IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v50y2021i2d10.1007_s00182-021-00756-2.html
   My bibliography  Save this article

Effort of rugby teams according to the bonus point system: a theoretical and empirical analysis

Author

Listed:
  • Federico Fioravanti

    (Universidad Nacional del Sur, CONICET)

  • Fernando Tohmé

    (Universidad Nacional del Sur, CONICET)

  • Fernando Delbianco

    (Universidad Nacional del Sur, CONICET)

  • Alejandro Neme

    (Universidad Nacional de San Luis, CONICET)

Abstract

Using a simple game-theoretical model of contests, we compare the effort exerted by rugby teams under three different point systems used in tournaments around the world. We consider a point system that awards four points to the winning team, no points to the losing team, and two points to each team in a case of a draw. The other two point systems award bonus points depending on the final score. They both award a bonus point for losing by only one try. One of these two systems gives an extra point to the team that scores four or more tries while the other gives it for scoring three more tries than the other team. We develop two models. One is a static one, intended to compare the joint efforts equilibria as to find which point system maximizes the effort exerted by the teams. The other is a dynamical model, providing a framework for the analysis of equilibrium payoffs and find the one in which teams exert more joint effort. In both models, the point system that maximizes the amount of effort in rugby is the one that awards a bonus point for scoring three more tries than the opponent. To evaluate the real-world validity of this claim we run empirical analyses using data from matches under the three point systems being evaluated. The empirical results confirm our theoretical conclusions.

Suggested Citation

  • Federico Fioravanti & Fernando Tohmé & Fernando Delbianco & Alejandro Neme, 2021. "Effort of rugby teams according to the bonus point system: a theoretical and empirical analysis," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 447-474, June.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:2:d:10.1007_s00182-021-00756-2
    DOI: 10.1007/s00182-021-00756-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-021-00756-2
    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/s00182-021-00756-2?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. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    2. Palomino, F.A. & Rigotti, L. & Rustichini, A., 1998. "Skill, Strategy and Passion : An Empirical Analysis of Soccer," Discussion Paper 1998-129, Tilburg University, Center for Economic Research.
    3. Peter-J. Jost, 2021. "“The ball is round, the game lasts 90 minutes, everything else is pure theoryâ€," Journal of Sports Economics, , vol. 22(1), pages 27-74, January.
    4. Niven Winchester, 2014. "Should bonus points be included in the Six Nations Championship?," New Zealand Economic Papers, Taylor & Francis Journals, vol. 48(1), pages 96-101, April.
    5. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    6. Scarf, Phil & Parma, Rishikesh & McHale, Ian, 2019. "On outcome uncertainty and scoring rates in sport: The case of international rugby union," European Journal of Operational Research, Elsevier, vol. 273(2), pages 721-730.
    7. P.-A. Chiappori, 2002. "Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer," American Economic Review, American Economic Association, vol. 92(4), pages 1138-1151, September.
    8. Liam J. A. Lenten & Niven Winchester, 2015. "Secondary Behavioural Incentives: Bonus Points and Rugby Professionals," The Economic Record, The Economic Society of Australia, vol. 91(294), pages 386-398, September.
    9. Helmut Dietl & Egon Franck & Martin Grossmann & Markus Lang, 2009. "Contest Theory and its Applications in Sports," Working Papers 0029, University of Zurich, Center for Research in Sports Administration (CRSA).
    10. Andrea Petróczi & Kjetil K. Haugen, 2012. "The doping self-reporting game: The paradox of a ‘false-telling’ mechanism and its potential research and policy implications," Sport Management Review, Taylor & Francis Journals, vol. 15(4), pages 513-517, October.
    11. Robert Butler & Liam J. A. Lenten & Patrick Massey, 2020. "Bonus incentives and team effort levels: Evidence from the “Field”," Scottish Journal of Political Economy, Scottish Economic Society, vol. 67(5), pages 539-550, November.
    12. Isabelle Brocas & Juan D. Carrillo, 2004. "Do the “Three-Point Victory†and “Golden Goal†Rules Make Soccer More Exciting?," Journal of Sports Economics, , vol. 5(2), pages 169-185, May.
    13. M. J. Maher, 1982. "Modelling association football scores," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 36(3), pages 109-118, September.
    14. Vincent (Vincent Peter) Hogan & Patrick Massey, 2015. "Teams’ Reponses to Changed Incentives: Evidence from Rugby’s Six Nations Championship," Working Papers 201518, School of Economics, University College Dublin.
    15. Winchester Niven, 2008. "Shifting the 'Goal Posts': Optimizing the Allocation of Competition Points for Sporting Contests," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(4), pages 1-17, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Avila-Cano, Antonio & Owen, P. Dorian & Triguero-Ruiz, Francisco, 2023. "Measuring competitive balance in sports leagues that award bonus points, with an application to rugby union," European Journal of Operational Research, Elsevier, vol. 309(2), pages 939-952.

    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. Avila-Cano, Antonio & Owen, P. Dorian & Triguero-Ruiz, Francisco, 2023. "Measuring competitive balance in sports leagues that award bonus points, with an application to rugby union," European Journal of Operational Research, Elsevier, vol. 309(2), pages 939-952.
    2. Juan D. Carrillo, 2007. "Penalty Shoot-Outs," Journal of Sports Economics, , vol. 8(5), pages 505-518, October.
    3. Carrillo, Juan, 2006. "Penalty Shoot-Outs: Before or After Extra Time?," CEPR Discussion Papers 5579, C.E.P.R. Discussion Papers.
    4. Scarf, Phil & Parma, Rishikesh & McHale, Ian, 2019. "On outcome uncertainty and scoring rates in sport: The case of international rugby union," European Journal of Operational Research, Elsevier, vol. 273(2), pages 721-730.
    5. Giancarlo Moschini, 2010. "Incentives And Outcomes In A Strategic Setting: The 3‐Points‐For‐A‐Win System In Soccer," Economic Inquiry, Western Economic Association International, vol. 48(1), pages 65-79, January.
    6. Carrillo, Juan & Brocas, Isabelle, 2002. "Do the 'Three-Point Victory' and 'Golden Goal' Rules Make Soccer More Exciting? A Theoretical Analysis of a Simple Game," CEPR Discussion Papers 3266, C.E.P.R. Discussion Papers.
    7. Federico Fioravanti & Fernando Delbianco & Fernando Tohmé, 2023. "The relative importance of ability, luck and motivation in team sports: a Bayesian model of performance in the English Rugby Premiership," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 715-731, September.
    8. Marta Boczoń & Alistair J. Wilson, 2023. "Goals, Constraints, and Transparently Fair Assignments: A Field Study of Randomization Design in the UEFA Champions League," Management Science, INFORMS, vol. 69(6), pages 3474-3491, June.
    9. Akifumi Kijima & Koji Kadota & Keiko Yokoyama & Motoki Okumura & Hiroo Suzuki & R C Schmidt & Yuji Yamamoto, 2012. "Switching Dynamics in an Interpersonal Competition Brings about “Deadlock” Synchronization of Players," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-10, November.
    10. Isabelle Brocas & Juan D. Carrillo, 2004. "Do the “Three-Point Victory†and “Golden Goal†Rules Make Soccer More Exciting?," Journal of Sports Economics, , vol. 5(2), pages 169-185, May.
    11. Isabelle Brocas & Juan D. Carrillo, 2022. "The development of randomization and deceptive behavior in mixed strategy games," Quantitative Economics, Econometric Society, vol. 13(2), pages 825-862, May.
    12. Katja Seim & Michael Sinkinson, 2016. "Mixed pricing in online marketplaces," Quantitative Marketing and Economics (QME), Springer, vol. 14(2), pages 129-155, June.
    13. Germán Coloma, 2007. "Penalty Kicks in Soccer," Journal of Sports Economics, , vol. 8(5), pages 530-545, October.
    14. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2017. "Serial correlation in National Football League play calling and its effects on outcomes," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 69(C), pages 125-132.
    15. Leif Brandes & Marc Brechot & Egon Franck, 2011. "The Temptation of Social Ties: When Interpersonal Network Transactions Hurt Firm Performance," Working Papers 00159, University of Zurich, Institute for Strategy and Business Economics (ISU), revised 2012.
    16. Robert Butler & Liam J. A. Lenten & Patrick Massey, 2020. "Bonus incentives and team effort levels: Evidence from the “Field”," Scottish Journal of Political Economy, Scottish Economic Society, vol. 67(5), pages 539-550, November.
    17. 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.
    18. Peter-J. Jost, 2021. "Competitive Balance and the Away Goals Rule During Extra Time," Journal of Sports Economics, , vol. 22(7), pages 823-863, October.
    19. Massimiliano Landi & Domenico Colucci, 2005. "Rational and boundedly rational behavior in sender-receiver games," Working Papers 14-2006, Singapore Management University, School of Economics, revised May 2006.
    20. Van Essen, Matt & Wooders, John, 2015. "Blind stealing: Experience and expertise in a mixed-strategy poker experiment," Games and Economic Behavior, Elsevier, vol. 91(C), pages 186-206.

    More about this item

    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:jogath:v:50:y:2021:i:2:d:10.1007_s00182-021-00756-2. 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.