Thank you Jonathan! This is very helpful. With metrics formed from Bernoulli trials (which is what I think you’re referring to in the Numerator/Denominator sense), the first two moments are sufficient. In fact, with only the first two moments, you are bound to use the Normal distribution.
While I can see a metric like “searches per searcher” being reasonably well-behaved, it certainly doesn’t need to be normal, although I suppose the normality assumption is sufficient?