Rating players by Laplace’s approximation and dynamic modeling

The Elo rating system is a simple and widely used method for calculating players’ skills from paired comparison data. Many have extended it in various ways. Yet the question of updating players’ variances remains to be further explored. In this paper, we address the issue of variance update by using the Laplace approximation for posterior distributions, together with a random walk model for the dynamics of players’ strengths and a lower bound on player variance. The random walk model is motivated by the Glicko system, but here we assume nonidentically distributed increments to deal with player heterogeneity. Experiments on men’s professional matches showed that the prediction accuracy slightly improves when the variance update is performed. They also showed that new players’ strengths may be better captured with the variance update.