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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


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.


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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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