IDEAS home Printed from https://ideas.repec.org/a/bpj/jqsprt/v17y2021i1p67-75n2.html
   My bibliography  Save this article

A Variance Gamma model for Rugby Union matches

Author

Listed:
  • Fry John

    (School of Management, University of Bradford, Bradford, West Yorkshire, BD7 1DP, UK)

  • Smart Oliver

    (Department of Computing and Mathematics, Manchester Metropolitan University, John Dalton Building, Chester Street, Manchester, M1 5GD, UK)

  • Serbera Jean-Philippe

    (Shefleld Business School, Shefleld Hallam University, City Campus, Howard Street, Sheffield, S1 1WB, UK)

  • Klar Bernhard

    (Karlsruhe Institute of Technology (KIT), Department of Mathematics, Englerstr. 2, 76131 Karlsruhe, Germany)

Abstract

Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

Suggested Citation

  • Fry John & Smart Oliver & Serbera Jean-Philippe & Klar Bernhard, 2021. "A Variance Gamma model for Rugby Union matches," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(1), pages 67-75, March.
  • Handle: RePEc:bpj:jqsprt:v:17:y:2021:i:1:p:67-75:n:2
    DOI: 10.1515/jqas-2019-0088
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jqas-2019-0088
    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-2019-0088?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. 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.
    2. Zhao, Peng, 2011. "Some new results on convolutions of heterogeneous gamma random variables," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 958-976, May.
    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. Fry, John & Serbera, Jean-Philippe & Wilson, Rob, 2021. "Managing performance expectations in association football," Journal of Business Research, Elsevier, vol. 135(C), pages 445-453.

    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. Craig, J. Dean & Winchester, Niven, 2021. "Predicting the national football league potential of college quarterbacks," European Journal of Operational Research, Elsevier, vol. 295(2), pages 733-743.
    2. Michal Friesl & Jan Libich & Petr Stehlík, 2020. "Fixing ice hockey’s low scoring flip side? Just flip the sides," Annals of Operations Research, Springer, vol. 292(1), pages 27-45, September.
    3. Buraimo, Babatunde & Forrest, David & McHale, Ian G. & Tena, J.D., 2022. "Armchair fans: Modelling audience size for televised football matches," European Journal of Operational Research, Elsevier, vol. 298(2), pages 644-655.
    4. 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.
    5. You, Yinping & Li, Xiaohu, 2015. "Functional characterizations of bivariate weak SAI with an application," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 225-231.
    6. Mansour Shrahili & Mohamed Kayid, 2022. "Characterizations of the Exponential Distribution by Some Random Hazard Rate Sequences," Mathematics, MDPI, vol. 10(17), pages 1-11, August.
    7. László Csató & Dóra Gréta Petróczy, 2024. "Bibliometric indices as a measure of performance and competitive balance in the knockout stage of the UEFA Champions League," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(4), pages 961-988, December.
    8. Fry, John & Brighton, Tom & Fanzon, Silvio, 2024. "Faster identification of faster Formula 1 drivers via time-rank duality," Economics Letters, Elsevier, vol. 237(C).
    9. 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.
    10. 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.
    11. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 817-849, November.
    12. Collingwood, James A.P. & Wright, Michael & Brooks, Roger J., 2023. "Simulating the progression of a professional snooker frame," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1286-1299.
    13. Singh, Aaditya & Scarf, Phil & Baker, Rose, 2023. "A unified theory for bivariate scores in possessive ball-sports: The case of handball," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1099-1112.
    14. Farbod Roosta-Khorasani & Gábor Székely, 2015. "Schur properties of convolutions of gamma random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 997-1014, November.
    15. Gyimesi, András, 2021. "Hosszú távú versenyegyensúly egy csapatsportliga közgazdasági modelljében [Long-term competitive balance in an economic model of a team sports league]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 585-616.

    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:17:y:2021:i:1:p:67-75:n: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: 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.