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.

翻译：埃洛等级分系统是一种基于配对比较数据计算棋手技能水平的简单且广泛使用的方法。许多学者在不同方向上对其进行了扩展，然而棋手方差更新问题仍有待进一步探究。本文通过后验分布的拉普拉斯近似，结合棋手实力动态变化的随机游走模型以及棋手方差的下界，解决了方差更新问题。该随机游走模型受格拉科系统启发，但在此我们假设非等分布的增量以处理棋手异质性。基于男子职业比赛的实验表明，执行方差更新后预测精度略有提升，同时方差更新能更有效地捕捉新晋棋手的实力水平。