Elo-MOV rating algorithm: Generalization of the Elo algorithm by modelling the discretized Margin of Victory

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).