elos

Elo ratings, and the plural form ELOs, refer to a family of relative skill scoring systems used to gauge the strength of players in zero-sum games. An ELO is a numeric value assigned to an individual player or team, intended to reflect expected performance against others with established ratings. The term is widely used in chess and has been adopted by many online platforms for a variety of competitive activities. The plural ELOs is commonly seen when discussing the ratings of multiple players or rating lists.

The system was developed by Arpad Elo in the 1960s to improve upon prior rating methods for chess. It has since become a standard reference in chess organizations and has inspired adaptations for other games and competitive environments. While ELOs share a common mathematical foundation, implementations vary in details such as the initial rating, the K-factor used to scale updates, and how draws are handled.

How it works: each match produces an actual score (S) of 1 for a win, 0 for a loss, and 0.5 for a draw. The expected score (E) is calculated from the difference between the players’ ratings, typically using a logistic function. After a game, both players’ ratings are updated by a factor of K times (S − E). Over time, ELOs converge toward a player’s demonstrated performance, with larger K-values producing faster changes.

Limitations include reliance on historical results, assumptions of constant skill, sensitivity to rating inflation or deflation, and less responsiveness for players who compete infrequently. Variants such as Glicko and TrueSkill introduce uncertainty or additional parameters to address some shortcomings while retaining the core idea of relative skill estimation.