Are made and missed different? An analysis of field goal attempts of professional basketball players via depth based testing procedure

Abstract

In this paper we develop a novel depth-based testing procedure on spatial point processes to examine the difference in made and missed field goal attempts for NBA players. Specifically, our testing procedure can statistically detect the differences between made and missed field goal attempts for NBA players. We first obtain the depths of two processes under the polar coordinate system. A two-dimensional Kolmogorov–Smirnov test is then performed to test the difference between the depths of the two processes. Throughout extensive simulation studies, we show our testing procedure with good frequentist properties under both null hypothesis and alternative hypothesis. A comparison against the competing methods shows that our proposed procedure has better testing reliability and testing power. Application to the shot chart data of 191 NBA players in the 2017–2018 regular season offers interesting insights about these players’ made and missed shot patterns.