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Probabilistic Transitivity in Sports

Author

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  • Tiwisina, Johannes

    (Center for Mathematical Economics, Bielefeld University)

  • Külpmann, Philipp

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We seek to find the statistical model that most accurately describes empirically observed results in sports. The idea of a transitive relation concerning the team strengths is implemented by imposing a set of constraints on the outcome probabilities. We theoretically investigate the resulting optimization problem and draw comparisons to similar problems from the existing literature including the linear ordering problem and the isotonic regression problem. Our optimization problem turns out to be very complicated to solve. We propose a branch and bound algorithm for an exact solution and for larger sets of teams a heuristic method for quickly finding a „good“ solution. Finally we apply the described methods to panel data from soccer, American football and tennis and also use our framework to compare the performance of empirically applied ranking schemes.

Suggested Citation

  • Tiwisina, Johannes & Külpmann, Philipp, 2016. "Probabilistic Transitivity in Sports," Center for Mathematical Economics Working Papers 520, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:520
    as

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    File URL: https://pub.uni-bielefeld.de/download/2901643/2902675
    File Function: First Version, 2014
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    References listed on IDEAS

    as
    1. Lim, Johan & Wang, Xinlei & Choi, Wanseok, 2009. "Maximum likelihood estimation of ordered multinomial probabilities by geometric programming," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 889-893, February.
    2. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    stochastic transitivity; trinomial; geometric optimization; ranking; branch and bound; linear ordering problem; elo; tabu search; football; soccer; tennis; bundesliga; nfl; atp;
    All these keywords.

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