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Bayesian optimal design of fixed knockout tournament brackets

Author

Listed:
  • Hennessy Jonathan

    (Houston Rockets, 1510 Polk Street, Houston, TX 77002, USA)

  • Glickman Mark

    (Department of Statistics, Harvard University, Cambridge, MA, USA)

Abstract

We present a methodology for finding globally optimal knockout tournament designs when partial information is known about the strengths of the players. Our approach involves maximizing an expected utility through a Bayesian optimal design framework. Given the prohibitive computational barriers connected with direct computation, we compute a Monte Carlo estimate of the expected utility for a fixed tournament bracket, and optimize the expected utility through simulated annealing. We demonstrate our method by optimizing the probability that the best player wins the tournament. We compare our approach to other knockout tournament designs, including brackets following the standard seeding. We also demonstrate how our approach can be applied to a variety of other utility functions, including whether the best two players meet in the final, the consistency between the number of wins and the player strengths, and whether the players are matched up according to the standard seeding.

Suggested Citation

  • Hennessy Jonathan & Glickman Mark, 2016. "Bayesian optimal design of fixed knockout tournament brackets," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(1), pages 1-15, March.
    • Handle: RePEc:bpj:jqsprt:v:12:y:2016:i:1:p:1-15:n:2
    DOI: 10.1515/jqas-2015-0033
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    References listed on IDEAS

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    1. Frederick Mosteller, 1951. "Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations," Psychometrika, Springer;The Psychometric Society, vol. 16(1), pages 3-9, March.
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    Cited by:

    1. Federico Della Croce & Gabriele Dragotto & Rosario Scatamacchia, 2022. "On fairness and diversification in WTA and ATP tennis tournaments generation," Annals of Operations Research, Springer, vol. 316(2), pages 1107-1119, September.

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