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Competitive intensity and quality maximizing seedings in knock-out tournaments

Author

Listed:
  • Dmitry Dagaev

    (National Research University Higher School of Economics)

  • Alex Suzdaltsev

    (Stanford Graduate School of Business)

Abstract

Before a knock-out tournament starts, the participants are assigned to positions in the tournament bracket through a process known as seeding. There are many ways to seed a tournament. In this paper, we solve a discrete optimization problem of finding a seeding that maximizes spectator interest in a tournament when spectators are interested in matches with high competitive intensity (i.e., matches that involve teams comparable in strength) and high quality (i.e., matches that involve strong teams). We find a solution to the problem under two assumptions: the objective function is linear in quality and competitive intensity and a stronger team beats a weaker one with sufficiently high probability. Depending on parameters, only two special classes of seedings can be optimal. While one of the classes includes a seeding that is often used in practice, the seedings in the other class are very different. When we relax the assumption of linearity, we find that these classes of seedings are in fact optimal in a sizable number of cases. In contrast to existing literature on optimal seedings, our results are valid for an arbitrarily large number of participants in a tournament.

Suggested Citation

  • Dmitry Dagaev & Alex Suzdaltsev, 2018. "Competitive intensity and quality maximizing seedings in knock-out tournaments," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 170-188, January.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:1:d:10.1007_s10878-017-0164-7
    DOI: 10.1007/s10878-017-0164-7
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    References listed on IDEAS

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    Cited by:

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    3. Arlegi, Ritxar & Dimitrov, Dinko, 2020. "Fair elimination-type competitions," European Journal of Operational Research, Elsevier, vol. 287(2), pages 528-535.
    4. Lunander Anders & Karlsson Niklas, 2023. "Choosing opponents in skiing sprint elimination tournaments," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 19(3), pages 205-221, September.
    5. Csató, László, 2023. "How to avoid uncompetitive games? The importance of tie-breaking rules," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1260-1269.
    6. Chen Cohen & Ishay Rabi & Aner Sela, 2023. "Optimal seedings in interdependent contests," Annals of Operations Research, Springer, vol. 328(2), pages 1263-1285, September.
    7. 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.
    8. Karlsson, Niklas & Lunander, Anders, 2020. "Choosing Opponents in Skiing Sprint Elimination Tournaments," Working Papers 2020:6, Örebro University, School of Business, revised 01 Sep 2020.

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