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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
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    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.
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    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.

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