Players That Laughed in the Face of The So-Called Usage-Efficiency Tradeoff

That title ought to have gotten your attention.

In an effort to look deeper into the (hypothesized) tradeoff between usage and shooting efficiency, I went to basketball-reference and compiled a list of every player-season of >100 FGA since the 3-pt shot came into effect. There are roughly 1800 unique players in the list and a little over 10,000 seasons (each represented by a row of data). I also captured the player's age, which you'll see in the plots that follow.

With these data in hand, I used the function lmer() in R (part of the lme4 package), to create the following linear mixed-effects model:

ts.lme<-lmer(TS.~USG. + Age | Player,data=usage_big,weights=FGA)

The idea is that TS% is a function of USG% and Age, in general, but also follows a dependence on the specific player. Basically, the function is finding the usage-efficiency (or "skill curve" as Dean Oliver referred to it) for each player. The nice part of all this is that everything was done essentially automatically, thus, saving me the effort of writing a lot more code.

The end result is that now I have a very large database that I can sort by these effects. In this post, I'll give you a taste of it, starting with plots for the players whose TS% actually improved the most as a function of USG%. Not surprisingly, there are some good players near the top. Here are the top 25 on the list (followed by some plots of individual players):

In the following plots, age is represented by the size of the points.

Clearly, these relationships are not perfect, but the results are interesting, nonetheless. There are outliers and the effects of age appear to be important in some (if not all) cases. More to work on for sure, but the internet is made for rapid communication of new findings, so I'll put the data/findings out there as I come upon them — as opposed to waiting until everything is perfect (which might be never).