Applying Braess’s Paradox and Other Network Concepts on Basketball
https://www-degruyter-com.proxy.library.cornell.edu/view/j/jqas.2010.6.1/jqas.2010.6.1.1217/jqas.2010.6.1.1217.xml
As someone who doesn’t consider himself particularly strong in math (and particularly the logic kind), Networks has occasionally built brick walls on my way to understanding how certain concepts work, often forcing me to ultimately boil down my line of thinking to “it just works” in order to keep myself from going crazy. One of the core reasons behind this is that Network-related concepts will often quantify qualitative concepts, using assumptions that I find myself hard to wrap my head around. That being said, this has also provided some of the more interesting insights towards how Networks functions in everyday society, and nowhere does this seem more apparent to me than the application of the Braess Paradox.
One of the reasons that the Braess Paradox is so attractive to me as a concept is that it’s easy to follow. I have no trouble believing that when most people approach seemingly trivial tasks like traveling to work, everyone won’t be driving routes out of consideration of decongesting the road for everyone else, nor will they consider any route with a long-term point of view. The second reason why I believe the concept is so fascinating is how, as a result, easily it can be applied to a number of scenarios in ways that would be considered as counterintuitive. One fascinating example that I came across was an article that applied the theory of networks with basketball.
The paper postulates as part of its central idea that, if players can be thought of as routes, it’s possible that removing the best player can improve the team’s overall performance. In order to quantify this, he assigns roles and values to different players that he labels numerically. Player 1 for example is “a quick and capable ball handler, but is mediocre at finishing around the rim,” while 2 is “not particularly good at driving the ball, but is significantly better at finishing around the basket.” Finally, the center 5 is “somewhere in the middle as a shooter: not as good as 2, but better than 1.” Under the observation that 2 is never more successful at driving than 1 and 1 is never more successful at shooting than 2 or 5, a Nash equilibrium can be calculated where there is no reason for 2 to drive or for 1 to shoot. This then leaves whether or not 5 should do the layup or pass to 2. However, removing player 5 from the network increases the odds of scoring by forcing only players 1 and 2 to share the shot between also sharing drives.
This is but one example of the many networks analogies that Brian Skinner uses in his paper, including his analysis of how removing Ray Allen from his team would virtually make no difference compared to constantly passing to him as much as they can (which would be considered the dominant strategy). Of course, he constantly emphasizes that many of his networks analogies are far from one-to-one and misses many of the deeper intricacies of basketball’s metagame. In particular, even though by removing hypothetical player 5 would theoretically increase the team’s scoring odds, it still isn’t the most optimal way of organizing the team (which Skinner goes into slightly more detail into his paper). However, it’s undeniable that many of the comparisons he has made towards common networks topics are still quite reasonable and can be applied in a multitude of ways that should be more closely considered. At the very least, it does show that, outside of some particularly extreme cases, over-reliance on one player may generally not reflect the best possible team play.