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A dynamic paired comparisons model: Who is the greatest tennis player?

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  • Baker, Rose D.
  • McHale, Ian G.

Abstract

We present a methodology for fitting time-varying paired comparisons models in which the parameters are allowed to vary deterministically, as opposed to stochastically, with time. Our dynamic paired comparisons model is based on a new closed-form for Stern’s continuum of paired comparisons models which include the Bradley–Terry model and the Thurstone–Mosteller model. The dynamic element of our model is facilitated by utilising barycentric rational interpolants BRIs. An incidental result of our work is to show that BRIs often provide a better fit to data than the obvious alternative of spline interpolation. We use our model to shed light on the debate of who is the greatest tennis player of the Open Era of men’s professional tennis since 1968. Constructing a single rankings list from our model is not trivial as there are many alternative metrics that could be used to identify which player was the best ever. We present three alternative rankings lists derived from our model. In general our rankings lists largely agree with the rankings list based on number of Grand Slam titles won, which, to some extent, validates our choice of metrics. So who is the greatest tennis player of the Open Era? Roger Federer seems like the most likely candidate, with Bjorn Borg and Jimmy Connors close behind.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:236:y:2014:i:2:p:677-684
    DOI: 10.1016/j.ejor.2013.12.028
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    References listed on IDEAS

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    1. McHale, Ian & Morton, Alex, 2011. "A Bradley-Terry type model for forecasting tennis match results," International Journal of Forecasting, Elsevier, vol. 27(2), pages 619-630, April.
    2. Mark E. Glickman, 1999. "Parameter Estimation in Large Dynamic Paired Comparison Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 377-394.
    3. Stern, Hal, 1992. "Are all linear paired comparison models empirically equivalent?," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 103-117, February.
    4. McHale, Ian & Morton, Alex, 2011. "A Bradley-Terry type model for forecasting tennis match results," International Journal of Forecasting, Elsevier, vol. 27(2), pages 619-630.
    5. Sitarz, Sebastian, 2012. "Mean value and volume-based sensitivity analysis for Olympic rankings," European Journal of Operational Research, Elsevier, vol. 216(1), pages 232-238.
    6. R. L. Plackett, 1975. "The Analysis of Permutations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(2), pages 193-202, June.
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    Cited by:

    1. Kovalchik, Stephanie, 2020. "Extension of the Elo rating system to margin of victory," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1329-1341.
    2. 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.
    3. repec:awi:wpaper:0600 is not listed on IDEAS
    4. 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.
    5. Araki, Kenji & Hirose, Yoshihiro & Komaki, Fumiyasu, 2019. "Paired comparison models with age effects modeled as piecewise quadratic splines," International Journal of Forecasting, Elsevier, vol. 35(2), pages 733-740.
    6. Blaž Krese & Erik Štrumbelj, 2021. "A Bayesian approach to time-varying latent strengths in pairwise comparisons," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-17, May.
    7. Christophe Ley & Yves Dominicy, 2017. "Mutual Point-winning Probabilities (MPW): a New Performance Measure for Table Tennis," Working Papers ECARES ECARES 2017-23, ULB -- Universite Libre de Bruxelles.
    8. 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.
    9. S. S. Dabadghao & B. Vaziri, 2022. "The predictive power of popular sports ranking methods in the NFL, NBA, and NHL," Operational Research, Springer, vol. 22(3), pages 2767-2783, July.
    10. Éva Orbán-Mihálykó & Csaba Mihálykó & László Koltay, 2019. "A generalization of the Thurstone method for multiple choice and incomplete paired comparisons," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 133-159, March.
    11. 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.

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