When a Point Is Not Worth a Point

The variety of responses to my article “The Hidden Value of the NBA Steal” has been amazing. I expected there to be a lot of questions and criticisms, but I didn’t anticipate the depth and thoroughness of reader analysis.

Some of the points people raised (pro and con) I expected; some I did not. For example, a number of people objected to my characterization of the hoop as only “slightly larger” than the ball. As I’ve learned, the diameter of a basketball (9.2 inches) is only 52 percent of the diameter of the rim (18 inches). I definitely thought the ratio was higher. The maximum distance a ball can clear the rim is only 4.4 inches, so perhaps I should have said “not too much larger” instead. But the point — that shooting is beautiful, and I understand why we devote so much attention to it — stands.

I���ve picked what I think are the four most common and most salient questions and comments, and will respond to them in four parts. Here’s the first:

“Can a steal really be worth NINE points?”

This question arose in various forms, many of which were not phrased as a question and some of which I can’t repeat in polite company.

Here’s one of the more gently worded versions, emailed in from “Johnny”:

Isn’t the “theoretical” upper bound on the value of a steal capped at 8 points? I say this by looking at the limiting case where on every possession we don’t steal the opposing team makes a three pointer, is fouled and then makes the free throw. Then on every possession where we steal, we make a three pointer, is fouled and then makes the free throw and every possession where we don’t steal we don’t score. In this case the value of a steal would be 8 points (saved 4 points from making the steal and gained 4 points from scoring after the steal). Now this is obviously completely unrealistic, but I find it hard to believe a steal could be worth anything more.

And here’s the language in my article that some people objected to:

Yes, this pretty much means a steal is “worth” as much as nine points. To put it more precisely: A marginal steal is weighted nine times more heavily when predicting a player’s impact than a marginal point.

The confusion here is somewhat understandable and probably stems from how we understand the word “worth” (the quotes were meant to signify that I was using a precise definition). The finding isn’t that getting a steal improves a team’s chances of winning by the same amount that adding nine points would. But kudos for being skeptical enough to imagine me capable of such absurdity. By “worth,” I meant the ability of steals to predict a player’s impact (as measured by the amount his team suffers when he doesn’t play) versus the ability of points to do the same.

Conversely, a few stats-savvy readers disliked this comparison from the opposite direction:

In other words, raw points scored have been so discredited in the advanced statistical community that using them as a basis of comparison is too easy! I should note that the outsize predictive value of steals is not especially controversial in that community either. For people interested in the cutting-edge, box-score-based predictive metrics, I recommend Daniel Myers’ work on “advanced statistical plus minus” and its ilk (check out the monster coefficient for steal percentage).

A good number of readers also concluded that comparing “worth” of steals to points in this way invited confusion, and thus may have been a mistake in presentation, if not of analysis. The logic goes like this: If a steal only nets us two points or so, you’re “inviting confusion” by saying it’s “worth” nine points. People know that two points is not nine points, so it looks ridiculous.

Perhaps they are right that this is difficult for someone unfamiliar with the issues to read idly. But the reason I phrased it that way originally, and stand by that language, is simple:

When it comes to predictions, a point is not worth a point.

I think understanding this concept is important, and inviting people to deal with it instead of skirting around it is worth the debate. This is a fundamental lesson of empirical thinking: The immediate value of something can be (and often is) very different from its predictive value.

Benjamin Morris researches and writes about sports and other topics for FiveThirtyEight.