Modeling Offense in Team Sports as a Network
Article/blog link: https://www.technologyreview.com/s/414784/basketball-and-the-theory-of-networks/
Paper link: https://arxiv.org/pdf/0908.1801.pdf
Injuries happen in sports, and often the best player on a team will have to sit out of several games. However, there have been cases where the loss of a player has apparently spurred everyone else to perform better, such that the team actually sees better results than before the injury. Such an effect is usually attributed to psychology; fans and commentators talk about weaker or more junior players stepping up to fill the shoes of the injured great.
The linked paper (summarized in the linked article) proposes a different explanation. Brian Skinner at the University of Minnesota writes that we can think of a sports team- basketball, in particular- as a network with players as nodes, passes as edges, and a scoring attempt as a goal. Skinner simplifies offensive basketball strategy into choosing the series of edges towards an attempted shot with the highest “efficiency,” which we can think of loosely as scoring probability. In this analogy, Skinner points out that the loss of a great player (one who has generally high efficiency in paths to the goal) has an effect similar to that of closing a major road in a traffic network, as the paths involving that player significantly lose efficiency or even disappear altogether. He then applies Braess’ Paradox to explain how this could lead to increased team efficiency overall; just as closing a road can change Nash Equilibrium to improve commute times, removing a great player could shift a team’s behavioral equilibrium (kind of like a Nash Equilibrium across paths) and lead to better overall utilization of the team. Skinner makes sure to point out that basketball is much more complex than in his model, but his conclusions could still provide valuable insight for coaches in choosing how to train and use players in basketball and other sports.
This paper connects nicely with the Braess’ Paradox, which we just covered in lecture, as well as re-emphasizes, like Prof Easley has been, that equilibrium does not imply optimality.