Shots, Part Deux

Here is the Part II to last week’s post looking at the relationship between Gilbert Arenas’s shooting volume and percentages.  First, some general thoughts.  Second, some responses to questions posed in the comments last week.  Then, a look at how some other Wizards compare.

First, a general statement/disclaimer:  When I started producing the charts using individual games as the data points, I was really just expecting a mess.  The result for Gilbert was interesting, of course, but it was when I then made the chart for Kobe that I really stopped and wondered.  Now that I've done it on more players, I'm still not entirely sure what to think. 

On the one hand, there are a lot of data points and they, especially for some players, tend to resemble just a cloud of data points.  The r-squared's (a measure of apparent explanatory value of the data series on each other) are very low for the most part (speaking just of the by-game charts).  This suggests perhaps the apparent positive/negative relationships are just coincidental.

On the other hand, as I've produced charts for more players, I have to say that they largely have come out as I would have expected.  And, even when they haven't, they still make sense.  Moreover, (this is based on limited observation, so take it with a grain of salt) players seem to have consistent results from one season to the next.  For each player for whom I've looked at more than one season of data, they end up with the same type of result each season, though differing in degree.  (i.e., I have seen players like Gilbert who were positive in each of different years, players like Kobe who were negative, and others who show no relationship).  Also, I believe the low r-squared value can be explained, to a great extent, by the nature of the data here.  For example, a player like Gilbert would probably have a dozen exactly-16-shot games over a season or two, making everywhere from 4 to 11 shots.  Having that many FG%s mapped on the same FGA value is going to make it hard to yield a strong r-squared. 

So, do the low r-squareds mean the lines are meaningless?  Intuitively, I don't think so.  But, I'm just not sure how much it *does* mean.

Ok, on to some responses to comments/questions:

(1)  I'd noted last week that I'd lost the data on Gilbert's 05-06/06-07 FGA/FG% by game chart before running the polynomial line.  Well, here it is:

Arenas chart for 05-06 and 06-07

The dip on the high end of FGAs is kind of interesting. 

(2)  Icantfeelmyface pointed out that Gilbert has a few games with exceptionally high #s of FGAs combined with good FG%, and asked whether that might be messing with the result.  I went back and took that out, and it made very little difference in the best-fitting-line (still positive, but the slope is every so slightly smaller).  It did, however, make the dip at the high FGA end of the curve a bit more pronounced.  And, again, Kobe too had some very good performances at the high end, but they didn't save him from the negative slope.

(3)  pantslessyoda1 suggested that the explanation for Arenas might be Arenas's role as PG on the team:  that playing PG gives Arenas a different profile than the Kobe/Ewing sort who are off-the-ball players. 

I took a look a season each from a few different prominent PGs:  Stockton (in one of his years with a higher FGA/game), Iverson (his MVP season), Billups (05-06, playing for Flip), and Cassell (03-04, playing for Flip).  Here are the results:

Point Guards

I was expecting Iverson to come out like Kobe.  Instead, his is like Arenas but moreso.  (Incidentally, his table produced easily the highest r-square value of any individual season, suggesting that his is most likely to be a meaningful relationship.)  Cassell's is the closest to Arenas's chart.  Stockton's and Billups' show no relationship. 

(4)  steadyhand pointed out that on Arenas's by-season chart, the positive relationship could probably be explained by his progression as a player over those years.  I.e., he just plain got better, meaning that he earned more shots and he was likely to make more of them. 

First, yes, Gilbert's shots essentially went up the longer he was in the league.  So, the upward slope of the line largely represents his progression in the league.  This shows up in the charts for many players.  The Wiz don't have many players who have had enough variety in their careers to show anything other than that sort of progression.  The exception is the Gentleman.  Antawn Jamison's career chart:

Jamison's Career, By Season

Small sample size, etc., etc., and there is a big cluster in the middle, but even so.  This had the strongest relationship of any chart I've done.  And Jamison's low and high FGA seasons did not have any time relationship.  He's just shot for higher %s when carrying a lighter load. 

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Now, onto Arenas's teammates. 

First, the three big shot-taking G/Fs-Caron Butler, Antawn Jamison, and Mike Miller.

Jamison-Butler-Miller

Next, the (non-Miller/Butler/McGuire) competition for SG minutes:

Randy Foye-DeShawn Stevenson-Nick Young

So, here we perhaps have a little more support for the idea of Jamison taking somewhat fewer shots.  And, maybe the most interesting thing is the chicken-and-the-egg conundrum posed by Young's chart.  Did he shoot better because he was getting more time and more shots?  Or did he get more time and more shots because he was shooting better?  Or, is this all random nonsense that is just killing time 'til training camp starts?