General Form Equation for the Most Energy-Efficient Basketball Shot

Authors

  • Jeffery Zhang University of Toronto Schools
  • Trevor J. Jones Princeton University

DOI:

https://doi.org/10.47611/jsrhs.v12i3.4706

Keywords:

Basketball, Physics, Mathematical Optimization, Kinematics, Optimal Release Velocity

Abstract

Although ball shooting is one of the fundamental skills of basketball, it is energy intensive and exhausts players quickly. Because of this, effective shooters will have less time to play on the court, which can be the difference between winning and losing for basketball teams. In the National Basketball League (NBA), pride, expectations, and millions of dollars in investments are at stake, making winning all the more critical. Improving basketball shooting accuracy may provide the most robust path forward to increasing team-specific wins. So, to boost shooter performance, we derived an equation that calculates the optimal velocity to shoot a basketball from every position on the court. This ‘optimal’ velocity minimizes a shooter’s energy expenditure so players can conserve their energy and stay effective in the game longer, boosting their team’s chances of winning. We used Newton’s second law and kinematics, vector algebra, and calculus to derive the optimal velocity equation and ultimately implemented it in Python for public use. We concluded that the optimal angle for mid-range shots (3 to 5 meters) is 55 to 51 degrees and 49 to 47 for three-point shots.

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Author Biography

Trevor J. Jones, Princeton University

Boozhoo! I am a PhD. candidate at Princeton University in the Liquids & Elasticity Laboratory. My work focuses on the adaptation of ’everyday’ and soft matter physics to inspire, inform, and design new technologies. This curiosity-driven research aims to develop predictive models of nonlinear systems inspired by mechanical instabilities, biology, and art. On the day-to-day you will find me using bubbles and balloons or beads and string as a craftman’s tools to build new materials.

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Published

08-31-2023

How to Cite

Zhang, J., & Jones, T. (2023). General Form Equation for the Most Energy-Efficient Basketball Shot. Journal of Student Research, 12(3). https://doi.org/10.47611/jsrhs.v12i3.4706

Issue

Vol. 12 No. 3 (2023)

Section

HS Research Projects

Copyright (c) 2023 Jeffery Zhang; Trevor J. Jones

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