Braess’ Paradox in Soccer
In lecture recently, we learned about Braess’ Paradox. The paradox states that for a network of roads where travel time along roads varies by the number of people driving on it, adding new roads can actually lead to slower travel times. This is applicable in other networks, including a soccer team.
Soccer can be considered a network, in which the nodes are the players and the edges are the passes. The possible routes the ball could travel are analogous to road traffic. For each “route”, there is a probability that the ball will be passed along that route. The probability is dependent on what play each player considers to be optimal. For example, the left and right wingers would likely pass to the center forward who is at an optimal spot to score. Thus, the Nash equilibrium is achieved only when the center forward takes a shot or passes.
The paradox lies in the prediction. If the best player, center forward, was not in the network, the left and right wingers would have an equal chance of scoring. With only 2 possible routes to the goal, the probability between left and right is just split 0.5-0.5. This actually in return improves the probability of scoring.
This model is not 100% a prediction of gameplay however, because the more complex factors of player fatigue as the game progresses and teammate chemistry plays a role in complicating the probability.