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So HYPSM definitely focus on stats, it would be impossible for them to have such high averages without a lot of high stat kids walking around campus.
Ok but HYPSM are in the top-10 schools with the highest averages, in fact a few higher than Vanderbilt. This is the list I saw recently:
1-10: Cal Tech, Chicago, MIT, Harvard, Yale, Princeton, Vanderbilt, WashU-Stl, Columbia, Stanford
The top 20 schools are NOT predictable in any way. Many, many, MANY kids with perfect scores and GPAs are declined. How can that be predictable. In essence you need to be at or extremely close to that level just to play the game. Then it becomes about all the other things.
Why would you assume that? If Vanderbilt has a reputation for favoring high scores, then you'd expect more high scoring applicants to apply there over Harvard. In fact Harvard would get more low scorers applying because they don't prioritize high scorers. The 1200/27 ACT applicant who thinks they're going to change the world will apply to Harvard over Vanderbilt, right? Of course, Harvard actually wants a ton of high scorers to apply, they're not going to have a bunch of 27/1200 running around campus.