Bookmaker consensus and agreement for the UEFA Champions League 2008/2009

Bookmakers odds are an easily available source of ‘prospective’ information that is often employed for forecasting the outcome of sports events. In order to investigate the statistical properties of bookmakers odds from a variety of bookmakers for a number of different potential outcomes of a sports event, a class of mixed‐effects models is explored, providing information about both consensus and (dis)agreement across bookmakers. In an empirical study of the Union of European Football Associations Champions League, the most prestigious football club competition in Europe, model selection yields a simple and intuitive model with team‐specific means for capturing consensus and team‐specific standard deviations reflecting agreement across bookmakers. The resulting consensus forecast performs well in practice, exhibiting high correlation with the actual tournament outcome. Furthermore, the agreement across the bookmakers can be shown to be strongly correlated with the predicted consensus and can thus be incorporated in a more parsimonious model for agreement while preserving the same consensus fit.