Parcells always used to say that it didn't matter whether you ran the ball well or not, just as long as you ran it, which was basically another way of saying that committing to the run can open up the pass -- but what it also says is that the running game doesn't have to be particular effective or efficient as long as it is USED.
In basketball, you have the idea of a usage-efficiency curve. You take someone like Carmelo Anthony, who may not be the most efficient shooter, but still forces the defense to account for him, which opens up other players and makes them statistically more efficient. When Melo is out of the game, his teammates' productivity actually tends to drop.
I've seen all the numbers that suggest the most efficient passing team wins at the end of the day, but I've yet to see a single stat that suggests the running game can't influence that in any way. A team who is rushing for less than 4 yards per carry may be doing so because they've forced the defense to stack the box and utilize fewer DBs in favor of bigger, slower personnel. That opens up the pass, and -- guess what -- makes it statistically more efficient. And that team probably wins not because of the running game, but because of the threat the running game posed.
More basketball analytics stuff if anyone cares:
http://www.countthebasket.com/blog/2008/03/06/diminishing-returns-for-scoring-usage-vs-efficiency/
http://www.economist.com/blogs/gametheory/2015/12/statistical-analysis-basketball