IDEAS home Printed from https://ideas.repec.org/a/bpj/jqsprt/v9y2013i3p229-238n3.html
   My bibliography  Save this article

When to challenge a call in tennis: A Markov decision process approach

Author

Listed:
  • Nadimpalli Vamsi K.

    (Zilliant, Inc., 3815 S. Capital of Texas Highway, Suite 300, Austin, TX 78704, USA)

  • Hasenbein John J.

    (Graduate Program in Operations Research and Industrial Engineering, Department of Mechanical Engineering, University of Texas at Austin, Austin, Texas, 78712, USA)

Abstract

In this paper, we develop a Markov decision process (MDP) model to determine when a player should challenge a line call in a game of tennis, if the objective is to maximize the probability of winning the game. The parameters in the model include the relative strength of the players and the fallibility of the officials. The player’s decision depends on the the current score, the number of challenges remaining, the outcome of a successful challenge, and his confidence that the line call is incorrect. The model developed is a multi-chain MDP operating under the long-run average cost criterion. We also performed extensive numerical studies when the player has one challenge remaining, varying the player strengths and the fallibility levels. These studies imply some general intuitive challenge strategies but also exhibit unusual strategic behavior in some game states. For example, in some states it is not optimal for very weak or very strong players to challenge calls. Furthermore, we demonstrate that the challenge decision is not “unimodal” as a function of the player’s strength, i.e., there may be multiple decision thresholds with respect to this parameter.

Suggested Citation

  • Nadimpalli Vamsi K. & Hasenbein John J., 2013. "When to challenge a call in tennis: A Markov decision process approach," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 9(3), pages 229-238, September.
  • Handle: RePEc:bpj:jqsprt:v:9:y:2013:i:3:p:229-238:n:3
    DOI: 10.1515/jqas-2012-0051
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jqas-2012-0051
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1515/jqas-2012-0051?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Klaassen F. J G M & Magnus J. R., 2001. "Are Points in Tennis Independent and Identically Distributed? Evidence From a Dynamic Binary Panel Data Model," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 500-509, June.
    2. S R Clarke & J M Norman, 2012. "Optimal challenges in tennis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(12), pages 1765-1772, December.
    3. Ran Abramitzky & Liran Einav & Shimon Kolkowitz & Roy Mill, 2012. "On The Optimality Of Line Call Challenges In Professional Tennis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 939-964, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Paserman, M. Daniele, 2023. "Gender Differences in Performance in Competitive Environments? Evidence from Professional Tennis Players," Journal of Economic Behavior & Organization, Elsevier, vol. 212(C), pages 590-609.
    2. Kendall, Graham & Lenten, Liam J.A., 2017. "When sports rules go awry," European Journal of Operational Research, Elsevier, vol. 257(2), pages 377-394.
    3. González-Díaz, Julio & Gossner, Olivier & Rogers, Brian W., 2012. "Performing best when it matters most: Evidence from professional tennis," Journal of Economic Behavior & Organization, Elsevier, vol. 84(3), pages 767-781.
    4. Romain Gauriot & Lionel Page, 2019. "Does Success Breed Success? a Quasi-Experiment on Strategic Momentum in Dynamic Contests," The Economic Journal, Royal Economic Society, vol. 129(624), pages 3107-3136.
    5. Alex Krumer & Mosi Rosenboim & Offer Moshe Shapir, 2016. "Gender, Competitiveness, and Physical Characteristics," Journal of Sports Economics, , vol. 17(3), pages 234-259, April.
    6. Holmes, Benjamin & McHale, Ian G. & Żychaluk, Kamila, 2023. "A Markov chain model for forecasting results of mixed martial arts contests," International Journal of Forecasting, Elsevier, vol. 39(2), pages 623-640.
    7. Cohen-Zada, Danny & Krumer, Alex & Rosenboim, Mosi & Shapir, Offer Moshe, 2017. "Choking under pressure and gender: Evidence from professional tennis," Journal of Economic Psychology, Elsevier, vol. 61(C), pages 176-190.
    8. Gil Aharoni & Oded H. Sarig, 2012. "Hot hands and equilibrium," Applied Economics, Taylor & Francis Journals, vol. 44(18), pages 2309-2320, June.
    9. Christophe Ley & Yves Dominicy, 2017. "Mutual Point-winning Probabilities (MPW): a New Performance Measure for Table Tennis," Working Papers ECARES ECARES 2017-23, ULB -- Universite Libre de Bruxelles.
    10. Klaassen, F.J.G.M. & Magnus, J.R., 2006. "Are Economic Agents Successful Optimizers? An Analysis Through Strategy in Tennis," Other publications TiSEM 73e12d86-8fe4-4a87-9181-7, Tilburg University, School of Economics and Management.
    11. Thierry Lallemand & Robert Plasman & François Rycx, 2008. "Women and Competition in Elimination Tournaments," Journal of Sports Economics, , vol. 9(1), pages 3-19, February.
    12. Guy Elaad & Alex Krumer & Jeffrey Kantor, 2018. "Corruption and Sensitive Soccer Games: Cross-Country Evidence," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 34(3), pages 364-394.
    13. Deutscher, Christian & Neuberg, Lena & Thiem, Stefan, 2023. "Who’s afraid of the GOATs? - Shadow effects of tennis superstars," Journal of Economic Psychology, Elsevier, vol. 99(C).
    14. Gimenez-Egido, José María & Ortega-Toro, Enrique & Palao, José M & Torres-Luque, Gema, 2020. "Effect of scaling equipment on U-10 players tennis serve during match-play: A nonlinear pedagogical approach," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    15. Romain Gauriot & Lionel Page & John Wooders, 2016. "Nash at Wimbledon: Evidence from Half a Million Serves," QuBE Working Papers 046, QUT Business School.
    16. Legge, Stefan & Schmid, Lukas, 2013. "Rankings, Random Successes, and Individual Performance," Economics Working Paper Series 1340, University of St. Gallen, School of Economics and Political Science.
    17. Picchio, Matteo & van Ours, Jan C., 2024. "The impact of high temperatures on performance in work-related activities," Labour Economics, Elsevier, vol. 87(C).
    18. Bar-Eli, Michael & Krumer, Alex & Morgulev, Elia, 2020. "Ask not what economics can do for sports - Ask what sports can do for economics," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 89(C).
    19. Tomi Ovaska & Albert J. Sumell, 2014. "Who Has The Advantage? An Economic Exploration of Winning in Men's Professional Tennis," The American Economist, Sage Publications, vol. 59(1), pages 34-51, May.
    20. Gery Geenens & Thomas Cuddihy, 2018. "Non‐parametric evidence of second‐leg home advantage in European football," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1009-1031, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:jqsprt:v:9:y:2013:i:3:p:229-238:n:3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.