In a good year, there's little benefit to an earlier NBA draft pick

1/17/2014 02:30:00 PM
During a college debate, I once accused our opponents of knowing nothing about sports, and went on to win the round. Those who know me know how hilarious that is.
Matt Yglesias has a post arguing, correctly, that having a lot of talent in this year's NBA draft class is a good reason for teams not to want the first draft pick as much as usual. But, I think Yglesias goes a little astray on the math. He frames the post in terms of decision making under uncertainty, which I will circle back to in a second, but I want to highlight that his point is just as valid even when there is no uncertainty.

So let's suppose we are NBA managers and that we have perfect clairvoyance such that we know exactly how valuable each player will be. So we can plot each of the players on an index like so:
With relatively few great players in the draft class, the marginal benefit of an earlier draft pick is potentially quite large.
This is a scenario where there are relatively few really good players in the draft class. As you can see, there is a huge advantage to having one of the first few draft picks. But this year's graph would look more like this:
When there are lots of great players in the draft class, the marginal benefit of an earlier draft pick is pretty small.
There are still some looser picks at the far right, but on the whole the marginal benefit of getting an earlier draft pick is much smaller. There's very little difference in the quality of the player you get between any two rounds of the draft, so it simply isn't as worthwhile to try to get an earlier draft.

Of course, what Matt Yglesias said about decision making under uncertainty is also true, but has nothing to do with the relative preponderance of great players in this year's draft class. Here's the first graph--representing a normal year with few great players--but with standard error bars added reflecting considerable uncertainty about their future value to the team:
Uncertainty about player quality also diminishes the marginal benefit of an earlier draft pick, regardless of how many great players there are.
Even though there's potentially a huge expected gain from an earlier draft pick, there's so much uncertainty that we can't actually be sure that the "best" picks are really much better than any of the other picks. In such a situation, there's less marginal incentive to try to get an earlier draft pick, because the benefits could turn out to be pretty small, or even negative.