Some Simplistic Assumptions That Would Justify My Play
First assume that after scoring to go down by four you stop them. (This assumption hurts my position because if you go for one and they come back to score a field goal, a rare last second comeback touchdown by you is a win rather than a tie [if you missed the two pointer]. But since this scenario is so rare, I will ignore it.)
Assume also that overtime is even money.
Now to throw out some reasonable numbers, we will say that after scoring and stopping them you have a twenty percent chance of scoring a touchdown if you need it (because you missed the two pointer). And if you don't need it you will come back and score a field goal 40% and a touchdown another 3%.
If a two conversion is 40% and a one pointer is 100% (the real numbers help my case a bit) then:
If you go for one you will win 23%. The touchdown plus half your chances of making a tying field goal.
If you go for two your chances of wining is 40%x43% = 17.2% when you succeed and score PLUS 60%x20% = 12% when you fail on your two pointer but come back with a touchdown. That adds up to 29.2%. Quite a bit better than 23%.
Drop the needed touchdown percent to 15% and we still have a clear edge for the two point attempt.
Again remember that these numbers assume the opponent is stopped. The real numbers are smaller.
It is important to realize that plays like this come up not only because of disadvantages of going for ties but also because of poker like advantages of going last. It is sometimes worth giving up a little bit of instant EV if it will make a later decision more clear cut. For instance suppose you dealt five cards to an opponent who drew to them and showed you his hand. You win if your five cards, after drawing, beat him. Knowing what you have to beat is enough of an advantage that you could lay a small price every hand. This football situation may be analogous.
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