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A Variance Gamma model for Rugby Union matches

  • John Fry EMAIL logo , Oliver Smart , Jean-Philippe Serbera and Bernhard Klar


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.


The authors would like to acknowledge Tom Hastings, seminar participants at the Royal Statistical Society international conference and exceptionally helpful comments and suggestions from two anonymous referees. The usual disclaimer applies. This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.


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Received: 2019-08-23
Accepted: 2020-03-24
Published Online: 2020-05-05
Published in Print: 2021-01-26

©2020 Walter de Gruyter GmbH, Berlin/Boston

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