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Passing, Winning, and Optimization

One of my favorite sites, Advanced NFL Stats, recently posted compelling evidence on "Passing = Winning" in the NFL.  As ANS observes, announcers, including former players and coaches, love to wax on about the importance of running.  He offers a specific example:

Just last season, Brian Billick, who was the offensive coordinator for the most prolific passing offense in history, told the audience of NFL Network's Playbook NFC that the real secret to the Saints' success was their running game. Right.

ANS then goes on to offer simple regression evidence showing the much tighter relationship between passing efficiency and wins as well as multivariate regression evidence taking account of other influences while showing the same thing.

ANS is not just a number cruncher.  He offers useful insights appealing to economists:

Theoretically, running should be just as important as passing due to game theoretic considerations. That's what is loosely meant by the adage "the run sets up the pass" and vice-versa. But despite this well-worn cliche, coaches and coordinators simply overdo the "setting up" part by over-playing the run on both sides of the ball. It's no different than a boxer who jabs too much.

Even though game theory is applicable, even simpler decision models of running and passing would support an equal incremental effect kind of solution.  So why do we not see expected values for a run and a passing closer together.  ANS may be right in attributing it to coaching habits-- there are examples of attachment to traditional practices in coaching.   The silly statements of  the announcing crowd would seem to bolster this view.  Before we settle on that conclusion, however, more investigation is needed.  The idea of equalizing expected values of running and passing assumes that the impacts of each are independent.  If running does help "setup the pass," then the optimal combination (the maximum output) is not necessarily where they equal each other.  Instead, the seeming loss of yards gained on the run may be more than offset by an increased impact on yards gained on pass plays.  I ran across a working paper the other day by Gibbons and Serrato providing evidence from re-examining 10 prior AER studies, suggesting that leaving out interactive effects can make large differences in results.