Sports analytics and optimization for team formation problems

Abstract

Operations Research (OR) has always covered a diverse domain of mathematical techniques applied to a variety of application areas since its inception as a field to leverage analytical techniques to improve decision-making. In this dissertation, we integrate the growing sub-domain of OR known as Analytics with the Team Formation Problem, specifically in the context of sports. To begin, we develop a novel weighted network clustering algorithm to classify players in the National Basketball Association (NBA) into archetypes. Next, drawing upon classical Team Formation Problem (TFP) literature, we integrate these archetypes, or team roles, into a nonlinear mixed-integer programming model that is the first to consider the NBA's draft, trade, and free agency aspects of player acquisition simultaneously. To inform vital parameters in this model, we develop predictive models to assign amateur players to archetypes, to quantify synergy between archetypes, and to predict the individual value of amateur players in the league. We show that this formulation prescribes a realistic and balanced team by using a case study from the 2019-2020 NBA off-season. Then, we develop a multi-team formation model that addresses decisions of multiple teams simultaneously, preference of free agents regarding selecting their team, and other league-specific considerations such as the economic value of Superstars that they bring to their team due to their popularity. We introduce a game-theoretic model that is designed to improve competitive balance across the league from a macro level. We show that our framework respects the preferences of autonomous free agents, prescribes realistic draft picks, and increases competitive balance across the league. Solving large-scale instances of the proposed model can become intractable due to its combinatorial nature, as evidenced by the near-optimal solutions that can only be reached after an hour of computing time. Therefore, in the final chapter, we generalize the team formation model and develop a column generation approach as well as a column generation-based heuristic, which provides a tight dual bound and high quality lower bound, respectively in order to close the optimality gap. This sets the foundation for a branch-and-price approach as an exact solution methodology to such problems. Overall, our contributions in this dissertation provide an analytical approach to team-building, in both a sports and generalized settings, accompanied by a solution methodology.