Nba Objective Function
Our project focuses on seeking successful strategies that a basketball team can use in order to maximize the expected number of points scored. For our basic model, we will set up an integer linear program that will be solved using branch and bound and use statistics available through the NBA to constrain our objective function by restricting the field goal attempts per quarter, 2- and 3-point shot attempts per quarter, and 2- and 3-point shots made per quarter. The objective function will look to maximize the expected number of points scored by maximizing the expected number of 2- and 3-point shots made and adding the average number of free throw points.
Our motivation is to optimize the athletes’ skills and talents to produce the highest …show more content…
Our objective function calculates the maximum expected number of points scored in one game by optimizing the number of 2-point and 3-point shots attempted per quarter and using the average success rate for 2-point and 3-point shots. $k$ is a constant variable equal to the average number of points from free throws. We can use this model to calculate the optimal strategy for the overall NBA, \href{https://stats.nba.com/teams/traditional/?sort=FG3M&dir=-1&PerMode=Totals}{specific teams}, or \href{https://stats.nba.com/leaders/?StatCategory=FG3M&PerMode=Totals}{a specific player's} statistics, depending on what results we are interested in. We will start by calculating the optimal strategy for the overall NBA and five NBA teams; the Golden State Warriors, the Dallas Mavericks, the Indiana Pacers, the Cleveland Cavaliers, and the Los Angeles …show more content…
$y_{i,j}$ gives the maximum number of the type of shot per quarter where i = [2,3] represents the type of FGA and j = [1,4] represents the quarter. For example, $y_{2,1}$ is the maximum number of 2-point shots attempted in the first quarter of a game. All of these maximums are taken from the last years seasons (2016-2017) unless otherwise stated. $x_{i,j}$ are explanatory variables that give the number of attempted i-point shots per quarter j. Lastly, $c_{i,j}$ gives the average success rates for the i-point shots per quarter j; therefore, $c_{i,j}$ will be [0,1].
Here, we assume that $s_j$ afftects FGA equally and that $b_j$ only affects 2-point shots. This is a very broad assumtion and will reduce the accuracy of the results; however, it is a good estimate.
We also note that $s_j, b_j \geq
Our motivation is to optimize the athletes’ skills and talents to produce the highest …show more content…
Our objective function calculates the maximum expected number of points scored in one game by optimizing the number of 2-point and 3-point shots attempted per quarter and using the average success rate for 2-point and 3-point shots. $k$ is a constant variable equal to the average number of points from free throws. We can use this model to calculate the optimal strategy for the overall NBA, \href{https://stats.nba.com/teams/traditional/?sort=FG3M&dir=-1&PerMode=Totals}{specific teams}, or \href{https://stats.nba.com/leaders/?StatCategory=FG3M&PerMode=Totals}{a specific player's} statistics, depending on what results we are interested in. We will start by calculating the optimal strategy for the overall NBA and five NBA teams; the Golden State Warriors, the Dallas Mavericks, the Indiana Pacers, the Cleveland Cavaliers, and the Los Angeles …show more content…
$y_{i,j}$ gives the maximum number of the type of shot per quarter where i = [2,3] represents the type of FGA and j = [1,4] represents the quarter. For example, $y_{2,1}$ is the maximum number of 2-point shots attempted in the first quarter of a game. All of these maximums are taken from the last years seasons (2016-2017) unless otherwise stated. $x_{i,j}$ are explanatory variables that give the number of attempted i-point shots per quarter j. Lastly, $c_{i,j}$ gives the average success rates for the i-point shots per quarter j; therefore, $c_{i,j}$ will be [0,1].
Here, we assume that $s_j$ afftects FGA equally and that $b_j$ only affects 2-point shots. This is a very broad assumtion and will reduce the accuracy of the results; however, it is a good estimate.
We also note that $s_j, b_j \geq