Sports analytics for balanced team-building decisions

We address a team-building problem for a basketball team, where the team decides on new players to draft, current players to trade with those of other teams, and/or which free agents to acquire, to maximize its total value. Here, the team value is considered as the “ability to win a match.” While the individual values of current players in the league are directly obtained from historical data, we propose a predictive model to predict the individual values of collegiate players. We also consider an additional value that comes from the synergy potential among players on the team. We consider “archetypes” of players that represent logical groupings of players based on their characteristics. To estimate the synergy potential between two players, we develop a new metric that encompasses the synergy potential between archetype pairs that each player belongs to. Since the archetypes of collegiate players are unknown, before the synergy estimation, a classification model is performed in order to predict archetypes of collegiate players. These inform a mixed-integer nonlinear programming model for the draft, trade and free agent acquisition problem that maximizes the total team value and balances the synergy among players. We reformulate the objective function in order to overcome computational challenges due to its nonlinearity. Finally, we conduct a case study on a National Basketball Association (NBA) team using 2019–2020 data. Results are discussed and compared with the actual decisions to validate our approach.