Estimating NBA Team Shot Selection Efficiency from Aggregations of True, Continuous Shot Charts: A Generalized Additive Model Approach

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Justin Ehrlich, Shane Sanders


We develop a novel type of basketball shot chart, a true shot chart, that uses a generalized additive model (GAM) to estimate total shot proficiency continuously in the half-court as a continuous, 3-D surface ( Unlike conventional shot charts, which do not consider free throw scoring pursuant to a shot from a given location, true shot charts incorporate total points, from the field and free throw line, pursuant to each shot in an NBA game (from 2016-2022 in the study) toward improved explanatory power of offensive efficiency variation across NBA team-seasons. Whereas conventional shot charts show a league-wide three-point premium over the period of the data, true shot charts show a deepening dispremium since 2018, as the free throw rate for three-point attempts is substantially less than that for two-point attempts. Lastly, we develop a novel shot chart summary measure, shot selection efficiency, as the Pearson correlation between expected proportional volume and expected true points, from the field and free throw line, across the half court space; polynomial regression and XGBoost modeling suggest shot selection efficiency is not only win productive, but a “Moneyball” or partly supra-payroll source of wins.