摘要翻译：
用统计技术分析足球得分数据，我们研究了比赛的高度合作性如何反映在平均属性上，如主客场球队的进球分布。结果表明，分布的尾部不能用独立的伯努利试验很好地描述，而是用负二项式或广义极值分布很好地建模。为了从第一性原理理解这种行为，我们建议修改伯努利随机过程，以包括一个简单的自我肯定成分，这似乎很好地描述了数据，并允许解释观察到的偏离高斯统计量。以前使用的现象学分布可以理解为这个框架内的特例。我们分析了欧洲多个联赛和国际比赛的历史足球得分数据，发现所提出的模型具有较高的通用性。特别是在这里，我们比较了男女联赛和冷战时期单独的德国联赛，发现了一些显著的差异。
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英文标题：
《Self-affirmation model for football goal distributions》
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作者：
Elmar Bittner, Andreas Nussbaumer, Wolfhard Janke, Martin Weigel
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out that in particular the tails of the distributions are not well described by independent Bernoulli trials, but rather well modeled by negative binomial or generalized extreme value distributions. To understand this behavior from first principles, we suggest to modify the Bernoulli random process to include a simple component of self-affirmation which seems to describe the data surprisingly well and allows to interpret the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments and found the proposed models to be applicable rather universally. In particular, here we compare men's and women's leagues and the separate German leagues during the cold war times and find some remarkable differences.
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PDF链接：
https://arxiv.org/pdf/705.2724