The Elo algorithm, due to its simplicity, is widely used for rating in sports competitions as well as in other applications where the rating/ranking is a useful tool for predicting future results. However, despite its widespread use, a detailed understanding of the convergence properties of the Elo algorithm is still lacking. Aiming to fill this gap, this paper presents a comprehensive (stochastic) analysis of the Elo algorithm, considering round-robin (one-on-one) competitions. Specifically, analytical expressions are derived characterizing the behavior/evolution of the skills and of important performance metrics. Then, taking into account the relationship between the behavior of the algorithm and the step-size value, which is a hyperparameter that can be controlled, some design guidelines as well as discussions about the performance of the algorithm are provided. To illustrate the applicability of the theoretical findings, experimental results are shown, corroborating the very good match between analytical predictions and those obtained from the algorithm using real-world data (from the Italian SuperLega, Volleyball League).
翻译:Elo算法由于其简单性,被广泛用于体育竞赛以及其他应用中的评级/等级是预测未来结果的有用工具。然而,尽管它被广泛使用,但仍缺乏对Elo算法趋同性能的详细理解。为了填补这一空白,本文件介绍了对Elo算法的全面(随机)分析,同时考虑到圆形(一对一)竞争。具体地说,分析表达方式是将技能和重要性能衡量标准的行为/演变定性为特征的。随后,考虑到算法行为与可控制的分级值之间的关系,提供了一些设计准则和关于算法表现的讨论。为了说明理论结论的适用性,实验结果已经显示,分析预测与使用真实世界数据(意大利超级利加、Volleyball联盟)从算法中获得的数据(意大利超级利加、Volleyball联盟)之间的非常匹配。