Some Universities seem to publicly announce the recipients of their most valuable institutional scholarships after May 1st. The students who are offered these scholarships must have choices, so I wonder what percentage of finalists are actually being offered the scholarships.
For example, Ohio State had 74 Eminence Fellows finalists in February 2020, then announced 21 selections on May 11th. Since all the finalists must have been exceptional, some must chose to go somewhere else. I wonder how many full-ride scholarships Ohio State and similar very-good-but-not-preeminent-universities are offering in order to yield the number of recipients they announce.
Any insights would be appreciated.
It’ll vary from school to school, especially when you consider factors such as location and academic “prestige” (which is mistakenly important to a lot of students.)
If you’re looking for merit scholarships, I recommend that you apply widely (safeties, matches, and reaches) and hope for the best! 
Hope that helps!
It would be typical for a college with a small number of full rides to offer the number of scholarships a college has available and then have a ranked waitlist. You may be told your position on the waitlist.
But that is not always the case. For example the UCs offer more Regents scholarships and then take into account the expected yield (ranging from ~10% yield at lower ranking UCs to 50% at UCLA/UCB because it’s not enough money to be decisive).
With regard to the college I know well (Utah), which has a separate application process after admission for competitive scholarships so filters out those who aren’t at all interested, they have 30 full rides per year, 60 are interviewed and then they go about 4-8 deep into the waitlist. But that may be on the low side because most offers go to instate students and Utah has one of the highest percentages in the country of college students staying instate.
It depends. UGA, for example, had a yield problem one year, when too many accepted the scholarship. They adjusted the number of offers the following year to get closer to their target number of acceptances. And yes, many winners had multiple full ride offers and/or multiple top 10 acceptances.