# Elo

Elo is a rating system used to determine the relative skill of individuals. It is commonly used in games such as Chess.

In Elo, each player is given a rating; it may be an existing rating or seeded from an existing rating; for example, Chess games may seed players with a ranking around 1500 for average players (or lower if the player believes to be inexperienced.)

## Rating

Scored in Elo change based on matches or other events. The following values are used:

• RA, rating for player A.
• RB, rating for player B.
• ${\displaystyle E_{A}={\frac {1}{1+10^{(R_{B}-R_{A})/400}}}}$, the expected score of player A.
• ${\displaystyle E_{B}={\frac {1}{1+10^{(R_{A}-R_{B})/400}}}}$, the expected score of player B.
• K, an adjustment factor (high for new players, or lower for more experienced ones)
• ${\displaystyle S_{A}}$ and ${\displaystyle S_{B}}$, the scores for players A and B
• ${\displaystyle R'_{A}=R_{A}+K_{A}(S_{A}-E_{A})}$, the new rating for player A
• ${\displaystyle R'_{B}=R_{B}+K_{B}(S_{B}-E_{B})}$, the new rating for player B
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