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 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.