how often is a player option accepted or rejected? what would make it more likely/unlikely to be accepted or rejected?

If it's for a lot of money, they seem to accept it most of the time.
If the algorithm thinks they'll get more total dollars, even if it's over 2 years, they seem to reject it.
I don't think there's a specific answer to this. You agree to a contract with a player or mutual option, you take your chances.
If you structure the contract so the last year is for low dollars, if the player is still good they will reject it.
You don't want to risk it? Guarantee the last season.