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Basketball and the Theory of Networks

Losing the best player on the team can sometimes improve its performance. Network theory explains why.

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It’s not hard to see how the game of basketball is like a network. Think of the pattern of passes that players make to score a basket as one route through a network of all possible combinations of passes.

But it’s much harder to imagine how to use this way of thinking to come up with useful strategies for coaches and players. Yet, that’s exactly what Brian Skinner, a physicist at the University of Minnesota in Minneapolis, has done.

His idea is that this kind of network is similar to one formed by cars travelling through a system of roads. Each car is like a single possession of the ball, which moves through the network until it reaches its goal.

Although traffic is notoriously hard to model accurately, network theory can give useful and important insights into the way that traffic behaves.

For example, traffic patterns tend toward a Nash equilibrium, in which selfish drivers calculate the best route in the same way, thereby failing to improve their journey times by taking a different route.

Were drivers to vary their routes occasionally, all would reach their destination more quickly, on average. That’s because the most heavily clogged roads, which act as bottlenecks, would run more smoothly. (Skinner talks about this with great clarity in the paper.)

Sometimes it’s possible to force drivers to change routes. In recent years, researchers have noticed how closing major roads has improved the flow of traffic through a city, a phenomenon called Braess’s Paradox.

That makes for an interesting basketball analogy. Players can be thought of as “routes” through the network. The implication of Braess’s Paradox is that removing the best player can sometimes improve a team’s performance, a phenomenon Skinner calls the Ewing Paradox.

Of course Skinner cautions against taking the analogy too far. His model doesn’t capture many of the complexities of basketball. For example, the actions of the defense aren’t modeled at all.

But it has interesting implications for analysts. It may be that many teams tend towards a Nash equilibrium in their choice of plays when there may be a better solution. Network theory could help them discover these better strategies.

And if it works for basketball, why not for other games in which a sequence of passes can be thought of as routes through a network of all possible passes? Think netball, soccer, hockey, etc.


Ref: arxiv.org/abs/0908.1801: The Price of Anarchy in Basketball

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