Handball has received growing interest during the last years, including academic research for many different aspects of the sport. On the other hand modelling the outcome of the game has attracted less interest mainly because of the additional challenges that occur. Data analysis has revealed that the number of goals scored by each team are under-dispersed relative to a Poisson distribution and hence new models are needed for this purpose. Here we propose to circumvent the problem by modelling the score difference. This removes the need for special models since typical models for integer data like the Skellam distribution can provide sufficient fit and thus reveal some of the characteristics of the game. In the present paper we propose some models starting from a Skellam regression model and also considering zero inflated versions as well as other discrete distributions in $\mathbb Z$. Furthermore, we develop some bivariate models using copulas to model the two halves of the game and thus providing insights on the game. Data from German Bundesliga are used to show the potential of the new models.

翻译：近年来，手球运动受到越来越多的关注，包括对该运动多个方面的学术研究。然而，由于比赛结果建模面临额外挑战，这一方向的研究兴趣相对较低。数据分析表明，每支球队的进球数相对于泊松分布呈现欠分散特征，因此需要建立新模型来解决这一问题。本文提出通过建模比分差来规避该问题。这种方法无需特殊模型，因为适用于整数数据的典型模型（如Skellam分布）能够提供充分拟合，从而揭示比赛的某些特征。本文提出了一系列模型：从Skellam回归模型出发，同时考虑零膨胀版本以及$\mathbb Z$上的其他离散分布。此外，我们利用Copula方法构建了双变量模型，用于刻画比赛上下半场之间的关联性，从而提供对比赛更深入的见解。德国手球甲级联赛数据被用于展示新模型的潜力。