^ I think what you’re suggesting is that a department with low PhD production isn’t necessarily a weak department. I’m inclined to agree with that. Is the converse likely to be true? Is it very likely that a weak department would motivate and prepare relatively many of its graduates to complete doctorates in the same field?
Look at the lists above. Is it just a coincidence that St. Olaf has especially high PhD production rates in Math? That (and choral music) seems to be one of its premier departments. Is it a coincidence that Colorado College and Eckerd have especially high rates in Geosciences? Look at a map, or satellite pictures, of CC’s and Eckerd’s locations. Those two schools are superbly sited for field work in geology (CC) and oceanography (Eckerd).
Is it a coincidence that most of the top LACs in geoscience PhD production are Keck Geology Consortium members?
(http://www.keckgeology.org/).
Is it a coincidence that Amherst’s numbers for physical sciences are relatively low? I don’t think so. It must be almost the only selective LAC that has not built a new science center in years.