Braess’s Paradox in Soccer
There are star players in any sport. There are the Tom Brady’s of football, Ronaldo’s of Soccer, Mike Trouts of baseball. As a coach, if a star player like this is on your team, you would be crazy not to play them. However, some people may argue that star players may actually decrease the team’s potential.
Trading a star player may relate to Braess’s paradox. Braess’s paradox is a theory of traffic networks. The classic example of Braess’s paradox is a traffic pattern. In large cities such as New York City and London, there are many examples of this seen in the roads. For example, they may open one road and people end up sitting longer in traffic. Alternatively, they may close a road and traffic actually speed up.
In terms of soccer, we can actually think about the game as a network. The players being the nodes, and the passes they make being the edges. The article gives a great example of Braess’s paradox. They set up the network with 2 defensemen, 2 mid-fielders, and a center. In this situation, the center always ends up shooting the ball. When the game is played out this is always the best option. However, when the center is taken out, Nash equilibrium and game theory actually prove that there is a better chance at taking a shot on goal. The network with the center had about a 33% chance of taking a shot at the goal. The network without the center had about a 37.5% chance of taking a shot at the goal.
This may have further implications for the game of soccer. If you have a star player go down, it may actually be beneficial to your team. It is always good to explore other options!
reference: https://mindyourdecisions.com/blog/2014/06/24/the-braess-paradox-in-soccer-how-a-team-can-be-better-without-its-best-scorer/
Commentary of Source: This source discusses the mathematics behind Braess’s Paradox in soccer. The team may have a star player, but that star player may not be the best thing for the team.