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


  • Wiper, Michael Peter
  • Forrest, David
  • Corona, Francisco
  • Tena Horrillo, Juan de Dios


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.

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  • Wiper, Michael Peter & Forrest, David & Corona, Francisco & Tena Horrillo, Juan de Dios, 2017. "Evaluating significant effects from alternative seeding systems : a Bayesian approach, with an application to the UEFA Champions League," DES - Working Papers. Statistics and Econometrics. WS 24521, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:24521

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    References listed on IDEAS

    1. Geenens, Gery, 2014. "On the decisiveness of a game in a tournament," European Journal of Operational Research, Elsevier, vol. 232(1), pages 156-168.
    2. P. A. Scarf & M. M. Yusof, 2011. "A numerical study of tournament structure and seeding policy for the soccer World Cup Finals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 43-57, February.
    3. Koning, Ruud H. & Koolhaas, Michael & Renes, Gusta & Ridder, Geert, 2003. "A simulation model for football championships," European Journal of Operational Research, Elsevier, vol. 148(2), pages 268-276, July.
    4. Corona Francisco & Wiper Michael Peter & Horrillo Juan de Dios Tena, 2017. "On the importance of the probabilistic model in identifying the most decisive games in a tournament," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 13(1), pages 11-23, March.
    5. Dmitry Dagaev & Alex Suzdaltsev, 2015. "Seeding, Competitive Intensity and Quality in Knock-Out Tournaments," HSE Working papers WP BRP 91/EC/2015, National Research University Higher School of Economics.
    6. Martin, Andrew D. & Quinn, Kevin M. & Park, Jong Hee, 2011. "MCMCpack: Markov Chain Monte Carlo in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i09).
    7. Wright, Mike, 2014. "OR analysis of sporting rules – A survey," European Journal of Operational Research, Elsevier, vol. 232(1), pages 1-8.
    8. Goddard, John, 2005. "Regression models for forecasting goals and match results in association football," International Journal of Forecasting, Elsevier, vol. 21(2), pages 331-340.
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