I wonder what the conservation law is connected to the 'analysis invariance', i.e. the fact that no matter how well you've thought through everything beforehand

I wonder what the conservation law is connected to the 'analysis invariance', i.e. the fact that no matter how well you've thought through everything beforehand, there will still be some recalcitrant pocket of the experiment that behaves confusingly. Maybe that's the 'conservation of surprise'.