Is there a mathematical expression in probability for the notion that unless someone is making a special effort (concerted or otherwise) they can't be any 'wronger' than 50% accuracy?

That's exactly what I was wondering. A perfect score presumably means either an amazing coincidence or perfect intelligence within the context of the decisions made. (Or is it just perfect information?) And a perfectly incorrect score would then mean the same thing. And a score that exactly matches randomness would seem to involve no intelligence or information at all, although it, too, could presumably also result from perfect information, if that was the objective.