Interpretable sports team rating models based on the gradient descent algorithm

We introduce several new sports team rating models based on the gradient descent algorithm. More precisely, the models can be formulated by maximising the likelihood of match results observed using a single step of this optimisation heuristic. The proposed framework is inspired by the prominent Elo rating system, and yields an iterative version of ordinal logistic regression, as well as different variants of Poisson regression-based models. This construction makes the update equations easy to interpret, and adjusts ratings once new match results are observed. Thus, it naturally handles temporal changes in team strength. Moreover, a study of association football data indicates that the new models yield more accurate forecasts and are less computationally demanding than corresponding methods that jointly optimise the likelihood for the whole set of matches.