I think the math is going to be roughly that if 1⁄3 of the prizes go to schools 1-10, 1⁄3 to schools 11-100, and 1⁄3 to schools 101-onwards, then the hit rate (in terms of prizewinners) goes up by an order of magnitude each time you narrow your target audience. So if you’re going to target non-elite schools, and you can’t fully support hundreds of schools, you’d want to do that outreach at least somewhat more cheaply—making books available or something.
I think the math is going to be roughly that if 1⁄3 of the prizes go to schools 1-10, 1⁄3 to schools 11-100, and 1⁄3 to schools 101-onwards, then the hit rate (in terms of prizewinners) goes up by an order of magnitude each time you narrow your target audience. So if you’re going to target non-elite schools, and you can’t fully support hundreds of schools, you’d want to do that outreach at least somewhat more cheaply—making books available or something.
Please see my reply to devanshpandey. Also, I edited that I was interested in seeing the math on standard deviations between universities.