Chess Rating System - Elo Rating System - Linear Approximation

Linear Approximation

Elo devised a linear approximation to his full system. With that method, a player's new rating is his or her old rating plus K×(W-L)/2 plus K/(4C) times the sum of D_i, where C=200, K=32, each D_i is the opponent's rating minus the player's rating, W is the number of wins, and L is the number of losses (Elo 1978:28–29).

The example of Portisch with K=10, with the sum of the rating differences being 1620 is:

2635+10*(10.5-4.5)/2-(10/800)×1620=2644.75 (Elo 1978:39).

The USCF used a modification of this system to calculate ratings after individual games of correspondence chess, with a K=32 and C=200.