This paper proposes a novel framework to assess individual player contributions in football, explicitly accounting for the cooperative nature of shot-ending offensive actions. By incorporating team interaction into player evaluation, it also supports economically sustainable decision-making, with practical implications for performance analysis and player scouting. Extending the expected Goal (xG) paradigm, we propose the expected Goal Action (xGA), a measure of shot quality that incorporates build-up play and passing networks. Furthermore, we adapt cooperative game theory and introduce the Player's Restricted Shapley (PRS) statistic, a contribution metric based on restricted coalition structures derived from observed passing interactions, where xGA is adopted to compute the cohesion function. Unlike traditional Shapley approaches, the PRS one restricts coalitions to tactically admissible player subsets, offering action-specific, interpretable measures of marginal contribution in a cooperative context. We apply the framework to 8,421 shot-actions from the Italian League Serie A season 2022/23, and the case studies of AC Milan and SSC Napoli reveal some heterogeneity in contributions within teams. Furthermore, combining the PRS statistic with a final efficiency metric highlights the discrepancies between cooperative engagement and goal conversion.

翻译：本文提出了一种新型框架来评估足球中个体球员的贡献，明确考虑了终结于射门的进攻动作的合作性质。通过将团队互动纳入球员评估，该框架同时支持经济上可持续的决策，对表现分析和球员球探具有实际意义。我们扩展了预期进球（xG）范式，提出了预期进球动作（xGA），这是一种融合了进攻构建和传球网络的射门质量度量。此外，我们改编了合作博弈论，引入了球员限制夏普利（PRS）统计量，这是一种基于从观测到的传球互动中得出的限制联盟结构的贡献度量，其中采用 xGA 来计算凝聚函数。与传统的夏普利方法不同，PRS 方法将联盟限制为战术上可行的球员子集，在合作背景下提供特定于动作的、可解释的边际贡献度量。我们将该框架应用于 2022/23 赛季意大利甲级联赛的 8,421 次射门动作，对 AC 米兰和 SSC 那不勒斯的案例研究揭示了团队内部贡献的异质性。此外，将 PRS 统计量与最终效率指标相结合，突出了合作参与和进球转化之间的差异。