Meaning down by 8 after having just scored 6 on a TD. And in a late Q4 situation where you have only one more realistic chance at the ball (either by defensive stop or onside kick recovery). We’re assuming that you get the ball back without the other team scoring and then score another TD. Otherwise the whole issue is moot anyway and you may as well go home. So the question is which option gives the best chance assuming you can pull off the hard part.
ISTM that the 2 pt option gives the best odds. Because it gives you a chance to win if you make it, and a chance to tie if you don’t.
My thinking is that you go for the 2pt conversion. If you make it, then you’re only 6 down. Then on your next TD you can go for the PAT and win the game outright. But even if you fail, then you go for the 2 pts again on your next TD, and can still tie it. By contrast if you go for the PAT both times you can at best tie.
I did the math assuming that 45% of 2 pt conversions are successful as are 99% of PATs. Based on these assumptions, the chances if going for the 2 pts are:
Assuming ties are a 50% chance of ultimate victory, breaks it down to:
By contrast, going for the PAT
Again assuming ties are a 50% chance of victory, breaks it down to:
Not a huge difference, although the discrepancy could be higher if the 2 point conversion percentage is higher (or the PAT percentage lower). But still, it seems clearly to be the better choice and I don’t recall an instance of a team going for the 2 in this situation - this came up most recently in the NY/Dallas game yesterday - or of the decision even being remarked on (although frankly it’s not the uppermost issue in the game at that point). Though I’m admittedly not a huge football fan and might have missed it.