While watching RichRod kick the extra point to send the UM/MSU game into overtime on Sat, I wondered: Why didn't he just go for two points and the win right then and there?

After a team scores a touchdown at the end of the game where the 6 puts you one shy of tying the game, as a coach you have two choices: kick the extra point and send the game to OT, or go for the two-point conversion and the win right then and there. I think most coaches play it conservative and kick in order to avoid the second guessing, but is this really the best strategy? If you go for the two, you have the ball on the 3 yard line with one shot to make those 3 yards, and no chance of the other team's offense getting on the field. If you go into OT, you have a coin toss, and one way or another you both get the ball at the 25, meaning you have to move the ball a bunch on plays that have to average more than 3 yards each anyway,  and you also have to play defense at some point.

Now I know the counter-argument is that by going for two, you only get one shot, and if something goes wrong, you don't get another play to make up for it. But so many things could go wrong on the extra point, on offense, on defense, that I think the odds are strongly in your favor to simply man up and take that single shot from the 3 yard line. I don't know the stat on percentage of two-pointers successfully converted, but unless your game played out in a defensive struggle where the only 2 TDs were scored by the respective defenses, I can't see how going to OT gives you a better chance of winning.