Going for it on 4th and 2

November 22, 2009 at 11:03 pm Leave a comment

Last week (November 15th) the game between the Patriots and the Colts came down to going for it on 4th and 2 in New England territory. The Patriots had the ball and decided to go for it instead of punting. They were leading by 6 points so the Colts needed a touchdown to win. Most analysts have criticized the decision by Coach Belichick. However, based on statistics, going for it on 4th and 2 was the best decision.

Here is why:  There were two ways for New England to win: a) They go for it on 4th and 2, either they get it and run the clock or don’t get it but can stop the Colts, or b) They punt the football and stop the Colts from scoring. If they punt the football, everyone in the football universe would agree that with 2 minutes to go and 3 timeouts available, Manning had at least 50% chance of scoring. Assume that the Patriots have a chance of 40% or less to make it on 4th down. The question is what gives the Colts a lower chance of scoring (and thus increases New England’s chances of winning)? Punting or going for it? It turns out going for it increased the Patriots’ chances of winning.

The reason is that if New England goes for the 4th down, for the Colts to then win depends on two events: 1) New England doesn’t get a first down and 2) New England cannot stop the Colts on defense. Note that once the first event has happened, the second does not depend on it. Hence, we can say that once New England doesn’t get a first down, the probability of the Colts scoring is an independent event. Thus, based on statistical theory, if New England goes for it we can say that:

 Prob. Of the Colts scoring =Prob. Of Patriots not making a first down x Prob. Of the Colts scoring when they get the ball

Because the Colts would get the ball in New England territory (around the 30-yard line) if New England doesn’t get a first down, we can assume the probability of the Colts scoring to be high between 70% and 90%! But that high probability of scoring first depends on stopping N. England on 4th down. Based on the table below, it only made sense for New England to punt if their chance of making it on 4th down was only 30% or less and the Colts chances of making it was 80% or higher.

 Probability of the Colts scoring:

Prob of not getting a 1st down on 4th and 2

Prob. Of Colts scoring a touch down
given that New England doesn’t make it on 4th and 2

Prob. Of Patriots not getting a first down and the Colts score

Correct Decision (assuming that Colts have 50% chance of scoring
if they start deep in their end zone)

50%

70%

35%

Go for it

50%

80%

40%

Go for it

50%

90%

45%

Go for it

60%

70%

42%

Go for it

60%

80%

48%

Go for it

60%

90%

54%

Don’t go for it

70%

70%

49%

Go for it

70%

80%

56%

Don’t go for it

70%

90%

63%

Don’t go for it

 Personally, I think that New England had at least a 40% chance of making it on 4th and 2 while the Colts had about a 70% chance of scoring a touchdown.  Of course, the correct call was to go for it. To me, this shows that Coach Belichick is a genius. Note that the thoughts expressed here are the results of Monday morning quarterbacking. Like most people, I would have gone for it and give my defense a pep talk on how defense wins championship.

This is why Coach Belichick will go to the hall of fame the very first time he’s eligible for it. I always knew there was a difference in how winners like him assess risks and make decisions.

Entry filed under: Sport, Sucess. Tags: , , , , , , , .

Dream versus Goal The difference between success and failure is small

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