Doing the math on Fourth and 1

It was another case of a questionable fourth-down call for Bill Belichick and the Patriots on Sunday in San Diego. Just as in Indianapolis last season, the Patriots went for it on fourth and short in their own territory with a slim lead late in the fourth quarter, and just as in Indy, they fell short. However, this time New England did not pay the ultimate price, winning the game when a potential game-tying field goal hit the upright.

So was going for it on fourth and 1 the right call?

ESPN.com's Stats and Info blog did the math on it, determining that -- by a slim margin -- it was not the right call. Using a win probability calculator, the analysis concluded that the Patriots had a 87 percent chance of winning the game if they punted in that situation Sunday and an 82 percent chance of winning if they went for it.

When they failed to convert the fourth down, the Patriots' win probability dropped all the way to 64 percent.

What do you think of analyses like these that are purely stats-based? Useful in making a case and explaining decisions?