LinNet: Probabilistic Lineup Evaluation Through Network Embedding

Abstract: Which of your team's possible lineups has the best chances against each of your opponents possible lineups? In order to answer this question we develop LinNet. LinNet exploits the dynamics of a directed network that captures the performance of lineups at their matchups. The nodes of this network represent the different lineups, while an edge from node j to node i exists if lineup i has outperformed lineup j. 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, LinNet builds a model on this latent space for the probability of lineup A beating lineup B. We evaluate LinNet 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 69%. In comparison, utilizing the adjusted plus-minus of the players within a lineup for the same prediction problem provides an accuracy of 56%. More importantly, the probabilities are well-calibrated as shown by the probability validation curves. One of the benefits of LinNet - apart from its accuracy - is that it is generic and can be applied in different sports since the only input required is the lineups' matchup performances, i.e., not sport-specific features are needed.