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A hidden benefit of incomplete round-robin tournaments: Encouraging offensive play

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  • L'aszl'o Csat'o

Abstract

This paper aims to explore the impact of tournament design on the incentives of the contestants. We develop a simulation framework to quantify the potential gain and loss from attacking based on changes in the probability of reaching the critical ranking thresholds. The model is applied to investigate the 2024/25 UEFA Champions League reform. The novel incomplete round-robin league phase is found to create more powerful incentives for offensive play than the previous group stage, with an average increase of 119\% (58\%) regarding the first (second) prize. Our study provides the first demonstration that the tournament format itself can strongly influence team behaviour in sports.

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  • L'aszl'o Csat'o, 2025. "A hidden benefit of incomplete round-robin tournaments: Encouraging offensive play," Papers 2509.13141, arXiv.org.
  • Handle: RePEc:arx:papers:2509.13141
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    References listed on IDEAS

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    1. Devriesere, Karel & Csató, László & Goossens, Dries, 2025. "Tournament design: A review from an operational research perspective," European Journal of Operational Research, Elsevier, vol. 324(1), pages 1-21.
    2. László Csató, 2020. "The UEFA Champions League seeding is not strategy-proof since the 2015/16 season," Annals of Operations Research, Springer, vol. 292(1), pages 161-169, September.
    3. Lee Yoong Hon & Rasyad A. Parinduri, 2016. "Does the Three-Point Rule Make Soccer More Exciting? Evidence From a Regression Discontinuity Design," Journal of Sports Economics, , vol. 17(4), pages 377-395, May.
    4. Giancarlo Moschini, 2010. "Incentives And Outcomes In A Strategic Setting: The 3‐Points‐For‐A‐Win System In Soccer," Economic Inquiry, Western Economic Association International, vol. 48(1), pages 65-79, January.
    5. Vincenzo Alfano & Lorenzo Cicatiello & Giuseppe Lucio Gaeta & Michele Gallo & Francesca Rotondo, 2021. "Three is a Magic Number: Evidence on the Effects of the Application of the Three-Point Rule in Italy’s Serie A," Journal of Sports Economics, , vol. 22(3), pages 329-356, April.
    6. Chater, Mario & Arrondel, Luc & Gayant, Jean-Pascal & Laslier, Jean-François, 2021. "Fixing match-fixing: Optimal schedules to promote competitiveness," European Journal of Operational Research, Elsevier, vol. 294(2), pages 673-683.
    7. Peter-J. Jost, 2021. "“The ball is round, the game lasts 90 minutes, everything else is pure theoryâ€," Journal of Sports Economics, , vol. 22(1), pages 27-74, January.
    8. László Csató, 2024. "Club coefficients in the UEFA Champions League: Time for shift to an Elo-based formula," International Journal of Performance Analysis in Sport, Taylor & Francis Journals, vol. 24(2), pages 119-134, March.
    9. Li, Miao & Van Bulck, David & Goossens, Dries, 2025. "Beyond leagues: A single incomplete round robin tournament for multi-league sports timetabling," European Journal of Operational Research, Elsevier, vol. 323(1), pages 208-223.
    10. M. J. Maher, 1982. "Modelling association football scores," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 36(3), pages 109-118, September.
    11. Sauer Pascal & Cseh Ágnes & Lenzner Pascal, 2024. "Improving ranking quality and fairness in Swiss-system chess tournaments," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 20(2), pages 127-146, June.
    12. László Csató, 2013. "Ranking by pairwise comparisons for Swiss-system tournaments," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 783-803, December.
    13. Krumer, Alex & Lechner, Michael, 2017. "First in first win: Evidence on schedule effects in round-robin tournaments in mega-events," European Economic Review, Elsevier, vol. 100(C), pages 412-427.
    14. Stefan Szymanski, 2010. "The Economic Design of Sporting Contests," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 1, pages 1-78, Palgrave Macmillan.
    15. Garicano, Luis & Palacios-Huerta, Ignacio, 2005. "Sabotage in Tournaments: Making the Beautiful Game a Bit Less Beautiful," CEPR Discussion Papers 5231, C.E.P.R. Discussion Papers.
    16. Dagaev Dmitry & Rudyak Vladimir Yu., 2019. "Seeding the UEFA Champions League participants: evaluation of the reforms," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(2), pages 129-140, June.
    17. András Gyimesi, 2024. "Competitive Balance in the Post-2024 Champions League and the European Super League: A Simulation Study," Journal of Sports Economics, , vol. 25(6), pages 707-734, August.
    18. Ralf Dewenter & Julian Emami Namini, 2013. "How to Make Soccer More Attractive? Rewards for a Victory, the Teams' Offensiveness, and the Home Bias," Journal of Sports Economics, , vol. 14(1), pages 65-86, February.
    19. Ehrenberg, Ronald G & Bognanno, Michael L, 1990. "Do Tournaments Have Incentive Effects?," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1307-1324, December.
    20. László Csató, 2017. "On the ranking of a Swiss system chess team tournament," Annals of Operations Research, Springer, vol. 254(1), pages 17-36, July.
    21. Aleksei Y. Kondratev & Egor Ianovski & Alexander S. Nesterov, 2024. "How Should We Score Athletes and Candidates: Geometric Scoring Rules," Operations Research, INFORMS, vol. 72(6), pages 2507-2525, November.
    22. Alexander Dilger & Hannah Geyer, 2009. "Are Three Points for a Win Really Better Than Two?," Journal of Sports Economics, , vol. 10(3), pages 305-318, June.
    23. José Correia Guedes & Fernando S. Machado, 2002. "Changing rewards in contests: Has the three-point rule brought more offense to soccer?," Empirical Economics, Springer, vol. 27(4), pages 607-630.
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