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The problem of shot selection in basketball
1Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota, United States of America. bskinner@physics.umn.edu
Plos One
|February 2, 2012
Summary
In basketball, players must decide when to shoot. This study reveals the optimal shot quality depends on remaining opportunities, suggesting NBA teams might shoot too infrequently early in the shot clock.
Area of Science:
- Sports Analytics
- Decision Theory
- Mathematical Modeling
Background:
- Basketball offense involves continuous shot selection decisions.
- The quality of shot opportunities varies randomly.
Purpose of the Study:
- To develop a theoretical model for optimal shot selection in basketball.
- To determine the minimum shot quality required to take a shot based on remaining opportunities.
Main Methods:
- A theoretical model assuming uniform distribution of shot quality.
- Derivation of a function for the lower cutoff of shot quality (f) based on the number of remaining opportunities (n).
- Inclusion of a finite turnover rate in the model.
Main Results:
- The optimal shot quality cutoff (f) is dependent on the number of remaining opportunities (n).
- Higher values of n necessitate higher-quality shots.
- The model predicts shooting rates for an optimal team and compares them to NBA data.
Conclusions:
- NBA teams may be too hesitant to shoot early in the shot clock.
- The theoretical model provides insights into basketball strategy but has limitations.
- Further research can refine understanding of shot selection dynamics.
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