论文标题
复杂性在足球比赛中标记动态的措施中出现
Complexity emerges in measures of the marking dynamics in football games
论文作者
论文摘要
在本文中，我们研究了足球比赛中标记的动态。为此，我们调查并分析了一个数据库，该数据库包含三支球队在三场专业比赛中的球队中的球员轨迹。我们通过构建近距离的时间两分网络来描述动力学。基于引入的接近概念，节点是玩家，并且在给定时刻彼此足够接近的对手之间定义了链接。通过研究游戏过程中网络的异质性参数的演变，我们表征了缩放定律的平均波动形状，并揭示了系统中复杂性的出现。此外，我们提出了一个简单的模型，以模拟从我们获得合成接近网络的演变的场地中的玩家运动。我们表明，该模型以显着的一致性捕获经验案例的复杂性，因此事实证明，它有助于阐明负责观察到的现象的基本机制。
In this article, we study the dynamics of marking in football matches. To do this, we surveyed and analyzed a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterized a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we proposed a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena.
