In backgammon, there comes a time when all pieces have passed each other; there is no more interaction, you are simply rolling it out until you can bear off all of your pieces. If one player is well ahead of the other at getting their pieces into their home board and bearing them off, then it might seem pointless to keep rolling it out; it may well be impossible, or at least extremely improbably, for the other player to make up the difference.
May the player who is behind resign in such a situation, or do they need to play it out in case of a gammon?
And if they are allowed to resign, are there any good rules of thumb to decide when it's worthwhile to do so, and when it's worthwhile to keep playing? For instance, has anyone calculated out the possibilities such that you can say "if player 1 has started bearing off, and player 2 has x pieces outside of their home board, there is no possible way for player 2 to win." Or, has anyone calculated out the probabilities, such that you can determine based on the position that there's only a one in a million chance of winning, and it's probably not worth hoping for that, while in another situation, you might have 10 to 1 odds and it's worth seeing if you make it.
edit to add: According to a thread on Backgammon Galore, along with their glossary, you can offer to resign with any outcome (backgammon, gammon, or a simple win). If you offer one of the lower outcomes (gammon or simple win), your opponent can refuse in order to take the chance at getting the higher outcome. Of course, this only applies if you're playing in a tournament, a rating system, or for money where the value of the win matters.
So, I've answered the first half of my question, but I'm still interested in the second half; when should you resign? Are there any good rules of thumb, or has anyone done a statistical analysis, of what points in the game one player can be guaranteed to lose, or have such a low probability of winning that it's worth it to just resign? Are there any good ways to tell when you should offer to resign with a gammon?