In yesterday's epic and, at least for Patriots' fans, calamitous matchup between the aforementioned Pats and the Indianapolis Colts, Bill Belichick did the stupidest thing ever done by a head coach in the history of the world. At least, that's what I've heard. Take it away, designated stand in for stupid opinions about football everywhere, Peter King:

Belichick was talking to Brady on the sidelines. I was sure they were talking about trying to draw the Colts offside with a hard count; there was no way he'd be authorizing going for it on fourth down. But back went Brady to the field, and he lined up in the shotgun, and started calling signals without the head-bob you normally associate with trying to draft a team offside.

"My God,'' I thought, "he's going for it!''

Two things had to factor in here. One: Belichick didn't want to give Manning the ball with two minutes to go; he'd just seen Manning take the Colts 79 yards in six plays for a touchdown. Two: He trusted Brady to get two yards. Let's place the odds of Brady getting two yards at 60, 65 percent. The odds of Manning going 72 yards to score a touchdown in less than two minutes ... that's maybe 35 percent.

You might say Manning's chance of taking his team 72 yards are better than 35 percent. Not sure I would.

Oh shit, Peter King is trying to do math. Here, put those numbers down before you hurt yourselves, and let the professionals try it.

The goal of any decision is to select the most optimal one with imperfect information. We typically do this by assigning percentages. Peter King has started down this path, but got halfway down it before he got distracted by a shiny object in the woods. Look out Peter King! That's a bear trap! NOOOOO!!

Once you are done gnawing your leg off, take my hand. I'll lead you the rest of the way.

We need to define three variables. They are as follows:

x: the chances that the Patriots will convert on 4th and 2.
y: the chances that the Colts score from the Patriots 30 yard line
z: the chances that the Colts score from their own 30 yard line

(Yes, I am aware that this is a somewhat simplified analysis, as it does not consider the odds of a shanked punt, or an interception return on the conversion attempt, or that the Colts could still win even if the Patriots convert, and all the other thousand things that can happen. Let's just say that those odds are small enough as to have no practical impact on the calculation outcome and move on with our lives, nerd.)

In situation 1, where the Patriots go for the conversion, the odds of a loss are as follows:

L = (1 - x) * y

In situation 2, where the Patriots punt, the odds of a loss are as follows:

L = z

Therefore, in order for a conversion attempt to be the correct choice, the following must be true:

z > (1 - x) * y

In Peter King's analysis, x = 60%, y = 100%, and z = 35%. Under this set of assumptions: 0.35 > (1 - 0.6) * 1 is NOT true. Except that these assumptions are actually very stupid. Why? This is why:

With 2:08 left and the Colts with only one timeout, a successful 4th-and-2 conversion wins the game for all practical purposes. A conversion on 4th-and-2 would be successful 60 percent of the time. Historically, in a situation with 2:00 left and needing a TD to either win or tie, teams get the TD 53 percent of the time from that field position.

King's estimate of x and z are about right, but he is assuming that y = 100%. This is way, way, wrong: even if the try failed, the Colts still had to get it in the end zone. And on average, teams only score touchdowns 53% of the time from that field position. Re-running the analysis shows that (1 - 0.6) * 0.53 = 0.21, which is significantly less than the 35% chance of Manning scoring after a punt. The conversion attempt was the right call by a significant margin.

To anticipate the response: these numbers are based on NFL averages, and Manning is not an average quarterback (as we all saw last night). And I agree. You probably need to increase the chances of him scoring from either position significantly. So instead of 53% maybe that's 75%. That also means that, instead of having a 35% chance of scoring from his own 30 yard line, he hasA something like a 50% chance. (1 - 0.6) * .75 = 30%, which is still much less than 50%! There is no internally consistent set of numbers that you can generate that makes a punt the correct choice.

But if this is true, then why all the backlash? And why was this conversion try such a rare event? Belichick didn't do what he was supposed to do, didn't do what every other coach does. While fans might think that coaches do what is in the best interest of their team, they really do is whatever is in the best interest of the coach. Often these interests intersect; in this case, they do not. What a punt would have done is deflect blame for a loss from the coach to the players. NFL head coach is a job with a high turnover rate. If a coach is perceived as being to blame for a loss, he is at great risk of being fired. However, if the coach can blame his players, he actually increases his own chances of retaining his job.

Three Super Bowl rings have given Belichick the job security necessary to make the right choice instead of the safe choice. Whatever other faults he may have, he should be applauded for that.