glicko algorithm, with the addition of a rating volatility
which measures the degree of expected fluctuation in a player’s rating, based on how erratic the player's performances are. For instance, a player's rating volatility would be low when they performed at a consistent level, and would increase if they had exceptionally strong results after that period of consistency. A simplified explanation of the Glicko-2 algorithm is presented below:
Step 1: Compute ancillary quantities
Across one rating period, a player with a current rating
and ratings deviation
plays against
opponents, with ratings
and RDs
, resulting in scores
. We first need to compute the ancillary quantities
and
:
where
Step 2: Determine new rating volatility
We then need to choose a small constant
which constrains the volatility over time, for instance
(smaller values of
prevent dramatic rating changes after upset results). Then, for
we need to find the value
which satisfies
. An efficient way of solving this would be to use the Illinois algorithm, a modified version of the ''
regula falsi'' procedure (see for details on how this would be done). Once this iterative procedure is complete, we set the new rating volatility
as
Step 3: Determine new ratings deviation and rating
We then get the new RD
and new rating
These ratings and RDs are on a different scale than in the original Glicko algorithm, and would need to be converted to properly compare the two.
See also
*
Chess rating system
A chess rating system is a system used in chess to estimate the strength of a player, based on their performance versus other players. They are used by organizations such as FIDE, the US Chess Federation (USCF or US Chess), International Correspond ...
References
External links
Professor Glickman's Glicko-Website*
TrueSkill
TrueSkill is a skill-based ranking system developed by Microsoft for use with video game matchmaking on Xbox Live. Unlike the popular Elo rating system, which was initially designed for chess, TrueSkill is designed to support games with more than t ...
br>
rating system by Microsoft borrows many ideas of Glicko.
forwardloop/glicko2sGlicko-2 implementation for the JVM
RobKohr/glickoJavaScript Glicko-2 implementation.
mmai/glicko2jsClient side javascript and node.js Glicko-2 implementation
deepy/glicko2Python Glicko-2 implementation.
sublee/glicko2Python Glicko-2 implementation.
PlayerRatingsR Glicko implementation by Alec Stephenson and Jeff Sonas.
scala-glicko2Scala Glicko-2 implementation.
dimos/glicko2Glicko-2 implementation for Scala and Scala.js
{{Sports rating systems
Chess in Australia
Chess rating systems