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Licensed Unlicensed Requires Authentication Published by De Gruyter January 17, 2023

A peculiar phenomenon and its potential explanation in the ATP tennis tour finals for singles

  • Itamar Lerner ORCID logo EMAIL logo

Abstract

The ATP finals is the concluding tournament of the tennis season since its initiation over 50 years ago. It features the 8 best players of that year and is often considered to be the most prestigious event in the sport other than the 4 grand slams. Unlike any other professional tennis tournament, it includes a round-robin stage where all players in a group compete against each other, making it a unique testbed for examining performance under forgiving conditions, where losing does not immediately result in elimination. Analysis of the distribution of final group standings in the ATP Finals for singles from 1972 to 2021 reveals a surprising pattern, where one of the possible and seemingly likely outcomes almost never materializes. The present study uses a model-free, optimization approach to account for this distinctive phenomenon by calculating what match winning probabilities between players in a group can lead to the observed distribution. Results show that the only way to explain the empirical findings is through a “paradoxical” balance of power where the best player in a group shows a vulnerability against the weakest player. We discuss the possible mechanisms underlying this result and their implications for match prediction, bettors, and tournament organization.


Corresponding author: Itamar Lerner, Department of Psychology, The University of Texas at San Antonio, San Antonio, TX, 78249-1644, USA, E-mail: .

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Abdi, H., and L. J. Williams. 2010. “Principal Component Analysis.” Wiley Interdisciplinary Reviews: Computational Statistics 2 (4): 433–59. https://doi.org/10.1002/wics.101.Search in Google Scholar

Bozóki, S., L. Csató, and J. Temesi. 2016. “An Application of Incomplete Pairwise Comparison Matrices for Ranking Top Tennis Players.” European Journal of Operational Research 248 (1): 211–8. https://doi.org/10.1016/j.ejor.2015.06.069.Search in Google Scholar

Gallagher, S. K., K. Frisoli, and A. Luby. 2021. “Opening up the Court: Analyzing Player Performance across Tennis Grand Slams.” Journal of Quantitative Analysis in Sports 17 (4): 255–71. https://doi.org/10.1515/jqas-2019-0015.Search in Google Scholar

Holmes, B., I. G. McHale, and K. Żychaluk. 2022. “A Markov Chain Model for Forecasting Results of Mixed Martial Arts Contests.” International Journal of Forecasting. https://doi.org/10.1016/j.ijforecast.2022.01.007.Search in Google Scholar

Ingram, M. 2019. “A Point-Based Bayesian Hierarchical Model to Predict the Outcome of Tennis Matches.” Journal of Quantitative Analysis in Sports 15 (4): 313–25. https://doi.org/10.1515/jqas-2018-0008.Search in Google Scholar

Irons, D. J., S. Buckley, and T. Paulden. 2014. “Developing an Improved Tennis Ranking System.” Journal of Quantitative Analysis in Sports 10 (2): 109–18. https://doi.org/10.1515/jqas-2013-0101.Search in Google Scholar

Klaassen, F. J., and J. R. Magnus. 2003. “Forecasting the Winner of a Tennis Match.” European Journal of Operational Research 148 (2): 257–67. https://doi.org/10.1016/s0377-2217(02)00682-3.Search in Google Scholar

Kodinariya, T. M., and P. R. Makwana. 2013. “Review on Determining Number of Cluster in K-Means Clustering.” International Journal of Advanced Research in Computer Science and Management Studies 1 (6): 90–5.Search in Google Scholar

Kovalchik, S. A. 2016. “Searching for the GOAT of Tennis Win Prediction.” Journal of Quantitative Analysis in Sports 12 (3): 127–38. https://doi.org/10.1515/jqas-2015-0059.Search in Google Scholar

Kullback, S., and R. A. Leibler. 1951. “On Information and Sufficiency.” The Annals of Mathematical Statistics 22 (1): 79–86. https://doi.org/10.1214/aoms/1177729694.Search in Google Scholar

Larson, A., and A. Smith. 2018. “Sensors and Data Retention in Grand Slam Tennis.” In Proceedings of the 2018 IEEE Sensors Applications Symposium (SAS), 1–6. Seoul.10.1109/SAS.2018.8336712Search in Google Scholar

Leitner, C., A. Zeileis, and K. Hornik. 2009. “Is Federer Stronger in a Tournament without Nadal? An Evaluation of Odds and Seedings for Wimbledon 2009.” Austrian Journal of Statistics 38 (4): 277–86. https://doi.org/10.17713/ajs.v38i4.280.Search in Google Scholar

Lloyd, S. 1982. “Least Squares Quantization in PCM.” IEEE Transactions on Information Theory 28 (2): 129–37. https://doi.org/10.1109/tit.1982.1056489.Search in Google Scholar

McHale, I., and A. Morton. 2011. “A Bradley-Terry Type Model for Forecasting Tennis Match Results.” International Journal of Forecasting 27 (2): 619–30. https://doi.org/10.1016/j.ijforecast.2010.04.004.Search in Google Scholar

Radicchi, F. 2011. “Who is the Best Player Ever? A Complex Network Analysis of the History of Professional Tennis.” PLoS One 6 (2): e17249. https://doi.org/10.1371/journal.pone.0017249.Search in Google Scholar PubMed PubMed Central

Spanias, D., and W. J. Knottenbelt. 2013. “Predicting the Outcomes of Tennis Matches Using a Low-Level Point Model.” IMA Journal of Management Mathematics 24 (3): 311–20. https://doi.org/10.1093/imaman/dps010.Search in Google Scholar

Wei, X., P. Lucey, S. Morgan, and S. Sridharan. 2013. “Sweet-Spot: Using Spatiotemporal Data to Discover and Predict Shots in Tennis.” In 7th Annual MIT Sloan Sports Analytics Conference. Boston.Search in Google Scholar

Received: 2022-05-31
Revised: 2022-11-03
Accepted: 2022-12-19
Published Online: 2023-01-17
Published in Print: 2023-03-28

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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