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Modeling outcomes of soccer matches. (English) Zbl 07024628
Mach. Learn. 108, No. 1, 77-95 (2019); correction ibid. 108, No. 2, 377-378 (2019).
Summary: We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalized version of it, while the posterior densities of the parameters of the hierarchical Poisson log-linear model are approximated using integrated nested Laplace approximations. The prediction performance of the various modeling approaches is assessed using a novel, context-specific framework for temporal validation that is found to deliver accurate estimates of the test error. The direct modeling of outcomes via the various Bradley-Terry extensions and the modeling of match scores using the hierarchical Poisson log-linear model demonstrate similar behavior in terms of predictive performance.

68T05 Learning and adaptive systems in artificial intelligence
gamair; R-INLA; LBFGS-B
Full Text: DOI
[1] Agresti, A. (2015). Foundations of linear and generalized linear models. Hoboken: Wiley. · Zbl 1309.62001
[2] Baio, G.; Blangiardo, M., Bayesian hierarchical model for the prediction of football results, Journal of Applied Statistics, 37, 253-264, (2010)
[3] Berrar, D., Dubitzky, W., Davis, J., & Lopes, P. (2017). Machine learning for Soccer. Retrieved from osf.io/ftuva.
[4] Bradley, RA; Terry, ME, Rank analysis of incomplete block deisngs: I. The method of paired comparisons, Biometrika, 39, 502-537, (1952)
[5] Byrd, RH; Lu, P.; Nocedal, J.; Zhu, C., A limited memory algorithm for bound constrained optimization, SIAM Journal of Scientific Computing, 16, 1190, (1995) · Zbl 0836.65080
[6] Cattelan, M.; Varin, C.; Firth, D., Dynamic BradleyTerry modelling of sports tournaments, Journal of the Royal Statistical Society: Series C (Applied Statistics), 62, 135-150, (2013)
[7] Davidson, RR, On extending the Bradley-Terry model to accommodate ties in paired comparison experiments, Journal of the American Stistical Association, 65, 317, (1970)
[8] DerSimonian, R.; Laird, N., Meta-analysis in clinical trials, Controlled Clinical Trials, 7, 177, (1986)
[9] Dietterich, T. G. (2000). Ensemble methods in machine learning (pp. 1-15). Berlin: Springer.
[10] Dixon, MJ; Coles, SG, Modelling association football scores and inefficiencies in the football betting market, Applied Statistics, 46, 265, (1997)
[11] Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. New Delhi: SIAM. · Zbl 0496.62036
[12] Epstein, ES, A scoring system for probability forecasts of ranked categories, Journal of Applied Meteorology, 8, 985-987, (1969)
[13] Firth, D. (2005). Bradley-Terry Models in R. Journal of Statistical Software, 12(1)
[14] Gneiting, T.; Raftery, AE, Strictly proper scoring rules, prediction, and estimation, Journal of the American Statistical Association, 102, 359-378, (2007) · Zbl 1284.62093
[15] Golub, GH; Heath, M.; Wahba, G., Generalized cross-validation as a method for choosing good ridge parameter, Technometrics, 21, 215, (1979) · Zbl 0461.62059
[16] Karlis, D.; Ntzoufras, I., Analysis of sports data by using bivariate Poisson models, Journal of the Royal Statistical Society D, 52, 381-393, (2003)
[17] Király, F.J., & Qian, Z. (2017). Modelling competitive sports: Bradley-Terry-Élo models for supervised and on-line learning of paired competition outcomes (pp. 1-53). arXiv:1701.08055.
[18] Lindgren, F.; Rue, H., Bayesian spatial modelling with r-inla, Journal of Statistical Software, Articles, 63, 1-25, (2015)
[19] Maher, MJ, Modelling association football scores, Statistica Neerlandica, 36, 109-118, (1982)
[20] Murphy, AH, On the ranked probability score, Journal of Applied Meteorology, 8, 988-989, (1969)
[21] Rue, H.; Martino, S.; Chopin, N., Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations, Journal of the Royal Statistical Society B, 71, 319-392, (2009) · Zbl 1248.62156
[22] Wahba, G. (1990). Spline models for observational data. Society for Industrial and Applied Mathematics. · Zbl 0813.62001
[23] Wikipedia (2018). UEFA coefficient — Wikipedia, the free encyclopedia. http://en.wikipedia.org/w/index.php?title=UEFA%20coefficient&oldid=819064849. Accessed February 09 2018.
[24] Wood, SN, Thin plate regression splines, Journal of the Royal Statistical Society. Series B: Statistical Methodology, 65, 95, (2003) · Zbl 1063.62059
[25] Wood, S. N. (2006). Generalized additive models: An introduction with R. Boca Raton: CRC Press. · Zbl 1087.62082
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