Why don't coaches understand fundamental math?

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Situation: it's 4th and goal from the 4 yard line with a little over 7 minutes on the clock and we're down by 19.

Our team kicks the field goal. The argument of course is you take the sure points and it puts you within 2 scores of tieing the game. If you go for it and miss, game over.

This is all true but it misses the entire point which is to MAXIMIZE OUR OVERALL CHANCES OF WINNING THE GAME. How could a high level coach who is paid millions of dollars get this wrong?

Scenario 1, Kick the field goal:
1. Successfully kick field goal
2. Score touchdown
3. 2 point conversion
4. Another touchdown
5. Another 2 point conversion
6. win in overtime

Scenario 2, go for it!
1. TD on 4th and 4
2. Score a touchdown
3. xtra point
4. Another TD
5. Another Xtra pnt.
6. We Win!

Points 2&4 cancel eachother out in both scenarios so let's look at the approximate probablilities of points 1,3,5,(6) in each scenario and figure our odds of success:

Scenario 1:

Kick field goal (~95%) * 2point conversion (~45%) * 2nd 2 point conversion (~45%) * win in OT (~50%) = .096

Scenario 2:

Go fo it (~35%) * xtra point (~95%) * xtra point (~95%) = .31

So basic math proves going for the field goal decreases our chances of winning by a factor of more than 3. It's not even close. (please let me know if i'm missing something here)

It consistently amazes me how often coaches in all sports ignore math and instead use prevailing wisdom/tradition in making game changing decisions.

Please discuss...