Well, you could just drop the random component entirely and flip a coin at the end of the week for all ties. I suspect that would make players a lot more unhappy though.
There are some subtle differences based of how extreme the magnitude is chosen. That’s approaching a level of complexity few readers will be able to follow though. The relevant part is that the random component doesn’t favor anybody. In the very rare cases it changes placements, it has the same chance to do so for both sides, and is guaranteed do to it equally often for both sides in the long run.
As weird as it sounds, randomness actually guarantees 0% unfairness when distributed evenly. You seem to be looking for something that doesn’t involve any randomness at all, I’m afraid that’s impossible unless you play something entirely deterministic like chess.