Elo

The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games. It was devised by Arpad Elo in the 1950s and became widely adopted in chess, where it has served as the standard for rating players and tracking performance across events. Over time, the model has been applied to many other games and online platforms.

Basic mechanics: Each player has a numerical rating. Before a matchup, a player’s expected score is E = 1 / (1 + 10^((R_opponent − R_player)/400)). After the game, the rating is updated with R_new = R_old + K × (S − E), where S is the actual score (1 for a win, 0.5 for a draw, 0 for a loss) and K is a factor that controls how quickly ratings change. K-values vary by organization and by player status, commonly ranging from 10 to 40. The system is designed so that stronger players tend to gain more rating points than weaker players lose.

Applications and interpretation: Elo ratings measure relative strength within a defined population. They are not absolute skill levels and are sensitive to the size and quality of the rating pool. Ratings are dynamic, reflecting recent performance; new players typically start with a provisional rating and adjust as they play more games. Variants such as Glicko and TrueSkill extend the model by incorporating uncertainty or different scoring approaches.

Limitations: The method assumes relatively stable skill and independent results; it can be affected by rating inflation or deflation and does not account for performance variability within individuals. Despite limitations, the Elo system remains widely used for ranking players in chess and many other competitive activities.