Braess’ Paradox and Basketball
In class, we learned about Braess’ Paradox in terms of road networks. Braess’ Paradox explains how the addition of resources in a particular system of congested roads can, instead of easing the congestion, can increase overall journey time. Intriguingly, the attached article extends this idea to the arena of sports, arguing that losing the best player on a basketball team can sometimes improve the overall performance of the team.
First, it is important to illustrate how basketball is like a traffic network. Each possession of the ball is a journey from point A to the destination, point B, where point B is the basket. There exist a variety of different routes the team can decide to take to get from A to B, with the path being the sequence of passes between the players. The question of concern for the team is of course which paths are the most efficient, and how often each path should be used.
As we saw in lecture, it has been observed that shutting down major roads has a positive effect on traffic flow, a phenomenon that also seems to apply to basketball. The article suggests that in some situations, removing a player can force the other players on offense to seek out a better solution, rather then relying on a Nash equilibrium, which is a phenomenon now known as the Ewing Paradox, named after Patrick Ewing of the New York Knicks.
What is especially interesting is that the Ewing Paradox seems to rely on the selfish behavior of the actors, not on psychological effects such as motivation. To demonstrate the Ewing Paradox, we can think of a player A who begins with the ball looking to pass to one other player, either B, C, D, or E, before that second player makes a shot. Additionally, lets suppose that player E is the team’s best player, and makes the shot more often than the rest. While the conclusion is far from obvious, it is common sense that passing to player E every time is not more efficient than choosing to also include passes to B, C, and D, as the former allows the other team to recognize and exploit a pattern of behavior. This relates back to what we learned about mixed equilibrium in game theory, in that it is crucial to create a situation in which the opponent cannot predict a team’s behavior and is therefore indifferent among the choice of possible actions.
When a basketball team’s best player is taken out of the game, the team is forced to rely on lower percentage shooters, which has the benefit of discouraging the other team from focusing too heavily on any one player. The main takeaway from this article is that relying on the highest-percentage play all or even most of a game is vastly different from achieving the best possible outcome, a point that is well clarified by network theory.
https://www.technologyreview.com/s/414784/basketball-and-the-theory-of-networks/
nice post!