Abstract
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.
Funding source: Natural Sciences and Engineering Research Council of Canada
Award Identifier / Grant number: RGPIN-2015-04221
Award Identifier / Grant number: RGPIN-2014-06187
Funding source: CANSSI Collaborative Research Team Grant
Acknowledgment
We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference numbers RGPIN-2015-04221 and RGPIN-2014-06187]. Additional support was provided by a CANSSI Collaborative Research Team grant. We would also like to thank Michael Schuckers and Nathan Sandholtz for helpful conversations regarding this work.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: This study was supported by Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference numbers RGPIN-2015-04221 and RGPIN-2014-06187] and CANSSI Collaborative Research Team grant.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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