We can construct passing networks when we regard a player as a node and a pass as a link in football games. Thus, we can analyze the networks by using tools developed in network science. Among various metrics characterizing a network, centrality metrics have often been used to identify key players in a passing network. However, a tolerance to players being marked or passes being blocked in a passing network, namely the robustness of the network, has been poorly understood so far. Because the robustness of a passing network can be connected to the increase of ball possession, it would be deeply related to the outcome of a game. Here, we developed position-dependent passing networks of 45 matches by 18 teams belonging to the Japan Professional Football League. Then, nodes or links were continuously removed from the passing networks by two removal methods so that we could evaluate the robustness of these networks against the removals. The results show that these passing networks commonly contain hubs (key players making passes). Then, we analyzed the most robust networks in detail and found that their full backs increase the robustness by often invoking a heavier emphasis on attack. Moreover, we showed that, by conducting correlation analyses, not just the number of passes but also the robustness of passing networks against the removals are important to win.

当我们在足球比赛中将球员视为节点，将传球视为链接时，我们可以构建传球网络。因此，我们可以使用网络科学中开发的工具来分析网络。在表征网络的各种度量标准中，集中度度量标准通常用于标识经过的网络中的关键参与者。然而，到目前为止，对于在传球网络中标记球员或传球被挡住的容忍度，即网络的鲁棒性，目前知之甚少。因为传球网络的健壮性可以与控球能力的提高联系在一起，所以这将与比赛的结果密切相关。在这里，我们建立了由属于日本职业足球联赛的18支球队进行45场比赛的与位置相关的传球网络。然后，节点或链接通过两种删除方法连续从传递的网络中删除，以便我们可以针对这些删除评估这些网络的健壮性。结果表明，这些传球网络通常包含集线器（进行传球的关键球员）。然后，我们详细分析了最健壮的网络，发现它们的后背经常通过加大对攻击的重视来提高健壮性。此外，我们表明，通过进行相关性分析，不仅要获得通行证的数量，而且通行网络抵制删除的鲁棒性也很重要。我们详细分析了最鲁棒的网络，发现它们的后背经常通过加大对攻击的重视来提高鲁棒性。此外，我们表明，通过进行相关性分析，不仅要获得通行证的数量，而且通行网络抵制删除的鲁棒性也很重要。我们详细分析了最鲁棒的网络，发现它们的后背经常通过加大对攻击的重视来提高鲁棒性。此外，我们表明，通过进行相关性分析，不仅要获得通行证的数量，而且通行网络抵制删除的鲁棒性也很重要。