The challenge with measuring PhD productivity on a program-by-program basis is not only that it’s tedious, but also that the denominator sizes become quite small. Even a large university like Berkeley or Wisconsin might be graduating only 20-40 physics majors per year. With data sets that small, year-over-year variances become more significant. So does the method of calculating the denominator. How for instance do you account for students other than physics majors who might be earning physics PhDs? So, it’s easier just to normalize by the whole institution size (which might be appropriate for LACs, or for a school like UChicago that has only a college of A&S, but not for multi-college schools like Cornell or for many state flagships).
FWIW as a complete and total outsider to this, just a mom of a physics/math major who loves physics with plans of pursuing a PhD, I am not sure just how relevant that level of analysis is for a high school student. This student should be far more focused on making sure that they are proactive in pursuing opportunities for research, earning a high GPA, and being able to score well on the physics GRE. If they can excel on their campus, whatever campus that is, that is going to make the difference when it comes to applying to grad school.
Thanks for your insightful input