论文标题
G-Elo：通过建模离散的胜利余量来对ELO算法的概括
G-Elo: Generalization of the Elo algorithm by modelling the discretized margin of victory
论文作者
论文摘要
在这项工作中，我们通过利用观察到的游戏点的差异（例如进球）（也称为胜利的利润率（MOV）），开发了一种在一对一比赛中评级团队（或球员）的新算法。我们的目标是获得ELO风格的算法，其操作易于实施和直观地理解。这是三个步骤完成的：首先，我们定义了团队技能和离散化的MOV变量之间的概率模型：这将概括为ELO算法的模型，其中MOV变量分为三类（Win/loss/Draw）。其次，在手头的形式概率模型的情况下，最大似然规则所要求的优化是通过随机梯度实现的。这产生了与ELO算法的特征相同的评级更新的简单在线方程：主要区别在于分数和预期分数的定义方式。第三，我们提出了一种简单的方法来估计模型的系数，从而定义了算法的操作。它是使用历史数据以封闭形式完成的，因此该算法是针对感兴趣的运动量身定制的，并且定义其操作的系数以完全透明的方式确定。还提供了基于优化的替代优化策略。我们根据英国英超联赛的协会足球和国家橄榄球联盟的美式足球的成绩展示了数值示例。
In this work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the Elo-style algorithm whose operation is simple to implement and to understand intuitively. This is done in three steps: first, we define the probabilistic model between the teams' skills and the discretized MOV variable: this generalizes the model underpinning the Elo algorithm, where the MOV variable is discretized into three categories (win/loss/draw). Second, with the formal probabilistic model at hand, the optimization required by the maximum likelihood rule is implemented via stochastic gradient; this yields simple on-line equations for the rating updates which are identical in their general form to those characteristic of the Elo algorithm: the main difference lies in the way the scores and the expected scores are defined. Third, we propose a simple method to estimate the coefficients of the model, and thus define the operation of the algorithm; it is done in a closed form using the historical data so the algorithm is tailored to the sport of interest and the coefficients defining its operation are determined in entirely transparent manner. The alternative, optimization-based strategy to find the coefficients is also presented. We show numerical examples based on the results of the association football of the English Premier League and the American football of the National Football League.
