  We address the question of how to quantify the contributions of groups of
players to team success. Our approach is based on spectral analysis, a
technique from algebraic signal processing, which has several appealing
features. First, our analysis decomposes the team success signal into
components that are naturally understood as the contributions of player groups
of a given size: individuals, pairs, triples, fours, and full five-player
lineups. Secondly, the decomposition is orthogonal so that contributions of a
player group can be thought of as pure: Contributions attributed to a group of
three, for example, have been separated from the lower-order contributions of
constituent pairs and individuals. We present detailed a spectral analysis
using NBA play-by-play data and show how this can be a practical tool in
understanding lineup composition and utilization.
