@liska21 most of the top Putnam scorers (including a few Putnam fellows) I know were either MOPpers and/or USAMO/IMO participants. My best guess is that the number of top-500 scorers on the Putnam is most strongly correlated with the number of such participants, not necessarily the caliber or size of the school.
Fwiw, my best Putnam score was 20, which narrowly missed the top 500 that year (I think 21 was the cutoff).