Evaluating significant effects from alternative seeding systems : a Bayesian approach, with an application to the UEFA Champions League

The paper discusses how to evaluate alternative seeding systems in sports competitions. Prior papers have developed an approach which uses a forecasting model at the level of the individual match and then applies Monte Carlo simulation of the whole tournament to estimate the probabilities associated with various outcomes or combinations of outcomes. This allows, for example, a measure of outcome uncertainty to be attached to each proposed seeding regime. However, this established approach takes no note of the uncertainty surrounding the parameter estimates in the underlying match forecasting model and this precludes testing for statistically significant differences between probabilities or outcome uncertainty measures under alternative regimes. We propose a Bayesian approach which resolves this weakness in standard methodology and illustrate its potential by examining the effect of seeding rule changes implemented in the UEFA Champions League, a major football tournament, in 2015. The reform appears to have increased outcome uncertainty. We identify which clubs and which sorts of clubs were favourably or unfavourably affected by the reform, distinguishing effects on probabilities of progression to different phases of the competition.