Thinking about the rushing/passing correlation, I wondered why it might be the way it is. After all, eight in the box should be a better defense against the run than seven in the box, right? That's why teams do it, right?
What if it isn't better but is actually just a different step in the risk/reward ratio versus running plays?
Consider the goal-line defense. Except for maybe a couple of corners and (maybe) a safety, everyone's stacked up at the line, 8, 9, or maybe even 10 "in the box." The idea is to stop a very small gain by the offense, which is generally all you have to stop when you're backed up against your own goal line on defense.
But how many times have we seen a short-yardage defense in a non-goal line situation when the running back bursts through and there's nobody else to tackle him, so he goes for a bunch of yards? It's anecdotal, but we've all seen that at least a few times.
If you think about it, that's probably how an eight-in-the-box defense should work. That extra defender is there to stop the back for a short gain if he gets through the first seven defenders, but if the back makes him miss, there's not much left to stop him from making a huge gain. It's just like blitzing against the pass -- you increase your chance of a big negative play (sack) for the offense but increase your risk of giving up a big offensive play.
If you played against a defense like that a lot, you might expect your rushing carries to look something like:
1, -4, 1, 4, 3, 0, 3, 3, 67, -1, -1, 3, 7, 2, 6, 5, -2, 0, 7, 1, -2
-1, -1, 2, 2, 6, 2, 40, 6, 0, 6, 1, 3, 0, 2, 0, 3, 0, 5, 5, 2
Hey, I think we've seen those stat lines before! (And thanks to Pacifist Viking for writing them out and making for an easy cut-n-paste.)
It's not pure, statistical proof, and I'm certainly not an NFL coach, but from a layman's point of view, it might be true that eight-in-the-box is good at stopping short gains but is vulnerable to the long gain. It's sort of like a less aggressive form of run blitzing. It may not have any effect on average rushing yards or total rushing yards, but would be more susceptible to the wild fluctuations and inconsistency we see in Adrian Peterson's numbers.
I'm not the first person to come up with this idea. I can remember, in my old Strat-o-Matic Football, that there were "zones" you would line up your defensive players in. There was one just behind the interior defensive line where the middle linebacker(s) typically lined up. You could "move up" those linebackers to linemen's zones to pass or run blitz and that could help you stuff the play. You could then move the free safety up to occupy the linebackers' original zone -- thus putting "eight in the box." However, there was a result on the cards for running plays that said if the linebackers' original zone had only one guy in it, you would add 10 yards to the result of the run. If there was nobody there, you'd add 20 yards. Interesting, that.
So maybe there is some credibility to the notion that a strong passing game would help Adrian Peterson become more consistent on a carry-by-carry basis. And maybe eight-in-the-box isn't actually a "better" defense than a seven-in-the-box strategy, no more than blitzing is a "better" pass defense than dropping into coverage. It probably just fits somewhere between full-on run blitzing and 7 ITB in terms of risk vs. reward.