The math behind basketball free throws - Chamorro Cupuerán, Kevin Andrés (2019)
Nowadays, mathematics and statistics are everywhere and are very important to improve the performance of a company or industry. For example, in basketball industry, professional teams, especially in the NBA use mathematics and statistics to improve the player´s performance and to win games through the study of free throws. Why study free throws? Statistical studies indicate that the number of points obtained in games through free throws is between 20-25% of the total points in a game. It means that the team that will win will be the team that has the highest probability in order to obtain a successful free throw. Therefore, we propose a mathematical model without interaction the board in 2D that which allows us to improve the probability to obtain a successful shot in a player through the analytical, numerical, probabilistic, and statistical study of the optimal release angle and release velocity. Since we are not robots to throw exactly with the angle and velocity that give us. We will find the maximum error allowed in release angle and velocity in order to continue having a successful shot. We use MATLAB software to solve the equations, and problems of univariate and multivariate optimization to obtain the solutions about the heights of Shaq 2.16 m and Kev 1.83 m (author). In addition, we will include Monte Carlo simulations to find the zone of success with the greatest probability of each throw and thus validate our model. Finally, we will our conclusions through a comparative analysis between simulated data and real data using a multiple regression model.