The ELO rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess or tennis. It is named after its creator Arpad Elo, a Hungarian-American physics professor. The ELO rating system is used by the World Chess Federation (FIDE) to rank chess players, and it has been adopted by many other sports and games.
In the ELO system, each player is assigned a rating based on their past performance. When two players compete, the winner gains points and the loser loses points based on the difference between their ratings.
Suppose Player One has a rating of 1400 and Player Two has a rating of 1600. The constant K is set to 32, which means that the result of the game will have a significant impact on the players ratings.
The expected outcome for each player is calculated based on their ratings and the probability of each player winning the game. Let's say that the expected outcome for Player One is 0.43 (meaning that they have a 43% chance of winning the game) and the expected outcome for Player Two is 0.57 (meaning that they have a 57% chance of winning).
If Player One wins the game, the new ratings for each player would be calculated as follows:
Player One: New Rating = 1400 + 32 * (1 - 0.43) = 1413
Player Two: New Rating = 1600 + 32 * (0 - 0.57) = 1587
If Player Two wins the game, the new ratings would be calculated as follows:
Player One: New Rating = 1400 + 32 * (0 - 0.43) = 1387
Player Two: New Rating = 1600 + 32 * (1 - 0.57) = 1613
In both cases, the new ratings reflect the outcome of the game and accurately reflect the relative strengths of the players. The ratings can then be used to compare the players to each other and to other players in the club or league.
The ELO rating system is designed to be self-correcting, so that players ratings will tend to converge on their true skill levels over time. This makes it an effective way to rank players and track their performance.
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