Lazy, unsolicited feedback: I wanted to read the high-level takeaways from this post without reading more than >30% of the entire thing, but it was hard. Maybe you could consider starting with a TL;DR, rather than caveats? :)
Granular evidence from my own high school indicates that many, and likely most, of the smartest students US college applicants (proxied by SAT) will get rejected from:
any particular top school they apply to
all of Harvard, Stanford, MIT, Yale, and Princeton (as an arbitrary example)
There’s more overlap between “great,” “good,” and “decent” schools in terms of students’ academic capability than one might expect (and I certainly expected), mostly because the top ~quarter of students at dozens of schools look pretty similar.
Therefore
The base rate of acceptance to any top US school among very top (99.5th+ percentile SAT-scoring, which is >median at all such schools) students, is low, maybe on the order of 20%; Phrased another way, using Princeton as an example random example:P(smarter than avg Princeton student | attends Princeton)=.5<P(accepted to Princeton | apply, smarter than most Princeton students)
Scott Aaronson’s rejection at 15, “from all five of “HYPMS” despite a 1600 SAT and a single-author paper in a major computer science conference” is an illustrative example, not an exception to it.
Lazy, unsolicited feedback: I wanted to read the high-level takeaways from this post without reading more than >30% of the entire thing, but it was hard. Maybe you could consider starting with a TL;DR, rather than caveats? :)
Added, thanks for the suggestion!
I love unsolicited feedback (not being sarcastic haha)!,
Yeah idk why adding TL;DR didn’t cross my mind. Will to get on that soon, thanks