Abstract Every shot in basketball has an opportunity cost; one player’s shot eliminates all potential opportunities from their teammates for that play. For this reason, player-shot efficiency should ultimately be considered relative to the lineup. This aspect of efficiency—the optimal way to allocate shots within a lineup—is the focus of our paper. Allocative efficiency should be considered in a spatial context since the distribution of shot attempts within a lineup is highly dependent on court location. We propose a new metric for spatial allocative efficiency by comparing a player’s field goal percentage (FG%) to their field goal attempt (FGA) rate in context of both their four teammates on the court and the spatial distribution of their shots. Leveraging publicly available data provided by the National Basketball Association (NBA), we estimate player FG% at every location in the offensive half court using a Bayesian hierarchical model. Then, by ordering a lineup’s estimated FG%s and pairing these rankings with the lineup’s empirical FGA rate rankings, we detect areas where the lineup exhibits inefficient shot allocation. Lastly, we analyze the impact that sub-optimal shot allocation has on a team’s overall offensive potential, demonstrating that inefficient shot allocation correlates with reduced scoring.

中文翻译：

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测量篮球的空间分配效率

摘要篮球中的每一投都有机会成本。一个球员的投篮机会消除了队友的所有潜在机会。由于这个原因，最终应该考虑相对于阵容的投篮效率。效率的这一方面（在阵容中分配镜头的最佳方法）是本文的重点。由于阵容中投篮尝试的分布高度取决于球场位置，因此应在空间范围内考虑分配效率。我们通过将球员的射门得分百分比（FG％）与他们在球场上的四个队友以及射门的空间分布情况进行比较的射门得分尝试（FGA）比率，提出一种新的空间分配效率度量。利用美国国家篮球协会（NBA）提供的公开数据，我们使用贝叶斯分级模型估算进攻性半场中每个位置的球员FG％。然后，通过订购阵容的估计FG％，并将这些排名与阵容的经验FGA速率排名配对，我们可以检测出阵容表现出无效的射门分配的区域。最后，我们分析了次优射门分配对球队整体进攻潜力的影响，证明了效率低下的射门分配与得分降低相关。