Linnet: Probabilistic lineup evaluation through network embedding

Abstract

Which of your team’s possible lineups has the best chances against each of your opponent’s possible lineups? To answer this question, we develop LinNet (which stands for LINeup NETwork). LinNet exploits the dynamics of a directed network that captures the performance of lineups during their matchups. The nodes of this network represent the different lineups, while an edge from node B to node A exists if lineup (Formula Presented) has outperformed lineup (Formula Presented). We further annotate each edge with the corresponding performance margin (point margin per minute). We then utilize this structure to learn a set of latent features for each node (i.e., lineup) using the node2vec framework. Consequently, using the latent, learned features, LinNet builds a logistic regression model for the probability of lineup (Formula Presented) outperforming lineup (Formula Presented). We evaluate the proposed method by using NBA lineup data from the five seasons between 2007–08 and 2011–12. Our results indicate that our method has an out-of-sample accuracy of 68%. In comparison, utilizing simple network centrality metrics (i.e., PageRank) achieves an accuracy of just 53%, while using the adjusted plus-minus of the players in the lineup for the same prediction problem provides an accuracy of only 55%. We have also explored the adjusted lineups’ plus-minus as our predictors and obtained an accuracy of 59%. Furthermore, the probability output of LinNet is well-calibrated as indicated by the Brier score and the reliability curve. One of the main benefits of LinNet is its generic nature that allows it to be applied in different sports since the only input required is the lineups’ matchup network, i.e., not any sport-specific features are needed.