With Great Volume Comes ... Great Efficiency?

Editor's Note: Bwoodsxyz writes a weekly stat-oriented column for Bullets Forever.  It appears every Wednesday at noon. 

No attempts at grand pronouncements this week.  Let's just play with some Gilbert Arenas-related charts instead. 

I recently came across this nice piece at GravityandLevity on the "Ewing Theory Paradox," speculating that the reason some teams see an apparent improvement after losing a key offensive player might be that the team's scoring efficiency is not hurt by the loss.  It is worth a read, but I'm most interested in one piece of it for now.  Part of the analysis involves the diminishing returns that result when there is an increase in a player's FG attempts.  Upping the volume hurts efficiency.

On the "Ewing Paradox" page are several charts mapping shots per game and FG%, by season (each season is a data point) for Patrick Ewing, Kevin Garnett, Kobe Bryant,* and Ray Allen.  The charts are used to make the point that if a player is called on to bear a heavier scoring load, then their scoring efficiency will fall.  And, indeed, for each player shown, the general trend was that an increase in shots per game yielded a decrease in FG%.  One might quibble with the metrics here (if I were doing this from scratch, then usage vs true shooting % might be an interesting way to try it, but let's not get into that right now), but the basic point is logical enough and seems sound. 

Of course, as a Wizards' fan, it is hard not to start immediately thinking about Gilbert Arenas when the subject of shooting volume/shooting efficiency comes up. 

Here is the equivalent chart for Agent Zero, throwing out (as did GravityandLevity for the other players) seasons with low minutes/attempts:

Arenas by-season FG Attempts and %s

Oddly, but somehow not surprisingly, this shows a positive relationship between shots per game and shooting percentage-i.e., his more efficient (by FG% alone) seasons are, generally speaking, the seasons he shot more. 

But, that's a very small sample size for the Agent.  And the result is largely dictated by that 39% season, Gilbert's first in Washington.  Regardless, 5 seasons with significant playing time is not nearly as significant as the data-rich charts for Shaq, Ewing, Ray Allen, and Kobe.

What if we break it down by game instead?  Here is an equivalent plot using Arenas's individual game stats from 05-06 and 06-07:

Arenas by-game FG attempts and %s 05-07

There are obviously a lot of data points here, and there is a lot of variability in shooting percentage from game to game for most any NBA player, but:  There is a clear positive relationship here with Hibachi taking MORE shots and making MORE of those shots. 

But maybe that is "normal" for players on a per-game basis.? Remember, those charts over at GravityandLevity were using entire seasons as data points.  Well, take a look at a season of Kobe:

Kobe 07-08

This is exactly what one would have expected--Kobe taking more shots generally equals Kobe shooting a lower percentage. Kobe's line trends the opposite of Gilbert's.

Does Arenas's increasing efficiency extend to those "quality shots" from beyond the arc?  It looks like it does:

Arenas 3-pt attempts and %s by game 05-07

And, even if we use a best-fitting-curve instead of best-fitting-line,**  we still show the same general trend, though with an added down-tick in efficiency after crossing the 11-3pt-attempt-in-a-game line:***

Arenas from 3 with curve

So, while you might expect that taking more shots, or attempting more threes, might lead to poor selection and decreased efficiency, this just hasn't been the case for Arenas.  Maybe he creates this relationship because he successfully recognizes when he will have mismatches and exploits them accordingly.  Maybe taking more shots helps him better find his rhythm.  Maybe on nights when he finds he isn't feeling it, he tends to take fewer shots.  Maybe it is coincidence, but that seems unlikely with this sample size of over 150 games.

Does he try to get his teammates more involved when he is shooting poorly?  Let's try to tell by mapping his assists with his FG%, again on a by-game basis for 05-06 and 06-07:

Arenas FG% and Assists by game 05-07

From this, there does not appear to be a strong tendency for Arenas to get more assists on the cold-shooting nights.****  Indeed, there is almost no correlation.  One possible explanation is that it might just be that, for Gilbert, his own scoring is critical to his ability to set up his teammates, and so he can not easily make up for his lost scoring production on cold-shooting nights by increasing his teammates' production.  Those in the "Arenas should shoot less and get his teammates involved more and the offense will run better" camp might have a little reason to worry if that's the case.  (Disclosure:  I'm not in that camp. And I am one of those who buys that his assists will probably go up some outside of the Princeton.)

Also, I'll take this opportunity to say I'm strongly in favor of bringing the "hockey assist" to basketball.  For all we know, while Gilbert did not get more direct assists when his own shot was off, he might have been creating a lot of opportunities that indirectly lead to baskets.  Indeed, while there is a positive correlation between how well Gilbert shot in a game and how well the team shot, it is not as strong as one might expect, and the team has had some very efficient scoring games even while Arenas struggled.  This chart maps the Team FG% on the Gilbert FG% by game for the 05-06 season:

Arenas FG% vs Team FG% 05-06

Of course, it helps here that (in general) when Arenas was cold he didn't keep shooting and dragging down the team percentages with even more inefficient volume.  There are other, better ways of trying to understand Arenas's impact on the offense, but that needs to be a post (or three) all its own sometime.

*          For anyone thinking that Gilbert Arenas does not belong on this list because he is *inefficient* and those guys are *efficient*-Arenas's career TS% and eFG% are the same as Kobe's career numbers and reasonably comparable to Garnett's.

**        I am kicking myself for losing my data set for FGA vs FG% before trying to fit a polynomial curve to it, but, just eyeballing it, I would expect the curve to be very little different from the best-fitting-line on that data set.

***      Ok, I'm not going to seriously argue that Gilbert's optimum number of 3-pt attempts per game is 10 . . . but I must admit I am intrigued.

****    It is probably just noise in the stats, but splitting it into the two component seasons indicates that in 05-06 the better he shot the fewer assists he had (which is what one might expect) while in 06-07 the better he shot the more assists he had (maybe you would explain that as meaning that when he shot well he opened things up for his teammates and got them more easy baskets?).  Speculations/explanations welcome.