Understanding draws in Elo rating algorithm

IF 1.1 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS

Journal of Quantitative Analysis in Sports Pub Date : 2020-05-04 DOI:10.1515/jqas-2019-0102

L. Szczecinski, Aymen Djebbi

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引用次数: 13

Abstract

Abstract This work is concerned with the interpretation of the results produced by the well known Elo algorithm applied in various sport ratings. The interpretation consists in defining the probabilities of the game outcomes conditioned on the ratings of the players and should be based on the probabilistic rating-outcome model. Such a model is known in the binary games (win/loss), allowing us to interpret the rating results in terms of the win/loss probability. On the other hand, the model for the ternary outcomes (win/loss/draw) has not been yet shown even if the Elo algorithm has been used in ternary games from the very moment it was devised. Using the draw model proposed by Davidson in 1970, we derive a new Elo-Davidson algorithm, and show that the Elo algorithm is its particular instance. The parameters of the Elo-Davidson are then related to the frequency of draws which indicates that the Elo algorithm silently assumes games with 50% of draws. To remove this assumption, often unrealistic, the Elo-Davidson algorithm should be used as it improves the fit to the data. The behaviour of the algorithms is illustrated using the results from English Premier League.

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理解借鉴了Elo评级算法

摘要:这项工作涉及到对各种体育评级中应用的众所周知的Elo算法产生的结果的解释。这种解释包括根据玩家的评级来定义游戏结果的概率，并且应该基于概率评级-结果模型。这种模型在二元博弈(赢/输)中是已知的，允许我们根据赢/输概率来解释评级结果。另一方面，三进制结果(赢/输/平局)的模型尚未被展示，即使Elo算法从设计之初就被用于三进制游戏中。利用Davidson在1970年提出的绘图模型，我们推导了一种新的Elo-Davidson算法，并证明了Elo算法是它的特殊实例。然后，Elo- davidson的参数与抽签频率相关，这表明Elo算法默默地假设游戏有50%的平局。为了消除这种通常不现实的假设，应该使用Elo-Davidson算法，因为它可以改善对数据的拟合。算法的行为用英超联赛的结果来说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Quantitative Analysis in Sports SOCIAL SCIENCES, MATHEMATICAL METHODS-

CiteScore

2.00

自引率

12.50%

发文量

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.