It has been football gospel for many decades that play action passing works if you first make your opponent afraid of your ability to run the ball. I seem to recall Football Outsiders providing good evidence that this is not the case at some point in the past, but guest columnist Ben Baldwin recently made a great case against the idea.
I urge you to read all of the gory mathematical details, but no matter how you slice it, the numbers bear out one over-arching point: the running game has no effect at all on your ability to use play action.