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What is the elo rating system?

The Elo rating system is a method for calculating the relative skill levels of players in two-player games such as chess and Go. It is named after its creator Arpad Elo, a Hungarian-American physics professor. The Elo system was originally invented as an improved chess rating system over the previously used Harkness system, but is also used as a rating system for multiplayer competition in a number of video games, association football, American football, basketball and other games.

If there are two teams, A and B, with respective Elo ratings of Ra and Rb, the expected score of team A is: Ea, the expected score of team B is: Eb.
The expected score of team A is given by:

Ea = 1 / (1 + 10^((Rb - Ra) / 400))

The expected score of team B is given by:

Eb = 1 / (1 + 10^((Ra - Rb) / 400))

In practice, Ea is the probability that team A will win and Eb is the probability that team B will win.
The formula for updating the ratings after a game is:

Ra' = Ra + K * (Sa - Ea)

Rb' = Rb + K * (Sb - Eb)

where:

Ra' = the new rating of team A
Rb' = the new rating of team B
K = the weight constant
Sa = the actual score of team A.
Sb = the actual score of team B.

The weight constant K is the maximum possible adjustment per game, it is a constant defined by the system.
The K factor is the maximum possible adjustment per game, it is a constant defined by the system.
In the simple case, the Sa, Sb are represented game results and Win = 1, Draw = 0.5, Lose = 0.
The K factor is usually set to 32, and the ratings are updated after each game.
So, we can adjust the K factor and other parameters to make the ratings more or less volatile.
In this web site, we use the simple Elo rating system to predict the winner of the next game and to evaluate the prediction results of the past games.

Reference

Elo rating system

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