Dynamic rating of sports teams

We consider the problem of dynamically rating sports teams on the basis of categorical outcomes of paired comparisons such as win, draw and loss in football. Our modelling framework is the cumulative link model for ordered responses, where latent parameters represent the strength of each team. A dynamic extension of this model is proposed with close connections to nonparametric smoothing methods. As a consequence, recent results have more influence in estimating current abilities than results in the past. We highlight the importance of using a specific constrained random walk prior for time-changing abilities which guarantees an equal treatment of all teams. Estimation is done with an extended Kalman filter and smoother algorithm. An additional hyperparameter which determines the temporal dynamic of the latent team abilities is chosen on the basis of the optimal one-step-ahead predictive power. Alternative estimation methods are also considered. We apply our method to the results from the German football league Bundesliga 1996-1997 and to the results from the American National Basketball Association 1996-1997.