Basketball possessions are like cars

Here's a fascinating paper making an analogy between basketball possessions and a well-known networking problem. The well-known problem being: suppose there are two cities A and B with two roads connecting them, one of them being a highway and the other being an alley shortcut. On the highway, a trip from A to B always takes ten minutes, no matter how many cars are on it at any given moment. The length of the same trip on the alley depends on how many cars are traveling with you: if you're by yourself, it'll take you one minute; if there's two cars, each will travel for two minutes; if there's three, the trip will take each three minutes, and so on. Suppose also that there are ten cars, and all drivers sequentially decide which road to take, but without knowing how many drivers are ahead of them in line. Then, the pure strategy Nash equilibrium is that all drivers pick the alley, and all of them travel for ten minutes. However, if there were a "central authority" that could force five drivers to pick the highway, and five to pick the alley, the total driving time would be reduced.

Now the analogy in the paper is: basketball possessions are like cars (the goal of each of them is to get from some starting point A to B, B being the basket), and different possible plays are like different roads. Some roads have higher initial efficiency; for example, Kobe Bryant shoots better than Derek Fisher. However, like with the shortcut alley, that efficiency is decreasing with use; the more possessions end with Kobe shooting, the more Kobe is defended against, so it is sometimes optimal for a team to make their best shooters shoot less than they actually do.

So far so good. However, like all game-theoretic arguments about sports that I've ever seen, this one also turns on one crucial assumption, which is that all sports teams care about is maximizing the probability of winning. I think this assumption is not true. Sure Lakers fans want Lakers to win; but they also want to see Kobe shoot a lot, and if Kobe shooting a lot decreases the probability of a Lakers win somewhat, well that's just the price that fans are willing to pay for a good show. So Kobe shooting a lot is not necessarily an inefficiency. The coaches probably know what they're doing: they're giving the audience what it wants.