I'll stop you right there. The problem with this exercise is that it assumes all probabilities are constant over each team. A team like the Giants who can't score from the red zone have a much lower 2 pt conversion percentage than the average. I agree that if you're going to go for 2 you're better off on the first TD, but my non-stat assessment of the Giants is that they do not have anywhere near a 50% chance of succeeding on a 2 point conversion. Frankly I think they'd have been better off kicking a quick FG rather than a TD at the end of the game. Clock more important.Stats nerds will like this, the people that post here that used to take our lunch money and stick us into lockers won't.
Here's my breakdown on the math behind going for two and why it was absolutely the right call mathematically. This is from another board. @Machinehead.
There has been a lot written about 2 point conversions being better value than extra points. So I won't go to the general theory behind that. However, I will take a look at today's specific situation and show that Shurmur was 100% right, at least mathematically. I have a friend that argues based on qualitative factors such as momentum why he was wrong. That's an argument that if it's possible to prove is beyond my pay grade. So I will just quantify the probabilities of going for 2 and not going about it the old-fashioned way.
First of all, here are my assumptions:
1) Two TDs will be scored in regulation and the Falcons will be stopped from scoring any more points. Without that, we lose regardless of what Shurmur's call was. I guess there are wacky scenarios like a TD and 3 FGs also winning, but let's not complicate things.
2) I count ties as losses as I'm sure any head coach worth his salt does. So not winning means tying or losing.
To do the math there are really only three probabilities that need to be known. Probability of a successful PAT, probability of a successful 2 pt conversion, and the probability of winning in OT.
Probability of a successful PAT and 2 pt conversion is covered in this (unfortunately slightly outdated) FiveThirtyEight article from November 15, 2016:
Prob of PAT: 0.944
Prob of 2pt Conversion: 0.479
I middled 2 6 pt teasers with the Giants, Atlanta pick'em and Giants +10.5. One thing about the Giants is that they lose games but usually don't get blown out. You can always count on garbage time Eli to make things look close. Parlays are sucker bets.