We modeled the dynamics of a soccer match based on a network representation where players are nodes discretely clustered into homogeneous groups. Players were grouped by physical proximity, supported by the intuitive notion that competing and same-team players use relative position as a key tactical tool to contribute to the team's objectives. The model was applied to a set of matches from a major European national football league, with players' coordinates sampled at 10Hz, resulting in ? 60,000 network samples per match. We took an information theoretic approach to measuring distance between samples and used it as a proxy for the game dynamics. Significant correlations were found between measurements and key match events that are empirically known to result in players jostling for position, such as when striving to get unmarked or to mark. These events increase the information distance, while breaks in game play have the opposite effect. By analyzing the frequency spectrum of players' cluster transitions and their corresponding information distance, it is possible to build a comprehensive view of player's interactions, useful for training and strategy development. This analysis can be drilled down to the level of individual players by quantifying their contribution to cluster breakup and emergence, building an overall multi-level map that provides insights into the game dynamics, from the individual player, to the clusters of interacting players, all the way to the teams and their matches.

中文翻译：

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足球比赛的点点滴滴：信息理论分析

我们基于网络表示对足球比赛的动力学进行建模，其中球员是离散地聚类为同质组的节点。球员按身体上的亲近度分组，并得到直观的观念的支持，即竞争和同队球员使用相对位置作为为球队目标做出贡献的关键战术工具。该模型已应用于欧洲某主要国家足球联赛的一组比赛中，以10Hz采样球员的坐标，结果为？每次比赛60,000个网络样本。我们采用了一种信息理论方法来测量样本之间的距离，并将其用作游戏动力学的代理。在测量值和关键匹配事件之间发现了显着的相关性，根据经验，这些相关性会导致玩家争抢位置，例如在努力获得未标记或标记时。这些事件增加了信息距离，而游戏中断则产生相反的效果。通过分析玩家集群过渡的频谱及其相应的信息距离，可以建立玩家交互的全面视图，对培训和策略制定很有用。通过量化单个玩家对集群破裂和出现的贡献，可以建立一个多层次的整体地图，从单个玩家到互动玩家的集群，深入分析各个玩家的水平，从而深入分析各个玩家的水平。球队及其比赛的方式。集群转换及其相应的信息距离，可以建立玩家互动的全面视图，对培训和策略制定很有用。通过量化单个玩家对集群破裂和出现的贡献，可以建立一个多层次的整体地图，从单个玩家到交互玩家的集群，深入分析各个参与者的游戏动态，从而深入分析单个玩家的水平。球队及其比赛的方式。集群转换及其相应的信息距离，可以建立玩家互动的全面视图，对培训和策略制定很有用。通过量化单个玩家对集群破裂和出现的贡献，可以建立一个多层次的整体地图，从单个玩家到交互玩家的集群，深入分析各个参与者的游戏动态，从而深入分析单个玩家的水平。球队及其比赛的方式。