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.

中文翻译：

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橄榄球联盟比赛的方差Gamma模型

在最近的关注中，我们讨论了橄榄球联合会比赛的方差伽马模型（可能适用于其他运动）。我们的模型是最近引入的Gamma差异分布的特例，尽管使用Variance Gamma分布的应用工作已有很长的历史，尤其是在金融领域。限于此特殊情况会增加分析的可处理性和计算的简便性。我们的三维模型扩展了足球的经典二维泊松模型。获得比赛结果，总分和奖励积分的分析结果。使用历史结果，庄家数据和锦标赛模拟来演示模型校准。