In terms of the Bellichick's call....in terms of winning percentage it's probably the better option.
I'm not sure how you put numbers to it...but say they convert the 4th down 50% of time. 50% of the time they run the clock out and win for sure. The other 50% they leave 2 minutes and Indy the ball at the 30. Say Indy will score a TD 65% of the time.
The chances NE wins = 0.5+0.5*(1-0.65) = 0.675
If they just punt the ball Indy will get the ball on avg at their own 30? Does Indy score a touchdown greater than one out of every three attempts with two minutes to go in that situation.
These are just numbers I made up...maybe NE makes a first down more often...then it makes his call even better.
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