Stochastic dynamic Thurstone-Mosteller models for sports tournaments
Cattelan, Manuela, Varin, Cristiano and Firth, David (2010) Stochastic dynamic Thurstone-Mosteller models for sports tournaments. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
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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.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Sports tournaments -- Mathematical models|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||25|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||Albert, J., Bennett, J., Cochran, J. J. eds. (2005) Anthology of Statistics in Sports, ASASIAM Series on Statistics and Applied Probability, SIAM, Philadelphia, ASA, Alexandria, VA, 2005. Barry, D. and Hartigan, J. A. (1993) Choice models for predicting divisional winners in major league baseball. Journal of the American Statistical Association 88, 766-774. Bradley, R. A. and Terry, M. E. (1952) Rank analysis of incomplete block designs I. The method of paired comparisons. Biometrika 39, 324-345. Brier, G. W. (1950) Verification of forecasts expressed in terms of probabilities. Monthly Weather Review 78, 1-3. Clarke, S. R. and Norman, J. M. (1995) Home ground advantage of individual clubs in English soccer. The Statistician 44, 509-521. Crowder, M., Dixon, M., Ledford, A., Robinson, M. (2002) Dynamic modelling and prediction of English football league matches for betting. The Statistician 51, 157-168. Dixon, M. J. and Coles, S. G. (1997) Modelling association football scores and inefficiencies in the football betting market. Applied Statistics 46, 265-280. Durbin, J. and Koopman, S. J. (1997) Monte Carlo maximum likelihood estimation for non-Gaussian state space models. Biometrika 84, 669-684. Fahrmeir, L. and Tutz, G. (1994) Dynamic stochastic models for time-dependent ordered paired comparison systems. Journal of the American Statistical Association 89, 1438-1449. Firth, D. and de Menezes, R. X. (2004) Quasi-variances. Biometrika 91, 65-80. Geweke, J. (1992) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, in Bayesian Statistics, eds. Bernardo J. M., Berger J., Dawid A. P. and Smith, A. F. M. Oxford University Press, Oxford. Glickman, M. E. (1999) Parameter estimation in large dynamic paired comparison experiments. Applied Statistics 48, 377-394. Glickman, M. E. and Stern, H. S. (1998) A state-space model for national football league scores. Journal of the American Statistical Association 93, 25-35. Goddard, J. and Asimakopoulos I. (2004) Forecasting football results and the efficiency of fixed-odds betting. Journal of Forecasting 23, 51-66. Harville, D. A. (1980) Predictions for national football league games via linear-model methodology. Journal of the American Statistical Association 75, 516-524. Harville, D. A. (2003) The selection or seeding of college basketball or football teams for postseason competition. Journal of the American Statistical Association 98, 17-27. Harville, D. A. and Smith, M. H. (1994) The home-court advantage: how large is it, and does it vary from team to team? American Statistician 48, 22-28. Heidelberger, P. and Welch, P. D. (1983) Simulation run length control in the presence of an initial transient. Operations Research 31, 1109-1144. Karlis, D. and Ntzoufras, I. (2003) Analysis of sports data by using bivariate Poisson models. Statistician 52, 381-393. Knorr-Held, L. (1997) Hierarchical Modelling of Longitudinal Data; Applications of Markov Chain Monte Carlo. Munich: Utz. Knorr-Held, L. (2000) Dynamic rating of sports teams. The Statistician 49, 261-276. Koning, R. H. (2000) Balance in competitions in Dutch soccer. The Statistician 49, 419-431. Kuk, A. Y. C. (1995) Modelling paired comparison data with large numbers of draws and large variability of draw percentages among players. The Statistician 44, 523-528. Maher, M. J. (1982) Modelling association football scores. Statistica Neerlandica 36, 109-118. Masarotto, G. and Varin C. (2010) Gaussian dependence models for non-Gaussian marginal regression. Submitted. McHale, I. and Scarf, P. (2007) Modelling soccer matches using bivariate discrete distributions with general dependence structure. Statistica Neerlandica 61, 432-445. Mosteller, F. (1951) Remarks on the method of paired comparisons. I. The least squares solution assuming equal standard deviations and equal correlations. Psychometrika 16, 3-9. Plummer, M., Best, N., Cowles, K., Vines, K. (2009) coda: Output analysis and diagnostic for MCMC. R package. Rue, H. and Salvesen O. (2000) Prediction and retrospective analysis of soccer matches in a league. The Statistician 49, 399-418. Thurstone, L. L. (1927) A law of comparative judgement. Psychological Review 34, 273-286. Train, K. E. (2003) Discrete Choice Methods with Simulation. Cambridge University Press, Cambridge.|
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