All the pundits are discussing this tonight, and most of their discussions are worthless. Football is a game of numbers, maybe more than any other game. Ten yards for a first down. Four chances to get ten yards. Penalties are assessed in yards, and are intended to directly influence the offending team’s chances of getting another first down or scoring points.

So, the right way to analyze the situation is actually the easiest: make some assumptions, run the numbers and see which option was best. First, I’ll show the numbers and the result, then I’ll describe my assumptions.

**The answer:**

Belichick was correct to go for it on 4th and 2 (and it’s not even close).

**The ma****th:**

On average, the Colts will end up scoring 2.45 points if the Pats punt to them. And, on average, the Colts will end up scoring 1.14 points if the Pats go for it on 4th down. Going for it on 4th down is clearly the best option since it yields the fewest points (on average) for the Colts.

**UPDATE**: I saw an article on CNNSI.com that compares the likelihood of the Pats winning using percentages, and I think that method is better than mine. So, for completeness, here are my numbers for this scenario: using the same assumptions I mention below, the Pats will win 84% of the time if they go for it on 4th and 2, and they’ll win 65% of the time if they punt.

**My assumptions:**

- If the Pats convert the 4th down, they will win the game.
- The Pats will convert the 4th down 75% of the time (based on the Pats’ previous 4th down conversion rate against the Colts).
- If the Colts receive the ball on downs, they will score a touchdown to win the game 65% of the time.
- If the Pats punt, the Colts will get the ball on their own 30-yard line (and need to drive 70 yards and score a touchdown to win).
- If the Pats punt, the Colts will score from their won 30-yard line 35% of the time.
- The Colts will get 7 points if they score a touchdown (e.g., they will never miss the PAT).

**My methodology:**

In general, I wanted to compare the Expectation of the Colts (in points scored) in two situations: 1) The Pats attempt to convert the 4th down; 2) The Pats punt to the Colts.

For 1), here’s how I broke it down: The Pats will convert the 4th down 75% of the time, and the game will end. Or the Pats will turn the ball over on downs, and the Colts will score a touchdown 65% of the time and win the game.

For 2), here’s how I broke it down: The Colts will receive the ball and begin their drive on their own 30-yard line. From their own 30-yard line, they will score a touchdown 35% of the time and win the game.

**What would it take for Belichick to be wrong?**

If the Pats would only convert the 4th down attempt 60% of the time, AND if the Colts scored a touchdown 90% of the time when they got the ball on downs, THEN Belichick would have been wrong to go for it. But only barely. (I did not modify the numbers for the punting scenario.)

**The math that would**

**make Bill wrong:**

Given the above statistics, on average, the Colts will still end up scoring 2.45 points if the Pats punt to them. And, on average, the Colts will end up scoring 2.52 points if the Pats go for it on 4th down. So, given the above assumptions, Belichick would have been marginally wrong to attempt the 4th down. But those assumptions seem *very* optimistic for the Colts. Even Peyton Manning wouldn’t score a touchdown 90% of the time from his opponent’s 28-yard line, and even when he’s using all four downs to do it.

**UPDATE**: I saw an article on CNNSI.com that compares the likelihood of the Pats winning using percentages, and I think that method is better than mine. So, for completeness, here are my numbers for this scenario: Using the assumptions mentioned above, the Pats will win 64% of the time if they go for it on 4th and 2, and they’ll win 65% of the time if they punt.

The great thing about my method is that it can be made more precise with more accurate data. For example, it should be possible to figure out how frequently Manning will score a touchdown from the Pats’ 28-yard line if he’s using all four downs. It should be pretty easy to find out how often the Pats can expect to convert a 4th down in that situation. It should be pretty easy to determine where, on average, the Colts would begin their drive if the Pats punted to them. And it should be pretty easy to figure out, on average, how often the Colts would score from that spot.

I’m not going to do that research because it’s not my job. Ironically, the people whose job it is probably won’t bother with it either because then they couldn’t pontificate about Belichick’s call for the next week.

**UPDATE**: I was wrong that nobody in the media would seriously analyze Belichick’s decision! Someone actually did a similar analysis for CNNSI. So, in the interest of full disclosure and eating a little crow, here’s a link to the article: CNNSI.com – Why Belichick Made the Right Decision