I would take the safety. Based on the fact that your placekicking game is nonexistent, you’re going to need to score a touchdown to win. If you take the safety and punt from your 20, unmolested, instead of from your 5, you should gain 15-25 yards of field position. Since you’re going to need a defensive stop and a touchdown to win, those yards, with time running out, could be crucial. Bottom line—if you have a low probability of eventually kicking a field goal, being down by 4 doesn’t hurt you any more than being down by 1, and the improved field position could help.
(Nobody else should bother answering. I am right.)
Wait, you said “down by 4” - a safety is 2 points so that would mean you would still be only down by 3 so a FG would tie up the game. Right?
Exactly my point. If the punt had been blocked for a TD, everyone would be questioning why the coach didn’t take the safe option.