The big question here is whether it is best to run out with both checkers to eliminate backgammons, or is it best to stay back. And then, if you stay back, do you stay back with one checker or two?
First, it's right to just leave and save the backgammon. But if you do decide to stay, it is better to leave with one because if White doesn't roll a 1 or 2 you can still escape with the other checker on the next roll and save the backgammon.
Now, let's suppose that White is 2-away and backgammons don't matter (Red loses the match whether he loses a gammon or backgammon). Then it is right to stay back with 2 checkers as you stop 1-1 and 2-2 from becoming Jokers and you get a nice double shot if White rolls a 2-3, 2-4, 2-5 or 2-6.