One of the claims made--on both sides--during the recent debates over running backs and per-carry averages is that the typical back will improve over the course of the game, as he gets more carries. This is a football truism that I've never had reason to question--it just sounds right--but I've also never attempted a systematic investigation into it, either. What follows is an attempt not only to discover if statistics back up this truism, but to find out the rate of improvement for different backs.
I wanted to contrast Reggie Bush and Pierre Thomas, since they're the ones the debate has centered around; but in order to see whether or not the phenomenon is real, I included a couple of other running backs: Michael Turner of the Falcons, and DeAngelo Williams of the Panthers.
For each of them, I made a scatter-plot graph that plots points on two axes, the short axis being number of carries, the long axis being yards-per-carry average for that game. Each point represents a single game for this season. The solid square point represents that back's seasonal average to date (after twelve games).
The hollow, red square point is something different. It represents what that back's average would be if you threw out both his worst performance and his best. I think this is probably a better representation of the rusher's actual average...though Dave the Falconer is apt to complain, because it penalizes Turner more than anyone.
At this point, I can assert that the data is accurate (I got it from NFL.com). But here, interpretation enters the picture, and I have to emphasize that I AM NOT A STATISTICIAN. The light-colored solid ellipse behind each group of points represents my best attempt to find a correlation among the points (ignoring those points that are strong anomalies). For Michael Turner, for instance, it's pretty strong. For Pierre Thomas, it looks more scattershot, but I think the data still follows a pattern. Your interpretation may be different, and probably has as much validity as mine.
Anyway, here are the graphs:
It would seem that for each of these running backs, the question "Does he improve with more carries?" would have to be answered "Yes." But the rate at which they improve is the part that fascinates me.
I made one last graph, which consists of a line cutting through the long axis of the colored ellipse in each chart, intersecting the "corrected" average. A perfectly vertical line would indicate no improvement whatever; the greater the angle from vertical, the greater the rate of improvement.
This graph shows several interesting things. First of all, and surprisingly, Michael Turner has the weakest rate of improvement. Bush comes next, but his rate is significantly better than Turner's. This suggests that if Bush got more carries, he could be as solid a runner as Turner is. (Doesn't prove...suggests.)
Even more interesting, Pierre Thomas and DeAngelo Williams are nearly identical in the angle of their improvement, both of which are significantly better than the other two. This strongly suggests (again: merely suggests) that Thomas could be as good as Williams if given the chance.
Finally, the hollow circle shows at what point that runner can be expected to reach a rate of 4.5 yards per carry--a pretty good, solid number for an NFL back. And here things get really interesting, because the first runner to reach it is Pierre Thomas--after only 7 carries per game (which happens to be what he's averaging, so we know the chart is accurate). DeAngelo Williams gets better at the same rate as Thomas, but not as early. He doesn't reach 4.5 until he gets 16 carries.
Bush reaches it at 19 carries. Now here we run into an interesting phenomenon. Nineteen carries at 4.5 yards a pop comes out to be 85.5 yards. Bush had 19 carries in one game, against Seattle in 2007, when he hit 97 yards and a 5.1 average--not at all far from what the chart predicts. So I have confidence that if Bush were in fact given more carries--yes, he would have a better rushing average. He's already done it.
Then there's Michael Turner. But he's Michael Turner, so who cares.
One last point to make:
As I said earlier, I feel confident the data plotted on the graphs is accurate. But one thing the graphs can't explain is why a running back's average goes up as his carries increase. It may be that teams stay with the run longer when it's working (when the back has a high average), and are quicker to abandon it when it's not working. That certainly describes the Saints, who tend to abandon the run on Wednesday. But the claim that rushers improve with carries has been the near-unanimous opinion of NFL running backs for as long as I can remember. For that reason, I feel confident that they know what they're talking about, and that this is in fact the real reason behind the improvement shown in the graphs.
Okay, I warned you I wasn't a statistician. It occurred to me this morning that if a straight vertical line shows no correlation in average with an increase in carries--because the average doesn't get better--a straight horizontal line would also show no correlation--because the carries don't increase. For that reason, the best angle--the one that would give you the most confidence that the data showed a meaningful correlation--would be 45 degrees. Any deviation from that, up or down, decreases the confidence that there is an actual connection between increase in carries and increase in average YPC. I added that line to each chart: a dashed grey line beginning at the 0/0 point (lower left).
That would mean that the running back I dismissed, Michael Turner, is actually--among the first four--the prototypical every-down, load-carrying back. (I can hear DTF chortling right now.)
Then I decided to do what I should have done to begin with: chart Deuce. The result is below, showing his last two full years: 2004 and 2006.
As you can see, his line is almost a perfect 45 degrees. In fact, if you remove all the games where he got less than 14 carries (the least that Turner had), his graph almost matches Turner's. Except that it's better: he hits 4.5 yards per carry at 22 (he's the purple line added to the graph above).
Now, on to Pierre...
It would seem now that Pierre's very horizontal line doesn't inspire a lot of confidence in the idea that he improves with usage. Both he and DeAngelo Williams would seem to be different kinds of backs: you get what you get, and you have no way of knowing what it will be from one week to the next. Having said that, they both are capable of turning in stellar performances...and the evidence shows that Pierre may be the better of the two. The only way to know is to play him more, since graphing his performances doesn't result in a high level of confidence that the result is meaningful.
But we all know that Williams is effective, so why not Pierre?