Mom24boys: I wish I had an answer to your question based on my analysis, but others may find what I cobbled together interesting. I wonder if prior years' results threads might provide any insight on selectivity based on class rank %.
Straw-man Selectivity Funnel for Chancellor's scholarships:
1) Total PITT Applicants = 25000 approx
2) Full Tution Offers = 1000 approx (less than 4% of total applicants) [1/25]
3) Chancellor's Invitees = 500 approx (range of 450-500 given) [1/50]
4) Submitted Chanc Applications = 250 approx (range of 250-300 given) [1/100]
5) Chanc Nominees Invites for interview = 50 approx (range of 50-60 given) [1/500]
6) Chanc Scholarships awarded = 10 approx (official source?) [1/2500]
7) Matriculating Chanc Awardees = ???? (curiousity only)
I wish I could recast the odds based on UHC eligible applicants instead of the total applicants. But the number of "UHC Eligible Applicants" is not readily avaialble, but it must be quite high given that nearly 4% are offered full tution. Offcial stats indicate that approximately 660 of the enrolled students (18% of 3678 in 2012) were UHC eligible.
1) University of Pittsburgh: Undergraduate Admissions & Financial Aid
(class of 2012 stats)
2) Post #17 of this thread (thanks, MTnest)
3,4,5) Frequently Asked Questions | Chancellor's Scholarship Application Website
6) Chancellor Scholarship - University of Pittsburgh, Pittsburgh Campus - College Scholarships and Grants