General Form Equation for the Most Energy-Efficient Basketball Shot

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.