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 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 margin of victory (MOV) variable. We thus use a predefined number of discretization categories, which generalizes the model underpinning the Elo algorithm, where the MOV variable is discretized to three categories (win/loss/draw). Second, with the formal probabilistic model at hand, the optimization required by the maximum likelihood (ML) rule is implemented via stochastic gradient (SG); this yields a simple on-line rating updates which are identical in general form to those of the Elo algorithm. The main difference lies in the way the scores and 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. This is done in 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. We show numerical examples based on the results of ten seasons of the English Premier Ligue (EPL).
翻译:在这项工作中,我们为一对一游戏中球队(或球员)的评分开发了一种新的算法,利用观察到的游戏点差异(如目标)(也称为胜利幅度)的观察差异(MOV)。我们的目标是获得Elo式算法,其操作简单,可以执行和直观理解。这分三个步骤完成:首先,我们界定了球队技能和分解的胜率(MOV)变量之间的概率模型。因此,我们使用一个预先界定的分解类别,将支持埃洛算法的模式(如目标)的模型(MOV变量)概括化为三种类别(双向/损益/减利差)。第二,在掌握正式的概率模型的情况下,最大可能性(ML)规则所要求的优化通过分级梯度梯度(SG)实施;这产生了一个简单的在线评分更新模式,与埃洛算法(MOV)变量的一般形式相同。主要差异在于如何界定埃洛算法的分和预期分。第三,我们提出了一个简单的方法来估算模型的系数,即MOV变量分为三个类别(双向/损/draw)。第二,用正式的概率模型的概率模型的概率模型的计算方法,从而界定了以历史运算法的方式界定了它所决定了运动的数值的数值的计算结果。