In 2004, when the Lakers played the Pistons in the NBA Finals, a lot was made of Kobe Bryant continually jacking up outside jumper after outside jumper—none too efficiently, most of the time—while monster center Shaquille O'Neal was taking fewer shots, but making them much more efficiently. On the surface, it sure seemed as though Shaq should have been getting more shots, and of course Shaq, never a wallflower at the quietest of times, was not loathe to point this out.In 2009, when the Lakers played the Magic in the NBA Finals, a lot was made of Kobe Bryant continually taking jumper after jumper—somewhat more efficiently than before—while his "newly tough" post player Pau Gasol was taking far fewer shots, but making them more efficiently. On the surface, it sure seemed as though Pau should have been getting more shots, and surprisingly Pau, generally a quiet fellow, pointed this out with a certain degree of mordacity.
Obviously, in retrospect, the two series turned out rather differently for the Lakers, which is why the former case was judged by many as the reason the Lakers lost the series, and the latter is just a footnote. Bryant's reputation as a ballhog, already in force before the 2004 Finals, was substantially bolstered by that series, and has only just faded within the last year or two. But is that fair? Is that the only possible interpretation for Kobe's shot-taking? Or could ballhoggery conceivably help a team?
Let me be clear here. There's no question in my mind that Kobe could stand to take fewer shots than he does (unless he's just red hot). The question isn't whether he should take as many shots as he does, but whether he should take shots even when he's shooting them at a lower percentage than the post players. And this really goes for any wing player who dominates the ball (e.g., LeBron, Wade, etc.). I just mention Kobe because I watch all the Lakers games.
I'm going to look at this from a game theory standpoint. Put into elementary game theory terms, Kobe and the Lakers have a set of tactical options, and the defenders have a set of tactical options. If each side optimizes its strategy with respect to the other side, then in the end, the game will reach what's called a Nash equilibrium: Neither side can improve its result by changing its strategy unless its opponent changes it too. (The equilibrium is not named after award-winning point guard Steve Nash of the Phoenix Suns, but John Nash, award-winning mathematician and subject of the award-winning book/movie, A Beautiful Mind.)
Suppose we simplify matters by assuming that the Lakers have just two options: Kobe shoots, or Kobe passes to the post, which then shoots. And the opponents likewise have just two options: double Kobe, or play man-to-man. And naturally, we assume that Kobe shoots a better percentage over man defense than over a double team, and the post shoots better when Kobe draws a double team than when the defense plays man-to-man.
The conditions of the game do not require either side to do the same thing each time. Strategies can be mixed. So Kobe can shoot 60 percent of the time, and pass 40 percent of the time. The defense can double 70 percent of the time, and play man 30 percent of the time. The defense can even have partial strategies like a weak double versus a strong double. Under these simple assumptions, it's fairly straightforward to find the Nash equilibrium, where neither side can unilaterally improve their result. What's interesting about this Nash equilibrium is that both Kobe and the post should shoot exactly the same percentage.
Plainly, that doesn't happen very often. Very often, Kobe shoots a lower percentage than the post (even when factors such as free throws and the three-point line are taken into account); by comparison, it's relatively rare that it happens the other way around. Ostensibly, with Kobe shooting the ball so much, he's not adequately punishing the defense for doubling him. He should instead pass the ball into the post more, gradually causing the defense to double less and play more man defense, up to the point where his shooting percentage rises to match that of the post.
[EDIT: The rest of this post is largely different from what it used to be, because what follows totally swamps in significance what used to be here.]
Having said all that, I'm going to go back and suggest that that strategy actually isn't optimal. How can it be sub-optimal, if it's at the Nash equilibrium? Because the game doesn't stop when the ball hits the rim, so the game theory shouldn't, either.
When players shoot the ball against straight-up defense, the defense has the advantage on rebounding any misses, because they're usually between their man and the basket. However, when a perimeter player shoots against a double team, the rest of the players have a man advantage. In our scenario, this advantage plays out in the post, which means that (a) the chances are much improved for an offensive rebound, and (b) if an offensive rebound is gained, it usually leads to a high-percentage shot.
What effect does that have? Suppose that the man advantage on rebounding leads to an increase of 15 percent in the offensive rebound rate; for example, if the offensive used to get 20 percent of the rebounds, they now get 35 percent. And suppose also that this leads to a successful shot 60 percent of the time. If the wing player misses, let's say, 60 percent of his shots against a double team, and he faces a double team 50 percent of the time, the offensive rebounds effectively amount to an increase in shooting percentage of 0.5 × 0.6 × 0.6 × 0.15, or 2.7 percent. That doesn't sound like much, perhaps, but it's about a standard deviation's worth, the difference between a top-10 guard and a middle-of-the-road guard. And it's how much worse the wing should shoot than the post at the true optimal strategy.
Again, I'm not suggesting that this is how Kobe thinks (although I'm pretty sure he does think that his misses can lead to easy baskets for his team), or that Kobe shoots exactly as much as he ought to. But it might explain why, even if he's shooting a lower (true) percentage than his post players are, he shouldn't necessarily shoot it less.
