I'm not sure anyone knows the odds of anything that happens with a non-slot player. Like I said, I was expecting a fight with the player I just signed. One of my previous draftees took five or six offers before he signed. I go back and look at previous drafts for the players who signed over slot, to get an idea of what I might need to budget. Expect the worst, hope for the best.
I've even seen a "Probably Won't Sign" player sign the initial offer. Probably super rare, but it did happen at least once.