Post a Comment On: The Game Designer

[Image] Photo by Keith Allison While most New England fans are still recoiling from today's loss to the Jets, I thought I would take a moment to draw your attention to a huge error by coach Belichick that significantly reduced our chance to win the game.

With less than two minutes left in the game, the Patriots scored a touchdown and kicked the extra point, to bring themselves within 7 points of the Jets.

Before the score, the Patriots were down 31-17. It's pretty clear at this point in the game that the only way the Patriots could win is to score two touchdowns while preventing the Jets from scoring.

So, any assessment of the correct strategy should assume that the Pats will score two touchdowns while holding New York scoreless.

First, let's look at the simplest possible decision: whether to go for two when you are behind by just one point (in other words, when you were down by seven points before you scored the touchdown).

The league average success rate for 2-point conversions is 47.9%. Here's a quick example of how the math works out in that situation:

(Based on results so far this year, the success rate of a 1-point conversion [aka "the PAT"] is 98.7%):

1) Team scores touchdown to bring score within 1 point. Team kicks extra point.

Chance of leading after this score: 0%.
Chance of being tied after this score: 98.7%.
Chance of trailing after this score: 1.3%.

2) Team scores touchdown to bring score within 1 point. Team goes for two.

Chance of leading after this score: 47.9%.
Chance of being tied after this score: 0%.
Chance of trailing after this score: 52.1%.

A team that ends the game in the lead wins that game. If they end the game trailing on the scoreboard, they lose. All things being equal, a team that ends the game tied has a 50% chance of winning that game.

So, we can award 1.0 wins for a result that puts the team in the lead; 0.5 wins for a result that ties the game; and 0.0 wins for a result after which the scoring team is still trailing.

Using those values, kicking the extra point produces 0.4935 wins but going for two results in only 0.4790 wins.

However, if the trailing team needs *two* touchdowns, the math is totally different.

1) Team trails by 14 points and scores two touchdowns. Team never goes for two:

Chance of leading after both scores: 0%.
Chance of being tied after both scores: 97.42%.
Chance of trailing after both scores: 2.58%.

2) Team trails by 14 points and goes for two after the first touchdown:

Chance of pulling within 6 points: 47.9%.
Chance of pulling within 7 points: 0%.
Chance of pulling within 8 points: 52.1%.

Then, when the team scores a 2nd time, they kick the extra point *if it would give them the lead*. If the team scored 8 points with the first touchdown, they have already tied the game before kicking the extra point.

2a) Team trails by 6 points before the touchdown, and kicks the extra point:

Chance of leading after both scores: 98.7%.
Chance of being tied after both scores: 1.3%.
Chance of trailing after both scores: 0.0%.

If the two-point conversion failed on the first touchdown, the team has to go for two in an attempt to just tie the game:

2b) Team trails by 8 points before the touchdown, and goes for two:

Chance of leading after this score: 0.0%.
Chance of being tied after this score: 47.9%.
Chance of trailing after this score: 52.1%.

To see the overall chance of winning the game with this strategy (going for two after the first touchdown), we have to combine the odds from 2a and 2b:

2) Team trails by 14 points and goes for two after the first touchdown

Chance of leading after both scores: 47.28%.
Chance of being tied after both scores: 25.58%.
Chance of trailing after both scores: 27.14%.

Assuming a 50% chance of winning tie games, here's what we get:

Going for two after the first score: .6007 wins
Kicking the extra point after the first score: .4866 wins

Going for two after the first score increases the chance to win the game by 23.4%. That's a huge difference (and one that Belichick shouldn't have passed up).

The key is that when you know that you need two touchdowns, you can make the decision whether to go for two on the second touchdown, and you already know whether you had a successful conversion on the first touchdown. If you weren't successful, then you need to go for two to tie the game. But if you succeeded on the first touchdown, you can just kick the extra point on the second touchdown, and win the game by 1 point.