How well do the medical school ranks correlate with academic residency and fellowship ranks? Or do the residency and fellowship ranks correlate more with hospital rankings? I came across a few threads and anecdotally saw that the higher the rank of the medical school, the more sought after the residency/fellowship. For example in IM places like UCSF/Hopkins/MGH/Penn rank much higher than top places which are ranked in the teens (Cornell/Vanderbilt/Pitt). Are these training sites ranked so high because of their associations with their respective medical schools?
Browsing a few threads on SDN I found that despite being qualitatively very similar in terms of resources and prestige, Columbia is a lot more desirable for IM than Mount Sinai because they have a better track record of sending their graduates into “top” (whatever that means?) fellowships in GI, cards, etc. Do fellowship directors look at Columbia residency more favorably because they get their better reputation from their medical school rank?
I think it goes without saying that while the student is the ultimate variable for where they end up; going to a top school that puts more graduates into desirable programs is advantageous (ie: Columbia vs Sinai for IM, neurosurgery, etc).
Tl;dr: Why do most top residencies correlate so well with the top ten medical schools?