Efficient Statistical Computation for K-Player Basketball Lineups Using Semilattice Structures

Basketball games are characterized by the large number of lineups that can be used by the coach during a game, e.g., with 12 players there are 792 possible lineups. This has led to the development of several statistics for the combinations of players on the court since team performance depends on synergy among players. It is of primary importance for a basketball team to understand the team performance and aid the coaching staff in making the proper decisions. In this work, we apply data mining and knowledge extraction techniques to basketball analytics. In particular, we propose an algorithm for answering questions (including filtering and maximization) about the team performance when any K-Player lineup is on the court (1≤K≤5). The algorithm uses a semilattice representation and a depth-first search traversal that incrementally computes the statistics by exploiting set theory properties. As a case study, we provide experiments by using lineups mainly from the EuroLeague Basketball but also from the National Basketball Association (NBA). Regarding the results, the proposed method is more than 30× faster than the baseline for the EuroLeague and 200× faster for the NBA. Indicatively, we can compute the key traditional cumulative and average statistics for all K-Player combinations of players of the EuroLeague of a single season in less than 1 s. Finally, we introduce indicative statistics using the computations mentioned.