循环赛Elo评分系统的mse最优k因子

IF 1.1 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS
Victor S. Chan
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引用次数: 0

摘要

Elo评级系统包含一个称为k因子的系数,该系数控制更新评级的变化量,通常由经验或启发式方法确定。关于k因子的理论研究很少,对于影响其在应用中的适当值的相关因素所知不多。本文有两个主要目标:在循环赛设置中,提出一种关于均方误差(MSE)标准的最佳k因子的新公式,并研究包括比赛参与者数量n在内的相关变量对最优k因子(基于模型平均MSE)的影响。研究发现,n和真实评分与赛前评分偏差的可变性对最优k因子有很强的影响。还提供了mse最优k因子与来自Elo和美国国际象棋联合会的k因子作为n的函数的比较。虽然研究结果也适用于类似环境下的其他体育项目,但本研究的重点是国际象棋,并利用了国际象棋世界的评级数据和k因子值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
MSE-optimal K-factor of the Elo rating system for round-robin tournament
Abstract The Elo rating system contains a coefficient called the K-factor which governs the amount of change to the updated ratings and is often determined by empirical or heuristic means. Theoretical studies on the K-factor have been sparse and not much is known about the pertinent factors that impact its appropriate values in applications. This paper has two main goals: to present a new formulation of the K-factor that is optimal with respect to the mean-squared-error (MSE) criterion in a round-robin tournament setting and to investigate the effects of the relevant variables, including the number of tournament participants n, on the optimal K-factor (based on the model-averaged MSE). It is found that n and the variability of the deviation between the true rating and the pre-tournament rating have a strong influence on the optimal K-factor. Comparisons between the MSE-optimal K-factor and the K-factors from Elo and from the US Chess Federation as a function of n are also provided. Although the results are applicable to other sports in similar settings, the study focuses on chess and makes use of the rating data and the K-factor values from the chess world.
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来源期刊
Journal of Quantitative Analysis in Sports
Journal of Quantitative Analysis in Sports SOCIAL SCIENCES, MATHEMATICAL METHODS-
CiteScore
2.00
自引率
12.50%
发文量
15
期刊介绍: The Journal of Quantitative Analysis in Sports (JQAS), an official journal of the American Statistical Association, publishes timely, high-quality peer-reviewed research on the quantitative aspects of professional and amateur sports, including collegiate and Olympic competition. The scope of application reflects the increasing demand for novel methods to analyze and understand data in the growing field of sports analytics. Articles come from a wide variety of sports and diverse perspectives, and address topics such as game outcome models, measurement and evaluation of player performance, tournament structure, analysis of rules and adjudication, within-game strategy, analysis of sporting technologies, and player and team ranking methods. JQAS seeks to publish manuscripts that demonstrate original ways of approaching problems, develop cutting edge methods, and apply innovative thinking to solve difficult challenges in sports contexts. JQAS brings together researchers from various disciplines, including statistics, operations research, machine learning, scientific computing, econometrics, and sports management.
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