  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.
