Formula used for rating calculation
The Elo rating system (named after it's developer Dr. Arpad Elo) is a numerical system in which differences in rating may be converted into scoring or winning probabilities and vice versa. Most competition rating systems today are based on Elo's system.
Since the stronger player does not always outperform the weaker player, a normal distribution function is used to represent the variable performance of a player. This normal distribution function simply says that deviations from the average level occur, and that large deviations occur less frequently than small ones. The deviation is measured in so called standard deviations, a spread which encompasses about 2/3 of a player's performances (the normal distribution function is one of the fundamental functions in statistics).
The normal probability function is derived from the normal distribution function, and this function determines the differences in ratings based on match results, or the expected match scores based on known rating differences.
P(D) can be approximated by the following function:
P(D)=1/(1+10^(-D/400))
D - Rating difference
P - Winning probability
This is the equation of the Elo system:
Rn = Ro + K * (W - P(D))
Rn - New rating after event
Ro - Pre-event rating
K - Rating point value of a single game score
W - Actual game score (1 for a win, 0 for a loss)
P(D) - winning probability
This equation is used to compute new ratings on a continuous basis (that is, after each game or event). This equation averages the latest performance into the prior rating. Earlier performances are smoothly diminished, while the full contribution of the latest performance is preserved. The logic behind the formula is that a player performing above his/her expectancy gains points and a player performing below his/her expectancy loses points.
The coefficient K determines the relative weight given to the pre-event rating and the event performance rating. A high K gives more weight to the most recent performance. In practice, K may range between 10 and 32. Ladder uses K=12.