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

Bookmakers odds are an easily available source of ``prospective" information that is thus often employed for forecasting the outcome of sports events. 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 for the UEFA 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 teams' agreement 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.

[1]  D. Bates,et al.  Mixed-Effects Models in S and S-PLUS , 2001 .

[2]  Herman Stekler,et al.  Do consensus forecasts exist , 1991 .

[3]  Mark J. Dixon,et al.  The value of statistical forecasts in the UK association football betting market , 2004 .

[4]  Michael P. Clements Consensus and uncertainty: Using forecast probabilities of output declines , 2008 .

[5]  Herman Stekler,et al.  The comparative accuracy of judgmental and model forecasts of American football games , 2007 .

[6]  Kajal Lahiri,et al.  On the normality of probability distributions of inflation and GNP forecasts , 1987 .

[7]  Achim Zeileis,et al.  Predicting the Winner of the EURO 2008. A statistical investigation of bookmakers odds. , 2008 .

[8]  H. Stekler,et al.  P redicting the outcomes of National Football League games , 2003 .

[9]  K. Hornik,et al.  Forecasting the winner of the UEFA Champions League 2008 / 09 , 2009 .

[10]  V. Su,et al.  An Evaluation of ASA/NBER Business Outlook Survey Forecasts , 1975 .

[11]  Herman Stekler,et al.  Measuring consensus in binary forecasts: NFL game predictions , 2009 .

[12]  H. Stekler,et al.  Is there a consensus among financial forecasters , 1996 .

[13]  Robert Simmons,et al.  Odds setters as forecasters: the case of English football , 2005 .

[14]  Kurt Hornik,et al.  Forecasting sports tournaments by ratings of (prob)abilities: A comparison for the EURO 2008 , 2010 .

[15]  Martin Spann,et al.  Sports forecasting: a comparison of the forecast accuracy of prediction markets, betting odds and tipsters , 2009 .

[16]  R. J. Henery Measures of over-round in performance index betting , 1999 .