论文标题
ELO评级算法的随机分析
Stochastic analysis of the Elo rating algorithm in round-robin tournaments
论文作者
论文摘要
ELO算法以其简单而闻名，广泛用于体育比赛和其他应用中。但是，尽管它广泛使用，但仍然缺乏对ELO算法的收敛特征的详细理解。为了填补这一空白，本文考虑了循环赛锦标赛，对ELO算法进行了全面的（随机）分析。具体而言，分析表达式描述了技能和性能指标的演变。然后，考虑到算法的行为与步进尺寸值之间的关系，这是可以控制的超参数，因此提供了有关算法性能的设计准则和讨论。显示实验结果证明了分析的准确性，并使用从意大利排球联盟Superlega获得的现实世界数据说明了理论发现的适用性。
The Elo algorithm, renowned for its simplicity, is widely used for rating in sports tournaments and other applications. However, despite its widespread use, a detailed understanding of the convergence characteristics 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 tournaments. Specifically, analytical expressions are derived describing the evolution of the skills and 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, design guidelines and discussions about the performance of the algorithm are provided. Experimental results are shown confirming the accuracy of the analysis and illustrating the applicability of the theoretical findings using real-world data obtained from SuperLega, the Italian volleyball league.
