Elo


What is elo?

The Elo rating system is used to represent relative skill levels in head-to-head competitive games. A “match” pairs two ratings along with a result (win or loss); based on the expected result, points are transferred between the two parties.


How does elo rating work?

The point exchange in an Elo match is always zero-sum (all points subtracted from one party are awarded to the other); therefore, it is not possible to improve a rating with a loss. A larger difference between the actual and expected result will result in a larger point transfer (e.g., an “upset,” where the heavily favored rating loses).


How is the elo rating calculated?

$$E_a$$ = Elo rating for player A, $$R_a$$ = New elo rating if player A wins

$$E_b$$ = Elo rating for player B, $$R_b$$ = New elo rating if player B wins

$$R_a = ({1 - {1 \over 1 + 10^{(E_b - E_a) \over 400}}}) * Kfactor$$

$$R_b = ({1 - {1 \over 1 + 10^{(E_a - E_b) \over 400}}}) * Kfactor$$


What is this K factor?

The “K factor” is a constant applied in the Elo formula that determines the sensitivity (amount of swing) in a given match. The higher the k-factor, the more points will be exchanged. Generally, the K factor can decrease over time as a rating approaches its “true” value.

Current K factors:

100 - 1st game against any player.

75 - 2nd game against same player during a month.

50 - all games after the 2nd game against same player during a month.