This is a review of the knapsack formulation research conducted by Pravek Karwe, Rishi Khera, Narain Krishnamurthy, and Sarah Tracy.
At the end of every season NBA teams need to evaluate those players who are now unrestricted free agents to determine which players would have the greatest impact on their team in future years. Simply looking at how many points a player scores will not give the team the entire picture. There are many intangible factors that need to be considered – players can positively affect game outcomes without actually scoring any points.
A starting point for evaluating a player’s value is the Player Efficiency Rating (PER). John Hollinger developed the PER, an all-in-one basketball rating, which attempts to boil down all of a player’s contributions into one number. The PER is standardized which makes it easier to compare players across the NBA. PER has some limitations in that it focuses mainly on offensive statistics, including only two defensive stats. It also does not include any intangible statistics.
In order to update the PER to include defensive and hustle skills, extra value will be added to each player by adding in five additional statistics: screen assists, ball deflections, loose balls recovered, ability to cause opponents to make fouls, and contested shots. This model will more accurately reflect the expected value of any player. Positional needs of the team and salary constraints are also incorporated within the model.
It must be kept in mind that while this model will determine the top choices for a team out of the group of free agents, other teams will also be trying to sign these players. As free agents are signed by other teams the model would have to be run again incorporating the remaining free agents to determine which of them are best suited to the team’s needs.
To further improve the model, the thought processes of the team should be taken into account. Depending on their previous season, teams can expect to make it to the playoffs the next year or may be plan to rebuild instead. Teams working towards making it to the playoffs will tend to want older, more experienced players who have already developed the skills needed to help lead the team. A team planning to rebuild will be more interested in signing young talent that they can help mold and grow into future leaders. This idea of the team’s thought processes was added into the model using the difference between the average age of players in the league and the age of the individual player. Younger players would have a positive difference while older players would have a negative difference.
Possible future enhancements to the model could include analyzing player styles and looking at salary cap exceptions.
This improved PER model assists analysts and teams in determining which free agent players will be able to assist the team in achieving their future goals.
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