Dynamic Rating of Sports Teams. (REVISED 1999)

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 in uence for estimating current abilities than results in the past We highlight the importance of using a speci c constrained random walk prior for time changing abilities which guarantees an equal treatment of all teams Estimation is done within an extended Kalman lter 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 and to the results from the American National Basketball Association NBA