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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Adler, I., Cao, Y., Karp, R., Pekaz, E., & Ross, S. (2017). Random knockout tournaments. Operations Research, 65(6), 1589–1596.
Bairner, R. (May 2018). Wimbledon announces 7.5% prize fund increase. Retrieved May 1, 2018 from http://www.wtatennis.com/news/wimbledon-announces-75-prize-fund-increase.
Dagaev, D., & Suzdaltsev, A. (2018). Competitive intensity and quality maximizing seedings in knock-out tournaments. Journal of Combinatorial Optimization, 35(1), 170–188.
Della Croce, F., Tadei, R., & Asioli, P. (1999). Scheduling a round robin tennis tournament under courts and players availability constraints. Annals of Operations Research, 92, 349–362.
Farmer, A., Smith, J. S., & Miller, L. T. (2007). Scheduling umpire crews for professional tennis tournaments. Interfaces, 37(2), 187–196.
Forrest, D., & Simmons, R. (2002). Outcome uncertainty and attendance demand in sport: The case of English soccer. Journal of the Royal Statistical Society: Series D (The Statistician), 51(2), 229–241.
Gatto, L. (April 2018). Roger Federer thinks prize money should be increased in tennis. Retrieved April 28, 2018 from https://www.tennisworldusa.org/tennis/news/Roger_Federer/54206/roger-federer-thinks-prize-money-should-be-increased-in-tennis/.
Glickman, M. (2008). Bayesian locally optimal design of knockout tournaments. Journal of Statistical Planning and Inference, 138, 2117–2127.
Hennessy, J., & Glickman, M. (2016). Bayesian optimal design of fixed knockout tournament brackets. Journal of Quantitative Analysis in Sports, 12(1), 1–15.
Horen, J., & Riezman, R. (1985). Comparing draws for single elimination tournaments. Operations Research, 33(2), 249–262.
Karpov, A. (2016). A new knockout tournament seeding method and its axiomatic justification. Operations Research Letters, 44(6), 706–711.
Karpov, A. (2018). Generalized knockout tournament seedings. International Journal of Computer Science in Sport, 17(2), 113–127.
Kendall, G., Knust, S., Ribeiro, C. C., & Urrutia, S. (2010). Scheduling in sports: An annotated bibliography. Computers & Operations Research, 37(1), 1–19.
Kuo, C.-C., Glover, F., & Dhir, K. S. (1993). Analyzing and modeling the maximum diversity problem by zero-one programming. Decision Sciences, 24(6), 1171–1185.
Maher, E. (July 2017). 2017 US Open prize money to top USD 50 million. Retrieved July 28, 2017 from http://www.usopen.org/en_US/news/articles/2017-07-18/2017_us_open_prize_money_to_top_50_million.html.
Newman, P. (January 2018). Novak Djokovic calls to increase prize money share met with mixed response from tour players. Retrieved January 15, 2018 from https://www.independent.co.uk/sport/tennis/novak-djokovic-australian-open-greater-prize-money-share-player-union-mixed-response-a8160021.html.
Reid, M., Morgan, S., Churchill, T., & Bane, M. K. (2014). Rankings in professional men’s tennis: A rich but underutilized source of information. Journal of Sports Sciences, 32(10), 986–992. pMID: 24506799.
Sackmann, J. (2020). Tennis ATP-database. https://github.com/JeffSackmann/tennis_atp.
Schwenk, A. (2000). What is the correct way to seed a knockout tournament. American Mathematical Monthly, 107(2), 140–150.
Telegraph, S. (June 2018). French open 2018 prize money: How much will Roland Garros champions win this year? Retrieved June 10, 2018 from https://www.telegraph.co.uk/tennis/2018/06/09/french-open-2018-prize-money-much-will-roland-garros-champions/.
Williams, V. V. (2010). Fixing a tournament. In Proceedings of the 24th AAAI conference on artificial intelligence (AAAI) (Vol. 1, pp. 895–900). AAAI.
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”.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Della Croce, F., Dragotto, G. & Scatamacchia, R. On fairness and diversification in WTA and ATP tennis tournaments generation. Ann Oper Res (2020). https://doi.org/10.1007/s10479-020-03517-8
- OR in sports
- Mixed integer programming
- Combinatorial optimization