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Understanding draws in Elo rating algorithm
Journal of Quantitative Analysis in Sports Pub Date : 2020-09-25 , DOI: 10.1515/jqas-2019-0102
Leszek Szczecinski 1 , Aymen Djebbi 1
Affiliation  

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.

中文翻译:

了解Elo评分算法中的抽奖

摘要这项工作涉及对在各种运动评级中应用的众所周知的Elo算法产生的结果的解释。解释在于根据玩家的评分来定义游戏结果的概率,并且应基于概率评分结果模型。这样的模型在二元博弈(赢/输)中是已知的,这使我们能够根据赢/输概率来解释评级结果。另一方面,即使从设计之初就在三元游戏中使用了Elo算法,三元结果模型(赢/输/平局)仍未显示。使用戴维森(Davidson)在1970年提出的绘图模型,我们推导出了一种新的Elo-Davidson算法,并证明了Elo算法是其特定实例。然后,Elo-Davidson的参数与平局频率相关,这表明Elo算法默默地假设有50%的平局游戏。为了消除这种通常不切实际的假设,应使用Elo-Davidson算法,因为它可以改善对数据的拟合度。使用英超联赛的结果说明了算法的行为。
更新日期:2020-09-25
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