Elo rating

The Elo rating system, developed by physicist Arpad Elo for ranking chess players, gives every competitor a single number representing their estimated skill. Before a match, the two ratings imply a win probability for each side; after the match, both ratings shift, the winner gains points and the loser loses points, with the size of the shift depending on how surprising the result was. Beating a much stronger opponent moves a rating more than beating a weaker one.

The win probability is typically modeled with a logistic function of the rating difference between the two competitors, and ratings are updated by a constant, often called K, multiplied by the difference between the actual result and the expected one. This differs from a simple win rate or win-loss record, because Elo accounts for opponent strength and updates continuously rather than resetting each season.

Beyond chess, Elo and its variants now rank national soccer teams, esports players, and are used inside betting markets to estimate match odds. It complements composite performance metrics such as wins above replacement or, in soccer analytics, expected goals, which describe a player's or team's underlying quality rather than a single competitive strength number. A common pitfall is comparing raw Elo numbers across sports or rating providers that use different starting points, K-factors, or update rules, since the scale is arbitrary and only meaningful within one consistent system.