Spatial point processes have been successfully used to model the relative efficiency of shot locations for each player in professional basketball games. Those analyses were possible because each player makes enough baskets to reliably fit a point process model. Goals in hockey are rare enough that a point process cannot be fit to each player’s goal locations, so novel techniques are needed to obtain measures of shot efficiency for each player. A Log-Gaussian Cox Process (LGCP) is used to model all shot locations, including goals, of each NHL player who took at least 500 shots during the 2011–2018 seasons. Each player’s LGCP surface is treated as an image and these images are then used in an unsupervised statistical learning algorithm that decomposes the pictures into a linear combination of spatial basis functions. The coefficients of these basis functions are shown to be a very useful tool to compare players. To incorporate goals, the locations of all shots that resulted in a goal are treated as a “perfect player” and used in the same algorithm (goals are further split into perfect forwards, perfect centres and perfect defence). These perfect players are compared to other players as a measure of shot efficiency. This analysis provides a map of common shooting locations, identifies regions with the most goals relative to the number of shots and demonstrates how each player’s shot location differs from scoring locations.

中文翻译：

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通过算法解构击球位置，以此作为曲棍球击球质量的一种方法

空间点过程已成功地用于为职业篮球比赛中每个球员的射门位置的相对效率建模。之所以能够进行这些分析，是因为每个参与者都制造了足够的篮子来可靠地适应点流程模型。曲棍球的球门非常罕见，以至于得分过程无法适应每个球员的球门位置，因此需要新颖的技术来获取每个球员的射门效率度量。Log-Gaussian Cox过程（LGCP）用于对每个NHL球员在2011–2018赛季中至少拍摄500张照片的所有射击位置（包括目标）进行建模。每个玩家的LGCP表面都被视为图像，然后将这些图像用于无监督的统计学习算法中，该算法将图片分解为空间基函数的线性组合。这些基函数的系数显示为比较玩家的非常有用的工具。为了合并目标，将导致目标的所有射门位置视为“完美球员”，并在同一算法中使用（目标进一步细分为完美的前锋，完美的中锋和完美的防守）。将这些完美球员与其他球员进行比较，以衡量射门效率。该分析提供了常见射击位置的地图，确定了相对于射击次数而言目标最多的区域，并演示了每个玩家的射击位置与得分位置之间的差异。导致进球的所有射门位置都被视为“完美球员”，并在同一算法中使用（目标进一步分为完美前锋，完美中锋和完美防守）。将这些完美球员与其他球员进行比较，以衡量射门效率。该分析提供了常见射击位置的地图，确定了相对于射击次数而言目标最多的区域，并演示了每个玩家的射击位置与得分位置之间的差异。导致进球的所有射门位置都被视为“完美球员”，并在同一算法中使用（目标进一步分为完美前锋，完美中锋和完美防守）。将这些完美球员与其他球员进行比较，以衡量射门效率。该分析提供了常见射击位置的地图，确定了相对于射击次数而言目标最多的区域，并演示了每个玩家的射击位置与得分位置之间的差异。