Sandy, I was one of the "PE Kids" who got WLed at HBS in Round 1 and applied to Stanford and Wharton in R2.
Do you think a "name-brand PE shop" (KKR/TPG/Apollo/Bain/Carlyle) + good stats (Ivy, 3.8, Physics, 770, very good college extracurrics) + very solid recs is good enough for Wharton? To be honest, very few people applied to Wharton in past years since most got in at H/S in Round 1. This year was pretty different.
Also, don't know where in the Wharton app you could've indicated that you really wanted to go there. Their career essay was 300 words and none of the others really lent themselves to that.
I assume Stanford is a total crapshoot no matter what.
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Your chances at Wharton are real good, esp. in R2, since I think they have accommodated (in 2nd year of this ) that they are now ,given early HBS r1 decison day, getting lots of overflow HBS-ding/wl crowd in R2, for whom W is now #1--to wit, YOU!
There was no need to state why Wharton this year, altho many still did, sorta Hail Mary-like, in those 300 words--to ZERO effect IMHO, altho others have told me it is super secret gold star at adcom, if so, someone tell me I'm wrong. I know lotsa kids into W round 1 w.out it, but who knows???
They used to ask directly, WHY WHARTON. WHY NOW, and when giving feedback, really told kids it is was weak answer to that which explained big part of ding (that was usually BS and they just did not have the genuineness to say, "dunno buddy, just a lot of other kids like you whom we liked more" which was absolute truth. And those accepted kids were not liked more b.c. of their execution of Why WHarton/Why now! )
Stanford is not a "total" crapshoot, it is a process with crapshoot elements once you very rationally ding 80 pct of applicants in 20 seconds for not having right stats, pedigree, connections etc. Among the remaining 20 pct it then becomes Frat Rush, where legacies, really good looking kids (by Stan lights) and diversity stars have a leg up--but within each of those silos there is crapshoot elements.