Elo Rating System
The Elo Rating System is a mathematical framework used for calculating the relative skill levels of players in zero-sum games. It is named after its creator, Arpad Elo, a physics professor and Chess master who developed the method to improve upon the previously used Harkness System. The fundamental principle of the system is that the performance of a player is a random variable that follows a Logistic Distribution over time.
In a competitive match, the Elo Rating System uses the difference in ratings between two opponents to predict the outcome of a game. According to the FIDE Rating Regulations, the winner takes points from the loser, with the total number of points exchanged determined by the K-Factor. If a high-rated player wins against a low-rated player, the rating change is minimal; however, an upset results in a significant transfer of points. This ensures that the system remains self-correcting and reflective of current skill levels.
Beyond its origins in Chess, the system has been widely adapted for use in Esports, where it powers Matchmaking algorithms for titles such as League of Legends and Counter-Strike. It is also utilized in physical sports rankings, including the FIFA World Rankings for association Football. Detailed historical analysis and mathematical derivations of the system can be found on Wikipedia and other statistical archives.