Can you show the math please?
There are four possible outcomes from the two decisions.
1) You go for 2 at the 7 minute mark and fail
2) You go for 2 later and fail
3) You go for 2 at the 7 minute mark and succeed
4) You go for 2 later and succeed
Now is anyone really going to argue that failing later improves your chances of winning the game? Is it better to be down 2 at the 1 or 0 minute mark kicking off than down 9 kicking off at the 7 minute mark? Remember you believed it was a one possession game and strategically left as little time on the clock as possible. Now you need to recover the on side kick with around a
10% chance of success, move the ball from the 45 or so to the 30 or so (25 yards) with little time. Lots of talk about how each team plays and momentum and what not, but the simple fact is that the team that knows they missed at 7 minutes is in a superior position to do something about it. They will be forced to play more aggressive and at the same time the opponent will be more conservative. Thus it will be easier to get the first score, sooner.
If you are going to fail, are you really going to argue that there is an advantage to failing later?
What if you score on the two point conversion, then it would be a wash correct? No! If you are down one with a few seconds to go you probably won't try for two (only a half dozen times has this happened - I think at roughly 50-50 results) but at least you have the option to win it on this play. That tiny advantage that most won't take still swings the math. And down one with a few seconds to go if the play doesn't stop for time outs or replays or whatever most of the time you should be ready to go for two and take advantage of that momentum that the go for one crowd says is so important. Of course some of you are probably arguing that it is dangerous to give coaches this option that having this option available makes going for two later the better choice. Of course for 20+ pages these same guys have been arguing that coaches are constantly making the optimal choices.
So failing earlier is better than failing later. And making it earlier is better than making it later. And there are really no other choices.
On page one you argued that the trailing team gets no new information that the leading team doesn't get. Both teams will thus adjust accordingly. The leading team will get more conservative the further out ahead they are and the trailing team will get more aggressive the further behind they are. The leading team would be better of being left in the dark in this case. Of course there are some coaches secure enough in their success that they don't play by the book. If that is your opposition there is even more reason to go for two.