[jstnrgrs]

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In superbowl XXXVIII, both teams scored 4 touchdwons and one field goal, but the patriots won by 3 in regulation. Why? Because Carolina attempted a two point conversion to early. The failed attempt ultimatly cost them three points, which was the Pats margin of victory.

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No, the failed attempt cost them slightly less than 1 point.

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IIRC, The score was 21-10 pats, car scored and failed a 2-point conversion 21-16 pats (net one point lost for car). Carolina scored again and again failed on a 2 pointer 22-21 car (net 2 points lost for car). The Pats scored, and made a sucesfull 2 pointer 29-22 pats (net 3 points lost for car).then carolina scored a touchdown, and the pats scored a field goal Final score 32-29 pats.

Both teams scored 4 touchdowns and a field gaol.

If carolina had not attempted the their first two pointer, none of the other 2 pointers would have been attempted. Assuming that the rest of the game went the same, had carolina not gone for two, the score would have been 31-31, and the game would have gone to overtime.

Perhapse you would rather look at it from an EV (I will call it EW for expected wins) perspective.

As I stated above, if Carolina had not gone for 2, the game would have been tied EW=0.5

Going for two:
1/8 of the time, the game will turn out as it did: 0.125*0

1/8 of the time, the pats would fail on their 2 pointer
this would have caused carolina to go for two after their final touchdown.
1/2 the time they would have made it, and the score at the end of regulation would be 30-30: 0.125*0.5*0.5
1/2 the time they would have failed, and the pats would win 30-28: 0.125*0.5*0

1/4 of the time, carolina would have been sucesfull on their second 2 pointer. This would have resulted in a 31-31 tie: 0.25*.05

1/2 the time, carolina would have been sucesfull on their first 2 point attempt. This would have caused the Pats to have to make a touchdown instead of a field goal as time expired. Lets assume the probability of them doing that is X: 0.5*X

EW=0.125*0+0.125*0.5*0.5+0.125*0.5*0+0.25*.05+0.5* X=0.15652+0.5*X

Since not going for 2 has an EW of 0.5, I then solve for X with EW=0.5

X=.17174

If you believe that the Pats chances of making a last second touchdown were less that 17.174%, then carolina was correct to go for 2. Otherwise they were not.