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An empirical Bayes model for time-varying paired comparisons ratings: Who is the greatest women’s tennis player?

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  • Baker, Rose D.
  • McHale, Ian G.

Abstract

We present a methodology for fitting a time-varying paired comparisons model using an empirical Bayes approach. The model simultaneously avoids two problems that typically arise with paired comparisons data: first, that extreme values of estimated strengths can occur for competitors appearing in and winning a small number of games, producing absurd rankings, and second, that the time-varying strengths ‘balloon’ over time. The empirical Bayes approach automatically shrinks the strength estimates towards the mean, thus avoiding both issues. We present our model and demonstrate its use in the setting of tennis in search of an answer to the question: who is the greatest women’s player of all time. Our results suggest that Steffi Graf is a strong candidate, but, using confidence intervals on the rankings themselves, others cannot be ruled out.

Suggested Citation

  • Baker, Rose D. & McHale, Ian G., 2017. "An empirical Bayes model for time-varying paired comparisons ratings: Who is the greatest women’s tennis player?," European Journal of Operational Research, Elsevier, vol. 258(1), pages 328-333.
    • Handle: RePEc:eee:ejores:v:258:y:2017:i:1:p:328-333
    DOI: 10.1016/j.ejor.2016.08.043
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    References listed on IDEAS

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    1. Baker, Rose D. & McHale, Ian G., 2014. "A dynamic paired comparisons model: Who is the greatest tennis player?," European Journal of Operational Research, Elsevier, vol. 236(2), pages 677-684.
    2. Mark Glickman, 2001. "Dynamic paired comparison models with stochastic variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 673-689.
    3. Rose Baker & Dan Jackson, 2014. "Statistical application of barycentric rational interpolants: an alternative to splines," Computational Statistics, Springer, vol. 29(5), pages 1065-1081, October.
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    1. Alberto Arcagni & Vincenzo Candila & Rosanna Grassi, 2023. "A new model for predicting the winner in tennis based on the eigenvector centrality," Annals of Operations Research, Springer, vol. 325(1), pages 615-632, June.
    2. P. Gorgi & Siem Jan (S.J.) Koopman & R. Lit, 2018. "The analysis and forecasting of ATP tennis matches using a high-dimensional dynamic model," Tinbergen Institute Discussion Papers 18-009/III, Tinbergen Institute.
    3. Collingwood, James A.P. & Wright, Michael & Brooks, Roger J, 2022. "Evaluating the effectiveness of different player rating systems in predicting the results of professional snooker matches," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1025-1035.
    4. Baker, Rose D. & McHale, Ian G., 2018. "Time-varying ratings for international football teams," European Journal of Operational Research, Elsevier, vol. 267(2), pages 659-666.
    5. Santos-Fernandez Edgar & Wu Paul & Mengersen Kerrie L., 2019. "Bayesian statistics meets sports: a comprehensive review," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(4), pages 289-312, December.
    6. Angelini, Giovanni & Candila, Vincenzo & De Angelis, Luca, 2022. "Weighted Elo rating for tennis match predictions," European Journal of Operational Research, Elsevier, vol. 297(1), pages 120-132.

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