IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v325y2023i1d10.1007_s10479-022-04563-0.html
   My bibliography  Save this article

Analysing a built-in advantage in asymmetric darts contests using causal machine learning

Author

Listed:
  • Daniel Goller

    (University of Bern
    University of St. Gallen)

Abstract

We analyse a sequential contest with two players in darts where one of the contestants enjoys a technical advantage. Using methods from the causal machine learning literature, we analyse the built-in advantage, which is the first-mover having potentially more but never less moves. Our empirical findings suggest that the first-mover has an 8.6% points higher probability to win the match induced by the technical advantage. Contestants with low performance measures and little experience have the highest built-in advantage. With regard to the fairness principle that contestants with equal abilities should have equal winning probabilities, this contest is ex-ante fair in the case of equal built-in advantages for both competitors and a randomized starting right. Nevertheless, the contest design produces unequal probabilities of winning for equally skilled contestants because of asymmetries in the built-in advantage associated with social pressure for contestants competing at home and away.

Suggested Citation

  • Daniel Goller, 2023. "Analysing a built-in advantage in asymmetric darts contests using causal machine learning," Annals of Operations Research, Springer, vol. 325(1), pages 649-679, June.
  • Handle: RePEc:spr:annopr:v:325:y:2023:i:1:d:10.1007_s10479-022-04563-0
    DOI: 10.1007/s10479-022-04563-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-04563-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10479-022-04563-0?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Marius Ötting & Christian Deutscher & Sandra Schneemann & Roland Langrock & Sebastian Gehrmann & Hendrik Scholten, 2020. "Performance under pressure in skill tasks: An analysis of professional darts," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-21, February.
    3. Michael C Knaus, 2022. "Double machine learning-based programme evaluation under unconfoundedness [Econometric methods for program evaluation]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 602-627.
    4. Jose Apesteguia & Ignacio Palacios-Huerta, 2010. "Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment," American Economic Review, American Economic Association, vol. 100(5), pages 2548-2564, December.
    5. Canice Prendergast, 1999. "The Provision of Incentives in Firms," Journal of Economic Literature, American Economic Association, vol. 37(1), pages 7-63, March.
    6. Arlegi, Ritxar & Dimitrov, Dinko, 2020. "Fair elimination-type competitions," European Journal of Operational Research, Elsevier, vol. 287(2), pages 528-535.
    7. Lechner, Michael, 2018. "Modified Causal Forests for Estimating Heterogeneous Causal Effects," IZA Discussion Papers 12040, Institute of Labor Economics (IZA).
    8. Konrad, Kai A., 2002. "Investment in the absence of property rights; the role of incumbency advantages," European Economic Review, Elsevier, vol. 46(8), pages 1521-1537, September.
    9. Dohmen, Thomas J., 2008. "Do professionals choke under pressure?," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 636-653, March.
    10. Daniel Goller & Tamara Harrer & Michael Lechner & Joachim Wolff, 2021. "Active labour market policies for the long-term unemployed: New evidence from causal machine learning," Papers 2106.10141, arXiv.org, revised May 2023.
    11. Victor A. Ginsburgh & Jan C. van Ours, 2003. "Expert Opinion and Compensation: Evidence from a Musical Competition," American Economic Review, American Economic Association, vol. 93(1), pages 289-296, March.
    12. repec:feb:natura:0056 is not listed on IDEAS
    13. Steffen Liebscher & Thomas Kirschstein, 2017. "Predicting the outcome of professional darts tournaments," International Journal of Performance Analysis in Sport, Taylor & Francis Journals, vol. 17(5), pages 666-683, September.
    14. Daniel Goller & Michael C. Knaus & Michael Lechner & Gabriel Okasa, 2021. "Predicting match outcomes in football by an Ordered Forest estimator," Chapters, in: Ruud H. Koning & Stefan Kesenne (ed.), A Modern Guide to Sports Economics, chapter 22, pages 335-355, Edward Elgar Publishing.
    15. Michael C Knaus & Michael Lechner & Anthony Strittmatter, 2021. "Machine learning estimation of heterogeneous causal effects: Empirical Monte Carlo evidence," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 134-161.
    16. Victor Chernozhukov & Iván Fernández‐Val & Ye Luo, 2018. "The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages," Econometrica, Econometric Society, vol. 86(6), pages 1911-1938, November.
    17. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    18. Susan Athey & Guido W. Imbens, 2019. "Machine Learning Methods That Economists Should Know About," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 685-725, August.
    19. 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.
    20. Harb-Wu, Ken & Krumer, Alex, 2019. "Choking under pressure in front of a supportive audience: Evidence from professional biathlon," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 246-262.
    21. Ella Segev & Aner Sela, 2014. "Sequential all-pay auctions with head starts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 893-923, December.
    22. Steven Levitt & John List, 2008. "Homo economicus evolves," Artefactual Field Experiments 00095, The Field Experiments Website.
    23. Kirkegaard, René, 2012. "Favoritism in asymmetric contests: Head starts and handicaps," Games and Economic Behavior, Elsevier, vol. 76(1), pages 226-248.
    24. X Nie & S Wager, 2021. "Quasi-oracle estimation of heterogeneous treatment effects [TensorFlow: A system for large-scale machine learning]," Biometrika, Biometrika Trust, vol. 108(2), pages 299-319.
    25. Stiglitz, Joseph E, 1976. "The Efficiency Wage Hypothesis, Surplus Labour, and the Distribution of Income in L.D.C.s," Oxford Economic Papers, Oxford University Press, vol. 28(2), pages 185-207, July.
    26. Michael Zimmert & Michael Lechner, 2019. "Nonparametric estimation of causal heterogeneity under high-dimensional confounding," Papers 1908.08779, arXiv.org.
    27. Lu Tian & Ash A. Alizadeh & Andrew J. Gentles & Robert Tibshirani, 2014. "A Simple Method for Estimating Interactions Between a Treatment and a Large Number of Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1517-1532, December.
    28. Zheng Cao & Joseph Price & Daniel F. Stone, 2011. "Performance Under Pressure in the NBA," Journal of Sports Economics, , vol. 12(3), pages 231-252, June.
    29. Klein Teeselink, Bouke & Potter van Loon, Rogier J.D. & van den Assem, Martijn J. & van Dolder, Dennie, 2020. "Incentives, performance and choking in darts," Journal of Economic Behavior & Organization, Elsevier, vol. 169(C), pages 38-52.
    30. 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.
    31. Jonathan M.V. Davis & Sara B. Heller, 2017. "Using Causal Forests to Predict Treatment Heterogeneity: An Application to Summer Jobs," American Economic Review, American Economic Association, vol. 107(5), pages 546-550, May.
    32. 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.
    33. Alex Krumer & Michael Lechner, 2018. "Midweek Effect On Soccer Performance: Evidence From The German Bundesliga," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 193-207, January.
    34. repec:feb:framed:0077 is not listed on IDEAS
    35. Dan Ariely & Uri Gneezy & George Loewenstein & Nina Mazar, 2009. "Large Stakes and Big Mistakes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(2), pages 451-469.
    36. Athey, Susan & Imbens, Guido W., 2019. "Machine Learning Methods Economists Should Know About," Research Papers 3776, Stanford University, Graduate School of Business.
    37. Olivier Gossner & Julio González-Díaz & Brian W. Rogers, 2012. "Performing best when it matters most: Evidence from professional tennis," PSE-Ecole d'économie de Paris (Postprint) hal-00812984, HAL.
    38. repec:feb:artefa:0095 is not listed on IDEAS
    39. Shapiro, Carl & Stiglitz, Joseph E, 1984. "Equilibrium Unemployment as a Worker Discipline Device," American Economic Review, American Economic Association, vol. 74(3), pages 433-444, June.
    40. Olivier Gossner & Julio González-Díaz & Brian W. Rogers, 2012. "Performing best when it matters most: Evidence from professional tennis," Post-Print hal-00812984, HAL.
    41. Cohen-Zada, Danny & Krumer, Alex & Shapir, Offer Moshe, 2018. "Testing the effect of serve order in tennis tiebreak," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 106-115.
    42. Hurley, W.J., 2009. "Equitable birthdate categorization systems for organized minor sports competition," European Journal of Operational Research, Elsevier, vol. 192(1), pages 253-264, January.
    43. Vira Semenova & Victor Chernozhukov, 2021. "Debiased machine learning of conditional average treatment effects and other causal functions," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 264-289.
    44. Ryan J. Tibshirani & Andrew Price & Jonathan Taylor, 2011. "A statistician plays darts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(1), pages 213-226, January.
    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. Michael C Knaus, 2022. "Double machine learning-based programme evaluation under unconfoundedness [Econometric methods for program evaluation]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 602-627.
    2. 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).
    3. Krumer, Alex, 2020. "Pressure versus ability: Evidence from penalty shoot-outs between teams from different divisions," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 89(C).
    4. Christoph Buehren & Marvin Gabriel, 2021. "Performing best when it matters the most: Evidence from professional handball," MAGKS Papers on Economics 202119, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    5. Gabriel Okasa, 2022. "Meta-Learners for Estimation of Causal Effects: Finite Sample Cross-Fit Performance," Papers 2201.12692, arXiv.org.
    6. Phillip Heiler & Michael C. Knaus, 2021. "Effect or Treatment Heterogeneity? Policy Evaluation with Aggregated and Disaggregated Treatments," Papers 2110.01427, arXiv.org, revised Aug 2023.
    7. Daniel Goller & Tamara Harrer & Michael Lechner & Joachim Wolff, 2021. "Active labour market policies for the long-term unemployed: New evidence from causal machine learning," Papers 2106.10141, arXiv.org, revised May 2023.
    8. Ricardo Manuel Santos, 2023. "Effects of psychological pressure on first‐mover advantage in competitive environments: Evidence from penalty shootouts," Contemporary Economic Policy, Western Economic Association International, vol. 41(2), pages 354-369, April.
    9. Michael Lechner, 2023. "Causal Machine Learning and its use for public policy," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 159(1), pages 1-15, December.
    10. Florian Lindner, 2017. "Choking under pressure of top performers: Evidence from biathlon competitions," Working Papers 2017-24, Faculty of Economics and Statistics, Universität Innsbruck.
    11. Daniel C. Hickman & Craig Kerr & Neil Metz, 2019. "Rank and Performance in Dynamic Tournaments: Evidence From the PGA Tour," Journal of Sports Economics, , vol. 20(4), pages 509-534, May.
    12. Nora Bearth & Michael Lechner, 2024. "Causal Machine Learning for Moderation Effects," Papers 2401.08290, arXiv.org.
    13. Klein Teeselink, Bouke & Potter van Loon, Rogier J.D. & van den Assem, Martijn J. & van Dolder, Dennie, 2020. "Incentives, performance and choking in darts," Journal of Economic Behavior & Organization, Elsevier, vol. 169(C), pages 38-52.
    14. Cockx, Bart & Lechner, Michael & Bollens, Joost, 2023. "Priority to unemployed immigrants? A causal machine learning evaluation of training in Belgium," Labour Economics, Elsevier, vol. 80(C).
    15. Goller, Daniel & Lechner, Michael & Moczall, Andreas & Wolff, Joachim, 2020. "Does the estimation of the propensity score by machine learning improve matching estimation? The case of Germany's programmes for long term unemployed," Labour Economics, Elsevier, vol. 65(C).
    16. Böheim, René & Grübl, Dominik & Lackner, Mario, 2019. "Choking under pressure – Evidence of the causal effect of audience size on performance," Journal of Economic Behavior & Organization, Elsevier, vol. 168(C), pages 76-93.
    17. Wen‐Jhan Jane, 2022. "Choking or excelling under pressure: Evidence of the causal effect of audience size on performance," Bulletin of Economic Research, Wiley Blackwell, vol. 74(1), pages 329-357, January.
    18. Wen‐Jhan Jane, 2023. "Hot hand or choking under pressure – Evidence from professional basketball," Kyklos, Wiley Blackwell, vol. 76(2), pages 223-254, May.
    19. Enzo Brox & Daniel Goller, 2024. "Tournaments, Contestant Heterogeneity and Performance," Papers 2401.05210, arXiv.org.
    20. Christoph Buehren & Lisa Traeger, 2020. "The Impact of Psychological Pressure and Psychological Traits on Performance – Experimental Evidence of Penalties in Handball," MAGKS Papers on Economics 202043, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).

    More about this item

    Keywords

    Operational research in sports; Causal machine learning; Heterogeneity; Contest design; Built-in advantage; Incentives;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D20 - Microeconomics - - Production and Organizations - - - General
    • Z20 - Other Special Topics - - Sports Economics - - - General

    Statistics

    Access and download statistics

    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:spr:annopr:v:325:y:2023:i:1:d:10.1007_s10479-022-04563-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.