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In this work we develop a new algorithm for rating of teams (or players) inone-on-one games by exploiting the observed difference of the game-points (suchas goals), also known as a margin of victory (MOV). Our objective is to obtainthe Elo-style algorithm whose operation is simple to implement and tounderstand intuitively. This is done in three steps: first, we define theprobabilistic model between the teams' skills and the discretized MOV variable:this generalizes the model underpinning the Elo algorithm, where the MOVvariable is discretized into three categories (win/loss/draw). Second, with theformal probabilistic model at hand, the optimization required by the maximumlikelihood rule is implemented via stochastic gradient; this yields simpleon-line equations for the rating updates which are identical in their generalform to those characteristic of the Elo algorithm: the main difference lies inthe way the scores and the expected scores are defined. Third, we propose asimple method to estimate the coefficients of the model, and thus define theoperation of the algorithm; it is done in a closed form using the historicaldata so the algorithm is tailored to the sport of interest and the coefficientsdefining its operation are determined in entirely transparent manner. Thealternative, optimization-based strategy to find the coefficients is alsopresented. We show numerical examples based on the results of the associationfootball of the English Premier League and the American football of theNational Football League.

G-Elo: Generalization of the Elo algorithm by modelling the discretized margin of victory