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On fairness and diversification in WTA and ATP tennis tournaments generation


Single-elimination (knockout) tournaments are the standard paradigm for both main tennis professional associations, WTA and ATP. Schedules are generated by allocating first seeded and then unseeded players with seeds prevented from encountering each other early in the competition. Besides, the distribution of pairings in the first round between unseeded players and seeds for a yearly season may be strongly unbalanced. This provides often a great disadvantage to some “unlucky” unseeded players in terms of money prizes. Also, a fair distribution of matches during a season would benefit from limiting in first rounds the presence of Head-to-Head (H2H) matches between players that met in the recent past. We propose a tournament generation approach in order to reduce in the first round unlucky pairings and also replays of H2H matches. The approach consists in a clustering optimization problem inducing a consequent draw within each cluster. A Non-Linear Mathematical Programming (NLMP) model is proposed for the clustering problem so as to reach a fair schedule. The solution reached by a commercial NLMP solver on the model is compared to the one reached by a faster hybrid algorithm based on multi-start local search. The approach is successfully tested on historical records from the recent Grand Slams tournaments.

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The very pertinent remarks and suggestions of two anonymous reviewers are gratefully acknowledged. This work has been partially supported by “Ministero dell’Istruzione, dell’Università e della Ricerca” Award “TESUN-83486178370409 finanziamento dipartimenti di eccellenza CAP. 1694 TIT. 232 ART. 6”.

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Correspondence to Federico Della Croce.

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Della Croce, F., Dragotto, G. & Scatamacchia, R. On fairness and diversification in WTA and ATP tennis tournaments generation. Ann Oper Res (2020).

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  • OR in sports
  • Fairness
  • Mixed integer programming
  • Combinatorial optimization