xwalker
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It's not. Throwing effectively and defending the pass effectively is what wins. Those things have very little to do with running the ball effectively. You do need to pass protect, though, and pressure the passer, so we can agree on that at least.
Be careful believing the passing correlation theories.
Those concepts are based on a very simplistic single variable statistical analysis.
Winning a football game is a complex multivariate statistical analysis.
Example:
You could probably show simple correlation between blow-out wins and high rushing attempts in the 4th quarter.
Using simplistic correlation you could conclude that the high rushing attempts were responsible for blow-out wins. In reality, we know that teams tend to rush more late in games when they have a big lead.
The problem as shown in the example is determining cause vs effect. The high number of rushing attempts was caused by the blow-out win. The high rushing attempts didn't cause the blow-out win.
The correlation of passing effectiveness does indicate that teams don't win on average if they lose the passing effectiveness battle; however, it does not prove anything about the effect of the running game.
The fact that rushing statistics don't "correlate" is not proof of the importance or lack of importance of the running game. It more likely shows that they are not able to track the relevant statistics. The statistic of how often a defense plays 8 men in the box vs 7 men in the box is not commonly available; however, it would be very important in determining the effect on the passing game of having a rushing threat. If the defense plays 8 in the box, the rushing statistics will suffer and the passing statistics will flourish.
There are other issues that would be very difficult to quantify with statistics. It's well known that defenses go to an all out pass rush on 3rd and long; whereas, at other points in the game they may play a read-and-react style. If there was not threat of a run, they would always go with an all out pass rush.
It was fairly easy to see that college pass rushers often played conservatively against running QBs like Manziel. In reviewing DEs for the draft, many of them played a completely different game against Manziel than they would against a guy like McCarron. It would be really difficult to correlate this to statistics. Manziel might not have had big statistics running in some games but he nonetheless affected how the the defense played against him.