Operations Research in Engineering and Technology Management
Free agents (Sports) -- Management -- Technological innovations, Integer programming, National Basketball Association, Mathematical optimization, Linear programming
The National Basketball Association (NBA) is a professional basketball league consisting of 30 teams and up to 15 players per team. The four main methods to build team rosters are through free agency signings, trades, development league call ups and drafting new college and international players.
There are existing tools for analyzing the effects of trades such as the ESPN NBA Trade Machine , but no widely available tools to determine optimal NBA free agent signings. An optimization model was made using R’s mixed integer linear programming package with an interactive user interface for sensitivity analysis. The user interface allows for adjustments in team salary spending and the model’s free agency pool can be adjusted to account for player signings on other teams.
The model uses win shares (WS) as the key performance indicator to optimize overall team WS, which improves team efficiency (WS/team salary). WS was developed by Oliver  and accounts for an individual player’s offensive and defensive contributions to team wins. Quantitative measures (WS, salary, position quantity) were used for simulation in place of qualitative measures (leadership, chemistry, behavior/attitude), which are subjective values that may vary based on a team’s assessment of the player.
While other models have attempted to predict a free agent’s value based on the available players over time , our model takes a reactionary approach,which initially outputs the optimal free agent signings for the team by position using the player’s last available salary. The offered salary can be adjusted based on a team’s valuation of each player. Since the other team’s evaluation of each player and the timing of free agents signings are unknown, a model that can quickly adapt to the fluid free agent market is more useful than a hypothetical predictive model.
The results show the optimal free agent signings for each of the 17 teams under the $116M salary cap for the 2020-2021 NBA season. As expected, the model selects high efficiency (WS/salary) players, many of which are on their rookie contracts and are selected as optimal picks for multiple teams. A general manager (GM) can use the initial results to finalize the team’s evaluation of a player and adjust offered free agent salaries to see the effect on team WS and roster composition. If a free agent is signed by another team, the player can be removed from the FA pool and the model can be run again for updated optimized selections.
The model is intended as a tool to optimize free agent signings. Future models can include the effects of potential draft picks on team WS. While first round draft pick salary scales are known, more analysis and modeling must be done to incorporate how amateur statistics translate to NBA impact.
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Rondema, Andrew; Yamamoto, Matt; Tonkal, Mert Cihan; Sissoko, Mahamadou; and Lopez, Manolo, "Constructing Winning NBA Teams Using Mixed Integer Programming" (2019). Engineering and Technology Management Student Projects. 2283.