Actually, it
is hard to figure out. To simplify this a little bit, let us assume that in either case the coach will successfully attempt an onside kick and get the ball back at his own 45 yard line, and at some point successfully convert a 2 point try. Taking these things for granted, there are four variables that a coach should consider:
A) % chance of scoring a TD on 4th and goal from the 2
B) % chance of successfully kicking a FG from the 2
C) % chance, at your own 45, of driving into FG range and successfully making a FG in the allotted time.
D) % chance, at your own 45, of driving 55 yards for a TD in the allotted time.
If you determine A x C to be greater than B x D, then you should go for it. If not, kick the FG.
A and B are fairly easy to estimate. A quick Google search told me that teams are successful in 2 point conversions about 44% of the time, and that kickers make their PATs about 95% of the time. Of course, in the circumstance we are talking about, the ball is at the 2, not the 3. Unlike the NFL, in college you kick PATs and attempt two point conversions from the 3 yard line. I would think that moving in a yard might increase 2 point conversion success a little bit, but have almost no effect on PATs. Also distorting these statistics a little bit is the fact that if a snap is muffed and the placeholder picks it up and trys to run it in but fails, this is considered a failed two point try, not a failed PAT. But these are just estimates anyways, and so we'll say A=.44 and B=.95.
C and D are much more difficult to estimate. C especially would depend on how good your FG kicker is. But I'll guess C has a 40% success rate, and that and D has about a 15% success rate.
So..
A x C= .44 x .40 = .1760
B x D= .95 x .15 = .1425
Answer: If these numbers were correct, then you should go for it. But who knows what numbers you should actually plug in for these variables. The point is that it's not an easy decision, and the right choice would be different from game to game based on a lot of different factors.
Also, left out of this analysis is the fact that if you go for it on 4th, make it, and then recover the onside kick, you now have a chance to not only send the game into overtime, but to win it with a TD. Even if you missed the 2 point conversion, you would still have this opportunity.
And what if you don't recover the onside kick, but are able to stop them and get the ball back at your own 20 with 30 seconds left. It would be a LOT easier to get a FG in this situation than to get a TD.
So I think most of the time you should go for it. If you have a bad FG kicker (but not so bad that he can't make it from the 2 yard line), then it might be smarter to take the 3 points.