You're throwing 'as well' in the equation, which contradicts your previous statements. The Patriots since 2007 have had the best stretch of offensive efficiency through the air the league has ever seen. So yes, if we could run the ball anywhere near that level, we'd have a better chance of winning football games. But the thing is, we don't. The passing offense is leagues beyond the running offense, and the latter greatly benefits from how teams are scared of the former. If the passing offense was 30% worse, this team would be in dire straits offensively, if the running offense was 30% worse, they absolutely could survive and still be highly productive, as 2007, 2010 and 2011 have shown us.
Fact is, throwing the football is WAY more valuable to this team than running it, and that's how they should look to attack the opponent. If the other team sells out to stop the pass and pratically begs us to run on them, we'll gladly take that, just like we did against Denver and Buffalo, with great success. Otherwise, we should never go into a game thinking "gotta run the ball here, keep that pass/run ratio close". No, you play to your strengths on offense, especially when those strengths directly mirror the opposing defense's weakness, as is the case with Houston. You were arguing that merely by runnng the ball more often, our chances of winning football games would increase. And that's a fallacy.