Hit rate is a measurement, not a tuning knob

What number should you measure instead of tuning the hit rate?

The number is not "hit rate". Hit rate is an outcome. The input is a distribution: how far apart in time the repeats of each item are. The useful and rarely taught fact is that this distribution can be measured independently of any cache, in one pass over the request log, and it predicts the hit rate for every cache size at the same time.

Cache sizing is therefore not an experiment. It is a measurement followed by arithmetic.