Can anyone/anything beat "The Law of Averages" or does it apply everywhere to everything all the time?

Typically, a “law of averages” presents a point of reference, a simplifying of relative data. Averages can change as new inputs arise, or as methods of averaging vary. So yes, I’d hypothesize there are things that can corrupt laws of average.

I’m aware of paltry few things that apply to everything, everywhere, all the time. Change, death, and gravity being among them.