Timing in the game is critical when it comes to deciding whether a 2-point conversion is worth it. There’s the infamous chart I hear commentators refer to at times, but it doesn’t take into account varriability. So, for instance, if you’re down by 18 in the first half, I can’t imagine going for 2, but in the examples given by the OP, with roughly 9 and 4 minutes left, I’d think it’s pretty much a given.
Yes, there’s the psychological factor involved, but if you’re going to get that whether you miss it earlier and now know you need two more touchdowns, or if you get to the end and need it to tie and then miss it. And if you make it, maybe it helps swing more momentum your way. But really, the big reason is that, if you miss it earlier, you get the chance to adjust for it.
As an example, let’s say you just kick the extra point, then you get the ball back and are driving but stall on your opponent’s 30, it’s 4th and 5. If go for it and made it, you can fairly comfortably kick the field goal. If you go for it and miss it, you know you have to go for it. But if you kick the extra point, you’ve just lost your ability to account for that variable in this situation, so essentially doubling down that decision.
So, basically, I guess, my point is, if you’ll have to go for 2, you want to do it as soon as reasonably possible without doing it so soon that you aren’t reasonably accounting for mulitple scoring opportunities by you and the other team. I’d say a rule of thumb is probably number of possessions remaining is roughly number of scores needed plus one. So, at roughly 9 minutes, you can expect to have 2-3 more possessions, and so being down by 12 and with the choice of the conversion, it makes sense.
And, of course, let us not forget that the extra point isn’t guaranteed either. Yeah, it’s usually a given, and teams usually don’t even really try to block it, but in a tight game you’ll see them go after it more aggressively.
That all said, I still think coaches in the NFL are, in general, way too conservative when it comes to this sort of stuff. Teams punting on their opponents 45 on 4th and 1, or whatever. Yeah, coaches get crap when they go for it and fail, but if it were more common, they’d get less flack for the mathematically sound decision. Don’t teams have someone either on staff or as a consultant that can analyze their stats and help them make these sorts of decisions like when to punt or go for field goals based on their pass performance in similar game conditions? Can’t they help them figure out odds on making the various conversions and how it would work out given the current game conditions?