The problem is that they are NOT different topics, despite the efforts of some people to make it seem as if they are. They are all a part of the same greater analysis.
Hell, I'm a stats geek myself. I simply understand the need for context, and I consider that far more important than shining Belichick's shoes when he screws up as royally as he did last night.
If the team runs the ball on 3rd down and forced the Colts to use their timeout, that changes the equation, because the Patriots would have had time to make up their mind and get the proper personnel on the field, and they wouldn't have pissed away that final timeout. Had the team run the ball and gotten the game to the two minute warning, that would have changed the equation, because replay could still have come from the booth. However, neither of those things happened because of the bonehead decision on 3rd down.
What did happen was that the bonehead decision on 3rd down, coupled with the communications failure and subsequent burned timeout, changed the equation from "It's a short yardage play, but at least we can get a bad spot reviewed" to "It's a short yardage play, and a poor spot can screw us, because we can't get it reviewed".
To me, that makes going for it on 4th down, under those circumstances and with Manning getting the ball at the 30 if there is a failed conversion, a decision that's about as stupid as it gets, particularly when you add in the idea of going in the formation they chose and using Faulk rather than Maroney as the running back, which would have at least kept the defense honest. Short yardage plays are so often about the spot of the ball that relying on that without a challenge is just idiotic. They had the lead, for crying out loud, and they pissed it all away on one idiotic call.