[fluidcruft]

> "X have upper hand" implies that on average X are better off than non-X.

I don't think that's a valid inference, honestly. Firstly, "average" is too tied to distribution and biased outliers and asymmetry. Perhaps you intended to compare medians.

"have the upper hand" I think means that when you compare proportions of X to non-X within strata that the proportion of X decreases with increasing status.