In this paper, we study interaction dynamics in the game of football–soccer in the context of ball possession intervals. To do so, we analyze a database comprising one season of the five major football leagues of Europe. Using this input, we developed a stochastic model based on three agents: two teammates and one defender. Despite its simplicity, the model is able to capture, in good approximation, the statistical behavior of possession times, pass lengths, and number of passes performed. In the last section, we show that the model's dynamics can be mapped into a Wiener process with drift and an absorbing barrier.

中文翻译：

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在足球比赛中模拟控球动力学

在本文中，我们研究了在控球间隔内足球与足球比赛中的互动动力学。为此，我们分析了一个包含欧洲五个主要足球联赛一个赛季的数据库。使用此输入，我们基于三个特工（两个队友和一个后卫）开发了一个随机模型。尽管模型简单，但仍能够很好地捕获占有时间，传球长度和传球次数的统计行为。在最后一部分中，我们展示了可以将模型的动力学映射到具有漂移和吸收障碍的维纳过程中。