Dynamic Rating of Sports Teams. (REVISED 1999).
Sonderforschungsbereich 386, Discussion Paper 98
We consider the problem of dynamically rating sports teams based on the categorical outcome of paired comparisons such as win, draw and loss in football. Our modelling framework is the cumulative link model for ordered response, 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 for 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 within an extended Kalman filter type approach. An additional hyperparameter which determines the temporal dynamic of the latent team abilities is chosen based on 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'' 1996/97 and to the results from the American National Basketball Association (NBA) 1996/97.