# Belichick: genius or madman?

The talk around the NFL is about New England Patriots' head coach Bill Belichick's decision on Monday night. For those who haven't heard, his team was up by 6 points with about two minutes left in the game. It was 4th and 2 from their own 30 yard line. In other words, almost everyone making the decision would have punted. But Belichick decided to go for it. He is either being accused of being arrogant for taking the risk or of not having confidence in his defense.

The play came up about 6 inches short (officially), Peyton Manning and the Indianapolis Colts got the ball back, and proceeded to score a touchdown with 13 seconds left to clinch the win.

Immediately after the game, the reaction on various internet forums that I visit was 99% against Belichick; I was one of the few sympathetic souls. Over the last 24 hours since the game ended, a few more people are coming to his defense.

The reason I believe very few people support Belichick's decision is that most people are not very good at probabilistic thinking. Hindsight is 20/20. As I see it, the decision is as follows:

A) Punt the ball. Colts get the ball around their own 30 or 40, and Peyton Manning has to go 60 or 70 yards in 2 minutes. I'd rate the chances of the Patriots stopping him at about 70%.

B) Go for the 4th down conversion. I'd give the chances of success better than even, say, 60%. If they get the first down, Patriots win. On the 40% chance that they don't get the first down, Peyton Manning has to go 30 yards in 2 minutes. I'd give the chances of the Patriots stopping him in that situation 30%.

Note that choice A yields a 70% chance of winning. Choice B yields at least a 60% of winning (converting the fourth down), and probably more (stopping Manning even if they don't convert the fourth down).

Now, I have no problem with anyone who agrees with all this and still thinks the right decision was punting, or anyone who thinks my percentages are off. Heck, I probably would have punted. But my points are:

1) It was a calculated risk.

2) Whether the decision was the correct one is evaluated *regardless of the outcome*. The correct decision often results in failure.

## Computing the probability

Let's take your numbers: making the 4th down conversion is 60% and the probability of stopping Manning on failure is 30%. Said the other way, the probability of Manning getting the ball is 40% and the probability of going 30 yards in 2 minutes is 70%. Multiply the two together and you get 28% chance of Patriots losing.

So, given your estimates, it is 70% vs. 72% chance of victory. Pretty much a wash.

## Football

I think your numbers are off, but they seem reasonable. I think since the Patriots were, so to speak, "this close" to getting the first down, the risk they took was a pretty good one. If they had just gotten those extra inches, everyone would be calling them genius.

If there are two minutes left in the game it is plenty of time for a team to go either 30 or 70 yards. One well placed throw can move a team from 70 to 30 yards out, so they would be back to where they were anyway.

## Jonathan, For fun, let's try

Jonathan,

For fun, let's try another approximate approach.

Assumptions --

1. The punt will net 29 yards, leaving 58 yards for a touchdown.

2. To start, assume that Manning has an 80% chance of ANY 29 yard advance.

3. The Patriots have a 50% probability of making the 4th down conversion.

Conclusion :

For the assumptions made, Manning has a 64% probability of a 58 yard TD drive, and the chances of a punt and a Patriot win are 36%.

The chances of a Patriot win if no punt are 50% plus 10% equals 60%.

Using other Manning success rates per any 29 yard advance, what are the Patriot winning probabilities?

100%-> 50% no punt, 0% punt

90% -> 55% no punt, 19% punt

80% -> 60% no punt, 36% punt

70% -> 65% no punt, 51% punt

60% -> 70% no punt, 64% punt

50% -> 75% no punt, 75% punt

40% -> 80% no punt, 84% punt

All of the above take a Manning 29 yard advance success rate, a 29 yard net punt, and a 50% Patriot 4th down conversion rate.

Now find the breakeven 4th down conversion rates, where the Patriots' winning probabilities are the same for punt/no punt :

100% -> 0%

90% -> 14%

80% -> 26%

70% -> 36%

60% -> 44%

50% -> 50%

40% -> 54%

Although it may be unrealistic to give Manning the same probility of advancing 29 yards to a TD as advancing 29 yards to the 29 yard line, the TD 29 yards should be more difficult and the 4th down conversion attempt is even more called for.

Regards, Don