Stop with the emotions and look at the math....Belichick made the right call

I'm watching all of the commentary and the consensus among people on this is that Belichick let the emotions get the best of him and let emotion override discretion and wisdom.  They made a stupid call and thats why the Patriots lost.  I really don't get it.  Don't these people realize that this is why the Belichick is Belichick?  Calls like this one are why he has won all those Super Bowls.  Seriously, the man has the numbers on his side.

Consider a thought experiment.  What should the Colts have done if the call was up to them?  Belichick calls timeout and crosses the field and tells Caldwell.  Its up to you.  I can punt or I can go.

If you are Caldwell, do you give up a sure opportunity for Manning to get the ball back with plenty of time left in order to gamble that Brady couldn't get 2 yards.  Or do you take the safe route and ask them to punt?

My guess is that nearly every commentator that is saying that Belichick should have punted there would have told Caldwell that he should have accepted a punt if it was up to him.  The thing is that is wrong.  Its just blatantly and obviously wrong.  If going was a mistake for the Pats, it had to be a benefit to the Colts.  And vice versa.  But the truth is, if Caldwell had done that he would have been making a huge and bad gamble.  

Here is the math:  I'm going to give the algebra first and then fill in the variables.  There might be some debate over the numbers, but this is the basic formula.  You really can't argue with the formula.  You can only change the numbers in it.

Psucc = Probability of converting 4th down

Pi65 = Probability of stopping from Indy from scoring giving Indy the ball 65 yards out.

Pi28 = Probability of stopping Indy from scoring giving them the ball 28 yards out.

If  Psucc + (1- Psucc) * Pi28 > Pi65, you should go for it.  If

Psucc + (1- Psucc) * Pi28 < Pi65 you should punt.  Its that simple.  Now, all you have to do is plug the appropriate numbers in. 

I have a fairly complicated model that I use.  It basically takes NFL averages and adjusts for the strength of the offense and the defense in question.  I have:

Psucc = 60%

Pi65 = 58%

Pi28 = 73%

Win Probability of going for it =

0.6 + (0.4 * 0.58) = 0.83

83% > 73%

The calculated and logical decision was to go for it.  The emotional decision was to give into the emotion of fear and punt.

I'm curious for all of the people that question the call, what numbers they were plugging into their calculations.

It seems to me like they are saying two sort of contradictory things.  They seem to think Pi28 is really low because Manning is the best QB on earth.  They also seem to think that Pi65 is really high because there is no way that Manning could score from 65 yards out with 2 minutes and a timeout left.  I'm not sure how those two facts seem to work together.  I wish that some of these people that are saying that punting is the "smart" decision would explain some of the logic behind their mathematical model because I really don't get it.  I've tried changing the variables around....making Manning stronger or weaker.  The thing is that when I change Pi28, I need to change Pi65 as well.  Any numbers that have any semblance to reality for probabilities say you should go for it.  I know this is strange and that it doesn't hold to conventional wisdom.  But remember conventional wisdom is long on convention and short on wisdom.

Thats the other weird thing about the "have confidence in your defense" argument.  Belichick did have confidence in his defense.  The 4th down move wasn't a bet that the offense would win the game on that play.  It was a bet that either the offense would win on that play or the defense would hold them for the last 28 yards.

Google David Romer 4th down.  Romer is a professor at Stanford.  He did a whole long mathematical analysis on this topic.   Nearly every other math person that has looked at this topic in any detail agrees with Romer.  The Patriots are the Patriots because they take calculated risks.  I'd expect gamblers or "sports investors" as a lot of the people on this blog seem to describe themselves as the kind of people that would instinctually understand this.

[Quote: Originally Posted by richardtonsj] but does the math model actually takes in account the field position and the game situation when going for it on 4th and 2?   [/Quote

Or the intangibles like how battered is the N. E. defense at that point.  I still would have punted so I wouldn't have to answer the question all week, but Bill figured he would "get it" and be the gutsy genious. Not an easy decision really the way Manning can move the ball in the prevent...but they would have been easier on him had he punted and lost while playing the best %'age.  

i respect math, especially when it comes to sports . . . but i'm curious, does romer have a large enough sample of plays of this nature to offer probability that are consistent with the theory of large numbers.   clearly, this was a reasonable 4th down play that was decisive to the game result, and not some 4th and 2 play when a team is on there own 28 and trailing by 5 points.  as we all know, decisive plays should be judged differently than either random plays or 4th down plays when a team is trailing and the play isn't considered decisive (winner take all) for both teams.

i'm not dismissing his math, but how many plays from his sample size came from a game of this nature ?  on the flipside, perhaps bill is just playing the averages . . . if he does that 10 times, he will be successful 8 times . . . we just happened to see one of the two.