Much has been made of the fact that our methodology finds Kobe Bryant, Lebron James, and many other high usage players to be undershooters. Over on TrueHoop, Devin Kharpertian made a post about this result of our research which, unsurprisingly, led to a good old fashioned Kobe vs. Lebron flame war, with each side refusing to believe the other’s hero is not a good for nothing chucker. When understood correctly this should not be a surprising result at all.

The fact is, very few elite players in our data were *not* under-shooters. Most teams would be better *in the short term*, if their superstars were more aggressive with the ball. And in fact, almost without exception, these superstars get much more aggressive with the game on the line and, I suspect, this is mostly in their teams best interest.

Being an under-shooter in our research simply means that if you were to create an additional scoring opportunity *on the margin* (estimating the usage curve for each player is very important here, I detail the math in the paper and will make an effort to post on the intuition soon), in any given period of the shot clock, that shot would be of better value than your team usually gets when you pass up that shot and your team looks for an opportunity later. Being an under-shooter or an over-shooter does not necessarily mean you are a good or a bad player or even an efficient or inefficient offensive player. It simply means that your team might see a boost in overall efficiency if you altered your threshold for taking a shot by a little bit. Given that players have limited amounts of energy and are exposing themselves to injury risk on every drive, it is only natural that elite players should err on the side of letting their teammates do more than their “optimal” share of the work. In fact we should not be surprised that many of the names at the top of the undershooting list are guys who have had or are having serious knee problems and may face an especially steep trade-off in terms of their own health.

Sadly, it is far beyond the power of this research to determine whether or not these superstars are optimally trading off their teams immediate offensive efficiency for their own long-term health, but it is clear that such a trade-off exists.

Just for fun, I am attaching the entire list of NBA players and our estimate of how much their shooting behavior deviates from dynamic efficiency. The numbers on the right are t-statistics which show how many standard deviations each player is from optimality. Just like with adjusted plus/minus, our results are not based on an infinite sample size and any given player’s t-statistic comes with a confidence interval of roughly +/- 2 (this means that players between -2 and 2 might still be optimal). Thus we hang our hats *NOT on our results for any given player*, but on the idea that the biggest deviation from optimality we observe (elite guys undershooting) can be easily justified and that the NBA appears to get shot selection mostly right.