MSE-Optimal K-factor of the Elo Rating System

Metro Toronto Convention Centre 

The Elo rating system contains a coefficient called the K-factor, which governs the amount of change to the updated rating. Currently theoretical studies on the K-factor are sparse, and little is known about the pertinent factors that impact its appropriate values in applications. In this talk we will present a K-factor that is optimal with respect to the mean-squared-error (MSE) criterion, as well as the results of a study of the optimal K-factor's sensitivity to relevant variables. We focus on the case in which the rating update is made after the completion of a round-robin tournament. A simple additive model for the true ratings is adopted to identify the factors that may affect the value of optimal K-factor. We discuss the results showing that the size of the tournament and the variability of the deviation between the true rating and the pre-tournament rating exert a substantial influence on the optimal K-factor. Comparison will be made between the optimal K-factor and the actual K-factor value used by the International Chess Federation in its Elo rating scheme.