<p>
</p>
<p>Admissions decisions are carefully considered, but several critical inputs to the strength of any particular file are uncontrollable by the applicant - namely the particular niche the school is looking to fill, plus questions of geographic and racial diversity. Because such a large part of what goes into the decision is effectively unknowable and resistant to influence by the applicant, it is random from the outside.</p>
<p>To answer the OPs question, statistics released by Stanford and Princeton suggest that for an unhooked applicant a top 5% rank and 2100+ SAT score is necessary for an unhooked applicant to be a reasonable contender, though “reasonable” is still a longshot - 80% of the kids with these stats still get rejected.</p>