<p>As I mentioned in other threads, the Revealed Preferences survey authors released data a while ago on the admissions rates by SAT range for several individual schools (graphs are published in the RP paper and in The Early Admissions Game), and substantially more detailed data for several categories of school: Ivy League, LAC, and the next few tiers below that. Their data was a random sample of students in the top 10 percent of good public high schools and top 20 percent of private schools. Those applicants with 1600 on the SAT were getting in at 75-90 percent probability at Ivy+2 category schools, 90-100 percent at LAC, and 100 percent (something like 40 out of 40 in their sample) to the next tier. You could see admissions rate go up fairly linearly with SAT scores.</p>
<p>If you look through Harvard’s articles each year celebrating their own selectiveness in the Crimson and the Gazette, some of those mention the rejection rates for valedictorians and perfect SAT scorers as evidence of selectivity. The reality is a bit different: a student from the top decile with high scores on a battery of tests is in at most of the top 10 schools. Extracurriculars are needed for those who don’t manage that. Tests are too discriminating and there are too few high scorers for the universities to be indifferent to a pattern of monster scores. Perhaps they are more indifferent if you are from a stereotypically high-testing population (Asians, Russian Jewish immigrants, maybe a limited number of other categories).</p>