  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.
