Not all that tricky. Just determine, did it have an adverse effect on the outcome. That's why you protest, just in case. Say the runner wound up scoring anyway, no bearing regardless of W or L.
Ex: R1 1 out, your team down by a run.
Fly ball to RF, R1 goes halfway to 2nd, see's the catch (2 outs) and is diving into 1B as F9 attempts to throw him out. The ball sails OOP.
The award would be 3B, umpire awards 2nd only, giving you the ole, he was going back to 1B (I've heard it to many times believe me).
You protest, next batter hit's a dinger, no bearing. Or K's, either way one could safely say, it had no bearing on the outcome.
Now say the same play and the first pitch to the next batter was a WP and now R2 advances to 3RD, the batter then K's, definetly could have had a bearing.
Now same play with 0 outs, and the next batter flies out to deep CF and you lose 1-0, easy to say the call had a bearing on the outcome.
You were down 13-0 at the time, wind up loosing 21-2, no bearing.
You win the game, no bearing.
But as others have stated, somebodies going to learn the correct ruling regardless if it's replayed or not, so worth the effort/s IMO.