Extended ordered paired comparison models with application to football data from German Bundesliga

A general paired comparison model for the evaluation of sport competitions is proposed. It efficiently uses the available information by allowing for ordered response categories and team-specific home advantage effects. Penalized estimation techniques are used to identify clusters of teams that share the same ability. The model is extended to include team-specific explanatory variables. It is shown that regularization techniques allow to identify the contribution of explanatory variables to the success of teams. The usefulness of the methods is demonstrated by investigating the performance and its dependence on the budget for football teams of the German Bundesliga.