Visualization: The Outer Limits of the Usage-Efficiency Relationship

I was going to call this the convex hull of the usage-efficiency relationship, but decided that would truly scare away everyone who was actually going to be interested in this.

You have probably heard of the usage-efficiency relationship. It's debatable in some circles, and taken for granted in others. The idea is that the more a player shoots, in general, the less efficient he becomes. Ideally, we would just regress TS% (or some other measure of efficiency) onto USG% (or some other measure of volume) and see a nice, tight (well-correlated) and linear relationship. Like this one for 2012 (data points are for players with greater than 500 possessions):

TS% vs. USG% for 2012 (players with > 500 possessions)

Huh. That looks pretty crappy and not at all what we were expecting to see, right?  Well, one complicating factor is that some players that don't shoot a lot sometimes are very efficient (see Tyson Chandler) while other players that don't shoot a lot are very inefficient (see Ben Wallace). This complicates the matter. Others have thought of ways to tease out the hypothesized effect (see Eli Witus' great study for one of the best examples).

I kind of stumbled upon another way to possibly see this effect. I was looking at players (since the 3-pt shot was installed) that have shot greater than 55% TS and had greater than 25% USG. I took these 300 or so players and plotted TS vs. USG  and this is what I found:

The "outer limits" of the usage-efficiency relationship.

A convex hull is the set of points that lies at the boundary of a N-dimensional function. In 1-D, it would simply be considered the two end points of a line. When we plot TS% vs. USG% for these top players, what we find is that there is a boundary running along the diagonal that corresponds very well with our intuition underlying the debate. And although I can't prove it, I think this is a real effect. And it's amazingly linear!

It's also interesting to see the names along that boundary. They are not unexpected, are they? Now, getting back to 2012. There are two players who come close, but fall short of greatness (defined in this way, at least):

LeBron James and Kevin Durant comes close to the convex hull, but fall a little bit short. It gives you some idea how great those other seasons were.

You are probably not shocked to find LeBron James and Kevin Durant near the boundary.

10 thoughts on “Visualization: The Outer Limits of the Usage-Efficiency Relationship”

  1. If the more a player shoots the less efficient he is—for some reason this discussion makes me want to go check Monta's stats with the Bucks—then you would be able to see the effect looking at players whose usage rate changes. But you would also have a selection effect. Bad shooters like Ben Wallace would probably be less efficient if they shot more (wait, where's Andris on here), but because they're bad they don't get the opportunity or don't want to shoot as much. I think the relationship works with players at the boundary because they are all stars, who are good shooters for the role they play. I would be interested in seeing who TS changes when players change teams and their usage changes (although of course the scheme and the players age would also be different).

    1. That's definitely true, but perhaps, that is also explained by the lower usage. Players who can create their own shots will tend to have higher USG. And obviously unassisted shots tend to be less efficient.

      Do you think it's random that the boundary is that straight? I wasn't expecting it.

      1. Am I correct in saying USG looks at who "ends" possessions (by way of a FGA, TOV, FTA etc.)?

        In that case, if Stockton dribbles the ball for 23 seconds, and then passes it to an open Malone who makes the shot, Malone gets all the USG credit, despite not being the focal point of the offense, or the opposing defense's attention.

        1. Yes, you are correct. And it's a point that is a good one has been noted many times. I don't disagree with it. You should repeat what I've done here taking into account assists. Maybe you can improve on my efforts!

  2. In regards to the boundary line, I found something similar when graphing the TS% of high scoring games (40 points and over) from 2007 to the present season.

    http://ascreamingcomesacrossthecourt.blogspot.com/2012/01/kobe-bryant-40-point-games-and.html

    Instead of one side for the boundary line there's two in mine. It's basically a pyramid. I'm going to do a follow up and include the past decade or two to see if that pattern holds over a larger sample of games.

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