The Elo rating system is a simple and widely used method for calculating players' skills from paired comparisons 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 distribution, together with a random walk model for the dynamics of players' strengths, and a lower bound on players' variances. The random walk model is motivated by the Glicko system, but here we assume nonidentically distributed increments to take care of 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.

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