Persistent homology of NBA lineups usage

We present a method to analyze lineup usage patterns in the NBA, based on topological data analysis. Traditional network analysis is based on which pairs of players are on the court together. Instead, we construct a simplicial complex using complete information about the lineups – all five players at once. We weight the lineups by possessions played and compute the persistent homology to detect ‘holes’ in the complex, reflecting groups of players who do not play together at the same time. We demonstrate the method on twenty years of NBA lineup data, give examples of how the results can be used and interpreted, and discuss further applications.