## Braess’ Paradox in Sports

The sports world turns out to have its own version of Braess’ Paradox. Humorously coined Ewing’s Paradox by sports writer Bill Simmons in 2001, it describes how teams mysteriously play better when their star player is not on the court or field. The name of the paradox refers to Patrick Ewing, whose teams (both the Georgetown Hoyas and the New York Knicks) fared better when he was injured or on the bench due to foul trouble. The Ewing Paradox can be applied to other sports as well. Other notable examples can be found on Simmons’ blog – http://proxy.espn.go.com/espn/page2/story?id=1193711. This phenomenon can be thought of as a consequence of the “price of anarchy,” where the selfish behavior of the players results in a less-than-optimal performance. A star player earns his reputation because his efficiency in one or more aspects of performance. According to Brian Skinner of the University of Minnesota, a Nash equilibrium strategy would state that (in the case of basketball) the star player would shoot until his performance equals that of the rest of his teammates. However, the opposing team is aware of this as well. As such, it will concentrate much of its defensive efforts on that one player, dramatically reducing his efficiency. According to Skinner’s research, “the team’s optimum strategy is for [the star player] to shoot almost exactly the same fraction of shots as his teammates.”

The Ewing Paradox is remarkably analogous to Braess’ Paradox. In both, there seems to be an apparent Nash equilibrium strategy. The extra capacity added to the network in Braess’ Paradox could be compared to the star player’s notable skills the Ewing Paradox. Braess’ Paradox describes how adding a shortcut to a traffic network could be ineffective because users of that network will begin to flood the shortcut, rendering it useless. In both paradoxes, the optimal strategy at first glance seems to be to use the path that guarantees the fastest/most effective result. However, due to the “price of anarchy,” the efficiency of that one path quickly becomes exhausted as it becomes overused and the other paths become quicker and more effective. In both cases, the Nash equilibrium is not the optimal strategy because the capacity of the route that seems best quickly becomes overwhelmed. Rather, the equal distribution of traffic/the ball amongst all possible routes is the best strategy.

http://arxiv.org/pdf/0908.1801v3.pdf

http://proxy.espn.go.com/espn/page2/story?id=1193711