Elo Rating System

An Elo Rating System is a rating system that calculates the relative skill levels of players in zero-sum games, such as chess, by predicting the outcome of matches based on differences in player ratings.

• Context:
  • ouptut: ELO Score.
  • It can quantify the skill level of players in various competitive activities beyond chess, including association football, American football, baseball, basketball, and esports.
  • It can be used to predict the outcome of a match, where a certain point difference between players' ratings implies a specific probability of winning.
  • It can adjust a player's rating based on the result of each game, with winners gaining points and losers losing points.
  • It can cause a significant transfer of rating points in the event of an upset, where a lower-rated player defeats a higher-rated one.
  • It can ensure that the ratings are comparative and valid only within the specific pool in which they were calculated.
  • It can be adapted for use in multiplayer competitions through system variations.
  • ...
• Example(s):
  • as used in international chess competitions to rank players.
  • as used for ranking teams in association football leagues.
  • as used in esports tournaments to seed players or teams.
  • as used in LMSYS Chatbot Benchmark Platform.
  • ...
• Counter-Example(s):
  • TrueSkill Rating System
  • Glicko Rating System
• See: Competitive Balance, Game Theory, Performance Rating, Rating Decay, Skill Assessment, Statistical Predictability.

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References

2024

• (Wikipedia, 2024) ⇒ https://en.wikipedia.org/wiki/Elo_rating_system Retrieved:2024-4-7.
  • 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 chess-rating system over the previously used Harkness system, but is also used as a rating system in association football, American football, baseball, basketball, pool, table tennis, various board games and esports, and more recently large language models.

    The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to score an equal number of wins. A player whose rating is 100 points greater than their opponent's is expected to score 64%; if the difference is 200 points, then the expected score for the stronger player is 76%. A player's Elo rating is a number which may change depending on the outcome of rated games played. After every game, the winning player takes points from the losing one. The difference between the ratings of the winner and loser determines the total number of points gained or lost after a game. If the higher-rated player wins, then only a few rating points will be taken from the lower-rated player. However, if the lower-rated player scores an upset win, many rating points will be transferred. The lower-rated player will also gain a few points from the higher rated player in the event of a draw. This means that this rating system is self-correcting. Players whose ratings are too low or too high should, in the long run, do better or worse correspondingly than the rating system predicts and thus gain or lose rating points until the ratings reflect their true playing strength. Elo ratings are comparative only, and are valid only within the rating pool in which they were calculated, rather than being an absolute measure of a player's strength. While Elo-like systems are widely used in two-player settings, variations have also been applied to multiplayer competitions.

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