Stochastic dynamic Thurstone-Mosteller models for sports tournaments

In the course of national sports tournaments, usually lasting several months, it is expected that the abilities of teams taking part in the tournament change in time. A dynamic extension of the Thurstone-Mosteller model for paired comparison data is introduced to model the outcomes of sporting contests allowing for time-varying abilities. It is assumed that the development of teams' abilities follows a stationary process and a team-specific home effect is considered. The likelihood function of the proposed model requires the approximation of a high dimensional integral. This difficulty is overcome by means of maximum simulated likelihood via the Geweke-Hajivassiliou-Keane algorithm. Ranking of teams and forecasting future match results are performed through a Metropolis-Hastings algorithm. The methodology is applied to sports data with and without tied contests, namely the 2006-2007 Italian volleyball league and the 2008-2009 Italian Serie A football season.

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