Summary statistics of football matches such as final score, possession and percentage of completed passes are not satisfyingly informative about style of play seen on the pitch. In this sense, networks and graphs are able to quantify how teams play differently from each others. We study the distribution of triad census, i.e., the distribution of local structures in networks and we show how it is possible to characterize passing networks of football teams. We describe the triadic structure and analyse its distribution under some specific probabilistic assumptions, introducing, in this context, some tests to verify the presence of specific triadic patterns in football data. We firstly run an omnibus test against random structure to asses whether observed triadic distribution deviates from randomness. Then, we redesign the Dirichlet-Multinomial test to recognize different triadic behaviours after choosing some reference patterns. The proposed tests are applied to a real dataset regarding 288 matches in the Group Stage of UEFA Champions League among three consecutive seasons.

中文翻译：

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使用黑社会人口普查分布测试比赛风格：在男子足球中的应用

足球比赛的汇总统计数据，如最终得分、控球率和传球成功率，并不能令人满意地了解球场上的比赛风格。从这个意义上说，网络和图表能够量化团队之间的比赛方式。我们研究了三元组人口普查的分布，即网络中局部结构的分布，我们展示了如何描述足球队的传球网络。我们描述了三元结构并在一些特定的概率假设下分析了它的分布，在这种情况下，引入了一些测试来验证足球数据中特定三元模式的存在。我们首先运行一个公共汽车针对随机结构进行测试，以评估观察到的三元分布是否偏离随机性。然后，我们重新设计 Dirichlet-Multinomial 测试以在选择一些参考模式后识别不同的三元行为。拟议的测试适用于连续三个赛季欧洲冠军联赛小组赛阶段 288 场比赛的真实数据集。