“The total number of the staff of an institution winning Nobel Prizes in Physics, Chemistry, Medicine and Economics and Fields Medal in Mathematics.”
The Nobel and the Fields are such tail events that while such winners add luster to a faculty, they are pretty meaningless as indicators of faculty excellence. Michigan has something like 6,000 faculty members (tenure, tenure track, instructor). Even half a dozen of such awardees would not meaningfully move the needle as to either scholarship or instructional heft. Further, the Nobel is typically granted for work done 25 to 40 years earlier and tells us where science in a field has been and where it went for 10 years after the work was done, but little about the future direction of a given field.
Of course this very short list of prizes leaves out many of the ones that actually count as far as potential value added to the instructional side of the picture: Sloan fellowship (said to be a strong indicator of Nobel potential…Michigan has probably had over 90 such fellows); the MacArthur fellowship…Michigan has had 23 alums (ranking it in the top 10 nationally, inclusive of publics and privates) win the prize and something like 35 on faculty (with significant overlap); the Pulitzer; the Guggenheim; the faculty Fulbright; national academy members in the arts and sciences…
In other words, the very short of list of prizes which are awarded points under this system is more notable for what it leaves out than for what it includes.
By the measure of citations, citation strength, patents, major teaching prizes won, research dollars awarded through grant, Michigan routinely ranks in the top 5-10 in the country by component; by aggregate, in the top five faculties in the country. Any other ranking is just wrong. Not residing in the top 10 doesn’t scan when the programs taught by those faculty members show 101 programs in the top ten in the nation, and a graduate program ranking (in aggregate) of 4th in the country (behind: Berkeley, Harvard and Stanford).