The effects of draw restrictions on knockout tournaments
-
László Csató
Abstract
The paper analyses how draw constraints influence the outcome of a knockout tournament. The research question is inspired by European club football competitions, where the organiser generally imposes an association constraint in the first round of the knockout phase: teams from the same country cannot be drawn against each other. Its effects are explored in both theoretical and simulation models. An association constraint in the first round(s) is found to increase the likelihood of same nation matchups to approximately the same extent in each subsequent round. If the favourite teams are concentrated in some associations, they will have a higher probability to win the tournament under this policy but the increase is less than linear if it is used in more rounds. Our results might explain the recent introduction of the association constraint for both the knockout round play-offs with 16 teams and the Round of 16 in the UEFA Europa League and UEFA Europa Conference League.
-
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Arlegi, R. 2022. “How Can an Elimination Tournament Favor a Weaker Player?” International Transactions in Operational Research 29 (4): 2250–62. https://doi.org/10.1111/itor.12955.Suche in Google Scholar
Arlegi, R., and D. Dimitrov. 2020. “Fair Elimination-type Competitions.” European Journal of Operational Research 287 (2): 528–35. https://doi.org/10.1016/j.ejor.2020.03.025.Suche in Google Scholar
Boczoń, M., and A. J. Wilson. 2018. Goals, Constraints, and Public Assignment: A Field Study of the UEFA Champions League. Technical Report 18/016. University of Pittsburgh, Kenneth P. Dietrich School of Arts and Sciences, Department of Economics. Also available at https://www.econ.pitt.edu/sites/default/files/working_papers/Working%20Paper.18.16.pdf.Suche in Google Scholar
Boczoń, M., and A. J. Wilson. 2022. “Goals, Constraints, and Transparently Fair Assignments: A Field Study of Randomization Design in the UEFA Champions League.” Management Science. in press, https://doi.org/10.1287/mnsc.2022.4528.Suche in Google Scholar
Cea, S., G. Durán, M. Guajardo, D. Sauré, J. Siebert, and G. Zamorano. 2020. “An Analytics Approach to the FIFA Ranking Procedure and the World Cup Final Draw.” Annals of Operations Research 286 (1–2): 119–46. https://doi.org/10.1007/s10479-019-03261-8.Suche in Google Scholar
Csató, L. 2021a. “A Simulation Comparison of Tournament Designs for the World Men’s Handball Championships.” International Transactions in Operational Research 28 (5): 2377–401. https://doi.org/10.1111/itor.12691.Suche in Google Scholar
Csató, L. 2021b. Tournament Design: How Operations Research Can Improve Sports Rules. Palgrave Pivots in Sports Economics. Cham: Palgrave Macmillan.10.1007/978-3-030-59844-0Suche in Google Scholar
Csató, L. 2022a. “Fairer group draw for sports tournaments with restrictions.” Manuscript, https://doi.org/10.48550/arXiv.2109.13785.Suche in Google Scholar
Csató, L. 2022b. “Group Draw with Unknown Qualified Teams: A Lesson from 2022 FIFA World Cup.” International Journal of Sports Science & Coaching. in press, https://doi.org/10.1177/17479541221108799.Suche in Google Scholar
Csató, L. 2022c. “Quantifying Incentive (In)compatibility: A Case Study from Sports.” European Journal of Operational Research 302 (2): 717–26. https://doi.org/10.1016/j.ejor.2022.01.042.Suche in Google Scholar
FIFA. 2022. Draw Procedures. FIFA World Cup Qatar 2022TM. Also available at https://digitalhub.fifa.com/m/2ef762dcf5f577c6/original/Portrait-Master-Template.pdf.Suche in Google Scholar
Goossens, D. R., J. Beliën, and F. C. R. Spieksma. 2012. “Comparing League Formats with Respect to Match Importance in Belgian Football.” Annals of Operations Research 194 (1): 223–40. https://doi.org/10.1007/s10479-010-0764-4.Suche in Google Scholar
Guyon, J. 2014. “Rethinking the FIFA World CupTM Final Draw.” Manuscript, https://doi.org/10.2139/ssrn.2424376.Suche in Google Scholar
Guyon, J. 2015. “Rethinking the FIFA World CupTM Final Draw.” Journal of Quantitative Analysis in Sports 11 (3): 169–82.10.1515/jqas-2014-0030Suche in Google Scholar
Guyon, J. 2022. “Choose Your Opponent”: A New Knockout Design for Hybrid Tournaments.” Journal of Sports Analytics 8 (1): 9–29. https://doi.org/10.3233/jsa-200527.Suche in Google Scholar
Horen, J., and R. Riezman. 1985. “Comparing Draws for Single Elimination Tournaments.” Operations Research 33 (2): 249–62. https://doi.org/10.1287/opre.33.2.249.Suche in Google Scholar
Hwang, F. K. 1982. “New Concepts in Seeding Knockout Tournaments.” The American Mathematical Monthly 89 (4): 235–9. https://doi.org/10.2307/2320220.Suche in Google Scholar
Jones, M. C. 1990. “The World Cup Draw’s Flaws.” The Mathematical Gazette 74 (470): 335–8. https://doi.org/10.2307/3618128.Suche in Google Scholar
Kendall, G., and L. J. A. Lenten. 2017. “When Sports Rules Go Awry.” European Journal of Operational Research 257 (2): 377–94. https://doi.org/10.1016/j.ejor.2016.06.050.Suche in Google Scholar
Kiesl, H. 2013. “Match me if you can. Mathematische Gedanken zur Champions-League-Achtelfinalauslosung.” Mitteilungen der Deutschen Mathematiker-Vereinigung 21 (2): 84–8. https://doi.org/10.1515/dmvm-2013-0034.Suche in Google Scholar
Klößner, S., and M. Becker. 2013. “Odd Odds: The UEFA Champions League Round of 16 Draw.” Journal of Quantitative Analysis in Sports 9 (3): 249–70.10.1515/jqas-2013-0016Suche in Google Scholar
Laliena, P., and F. J. López. 2019. “Fair Draws for Group Rounds in Sport Tournaments.” International Transactions in Operational Research 26 (2): 439–57. https://doi.org/10.1111/itor.12565.Suche in Google Scholar
Lasek, J., and M. Gagolewski. 2018. “The Efficacy of League Formats in Ranking Teams.” Statistical Modelling 18 (5–6): 411–35. https://doi.org/10.1177/1471082x18798426.Suche in Google Scholar
Lenten, L. J. A., and G. Kendall. 2021. “Scholarly Sports: Influence of Social Science Academe on Sports Rules and Policy.” Journal of the Operational Research Society. in press, https://doi.org/10.1080/01605682.2021.2000896.Suche in Google Scholar
Rathgeber, A., and H. Rathgeber. 2007. “Why Germany Was Supposed to Be Drawn in the Group of Death and Why it Escaped.” Chance 20 (2): 22–4. https://doi.org/10.1080/09332480.2007.10722842.Suche in Google Scholar
Scarf, P., M. M. Yusof, and M. Bilbao. 2009. “A Numerical Study of Designs for Sporting Contests.” European Journal of Operational Research 198 (1): 190–8. https://doi.org/10.1016/j.ejor.2008.07.029.Suche in Google Scholar
Schwenk, A. J. 2000. “What Is the Correct Way to Seed a Knockout Tournament?” The American Mathematical Monthly 107 (2): 140–50. https://doi.org/10.1080/00029890.2000.12005171.Suche in Google Scholar
UEFA. 2015. Regulations of the UEFA Champions League 2015-18 Cycle. 2015/16 Season. Also available at http://web-old.archive.org/web/20201018192502/https://www.uefa.com/MultimediaFiles/Download/Regulations/uefaorg/Regulations/02/23/57/51/2235751_DOWNLOAD.pdf.Suche in Google Scholar
UEFA. 2019. 2019/20. UEFA Club Competitions Revenue Distribution System. Also available at https://www.uefa.com/insideuefa/stakeholders/clubs/news/newsid=2616265.html.Suche in Google Scholar
UEFA. 2020a. FIFA World Cup 2022 Qualifying Draw Procedure. Also available at https://www.uefa.com/MultimediaFiles/Download/competitions/WorldCup/02/64/22/19/2642219_DOWNLOAD.pdf.Suche in Google Scholar
UEFA. 2020b. Regulations of the UEFA Europa League 2018-21 Cycle. 2020/21 Season. Also available at http://web.archive.org/web/20210517095618/https://documents.uefa.com/r/Regulations-of-the-UEFA-Europa-League-2020/21-Online.Suche in Google Scholar
UEFA. 2021a. Regulations of the UEFA Europa Conference League 2021-24 Cycle. 2021/22 Season. Also available at https://web.archive.org/web/20220208043024/https://documents.uefa.com/r/Regulations-of-the-UEFA-Europa-Conference-League-2021/22-Online.Suche in Google Scholar
UEFA. 2021b. Regulations of the UEFA Europa League 2021-24 Cycle. 2021/22 Season. Also available at https://web.archive.org/web/20220207235133/https://documents.uefa.com/r/Regulations-of-the-UEFA-Europa-League-2021/22-Online.Suche in Google Scholar
Wright, M. 2014. “OR Analysis of Sporting Rules – A Survey.” European Journal of Operational Research 232 (1): 1–8. https://doi.org/10.1016/j.ejor.2013.03.043.Suche in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Research Articles
- Modelling Australian Rules Football as spatial systems with pairwise comparisons
- The effects of draw restrictions on knockout tournaments
- ‘Form is temporary, class is permanent’: identifying a longer-term hot hand in golf
- Bayesian modelling of elite sporting performance with large databases
Artikel in diesem Heft
- Frontmatter
- Research Articles
- Modelling Australian Rules Football as spatial systems with pairwise comparisons
- The effects of draw restrictions on knockout tournaments
- ‘Form is temporary, class is permanent’: identifying a longer-term hot hand in golf
- Bayesian modelling of elite sporting performance with large databases
