There are some obvious problems with the concept that "passing more efficiently wins games regardless of the running game" concept.
If that were 100% correct, then LBs and Safeties would be replaced by CBs.
Nobody said it was 100% correct. You can pass more effectively and still lose for any number of reasons -- fumbles, special teams, etc. But the vast majority of the time (roughly 80%, in most seasons), you will win the game if you pass it better.
And it's illogical to say that something that has been proved cannot be correct because of the lack of some arbitrary decision by coaches. That's like saying that turnovers can't be important or else teams would do something drastic to avoid them, such as never passing in any situation or even just taking a knee on every snap. (Not to mention that replacing linebackers and safeties with backup cornerbacks wouldn't necessarily help you play better pass defense -- they'd represent almost no pass-rush threat, would severely reduce your ability to tackle, they'd be mismatched against tight ends, they'd be much less intimidating to receivers going over the middle, etc.)
Anyhow, you can imagine what might happen in some theoretical situation all you want, but in reality -- in the way the NFL is actually played -- what is true is true, regardless of whether you want to believe it.
What should really be said is that "the effect of the running game can't easily be determined using statistics"
In other words, rushing success or failure has no significantly measurable effect on the game.
Passing more efficiently = wins is similar to say scoring more points = wins.
Now you're getting the idea. In most games, passing more efficiently is pretty much inherent to the team that wins.
You could probably use statistics that would make it appear that more rushing attempts in the 4th quarter lead to blowout wins. In reality, we know that teams that are way ahead on the scoreboard in the 4th quarter often run the ball more than they normally would. We know that to be true, but the statistics can't show the difference in cause and effect.
So you're saying that teams pass more effectively BECAUSE they are winning, and they pass more effectively BECAUSE they are losing? Good luck trying to come up with any evidence of that being even partly true.
Defenses dynamically adjust to good rushing teams and their pass coverage often suffers, but it's really difficult to show using simple statistics.
Right, "simple statistics" such as yards, turnovers, points and, you know, wins -- all those meaningless football statistics.
The same defense might play 2 offenses and limit the running game of both offenses to 50 yards; however, if the defense played 8 men in the box against 1 offense and played 7 men in the box against the other offense, then the offense that faced 7 men in the box would have an advantage in the passing game, but it wouldn't show up in the rushing statistics.
Do you think teams randomly choose when to play "eight in the box" or "seven in the box"? Or might they use "eight in the box" against better rushing teams and "seven in the box" against better passing teams? (I'm assuming you had a typo when you said that a team facing seven in the box would have an advantage in the passing game -- that would make no sense if you actually meant it.) If teams stack the box against better rushing teams, then you're saying that those teams should have an advantage in the passing game, correct? And if that's true, then that "advantage" should be measurable -- but there is very little correlation. One reason is that game situations typically dictate what type of defense is played, especially in passing situations. When it's third-and-8 (or third-and-20), or when you've got 80 yards to go in less than 2 minutes, being a good rushing team probably won't make a lick of difference -- you'd better be able to throw the ball against a defense that knows you're going to pass. And those are often the situations that determine who wins the game.
