Caltech does not need to “just admit by SAT scores until they run out of slots” to get stats as high as it does because it only needs to admit about 550 students to get to its class size of ~235. With a class size that tiny and lots and lots of kids out there with high test and GPA stats, they can get pretty far down their CDS list of factors considered without compromising on the stats.
So, although they do have a mid-50% SAT II Math 2 of 800-800, they can also still look for students with Why Us?, Why STEM?, Honor Code, and other essays that look like a fit for the quirky Caltech culture. And, they can look through the high-stat pool for STEM research and competition success.
Yes, I expect they do look at URM status, 1st gen status, and sports as a tie-breaker when getting the admit list down to the right size. I don’t guess they look at ethnicity between Asian and white at all. Caltech’s incoming class is 16% URM.
I’m sure Caltech coaches know that athletes are going to have to be some of the stronger kids academically because of the extra time commitment of sports.
Legacy status is not that big a deal, considering that Caltech has only about 20-25,000 living alumni, and a lot fewer than that have high school graduates in any one year. An alum would know how tough Caltech is and would not want their kid to attend if they knew the kid wasn’t qualified.
The CDS list does not ask whether gender is considered. I believe it is, as they stated this year that 52% of Class of 2021 admits and 46% of incoming students are female. For comparison, the previous year’s CDS says about 26% of applicants were female. Having a more balanced undergrad class is important to them and to students (both male and female) who are attending.
Note that geography is not considered on the CDS, and the percent of California students (along with Asians) is higher than our representation in the general population. Though that is to be expected since Caltech is better known on the West Coast.
They aren’t kidding about wanting course rigor, though. Caltech has an optional (highly-encouraged) summer online course for incoming freshmen called “Transition to Mathematical Proofs.” It is quite challenging and seems to assume some prior knowledge not just of calculus, but also of set theory and more. When everyone has to take at least 3 quarters of proof-based math and physics using the Apostol textbooks (with a side of the Feynman lectures), they can’t admit a bunch of students who found the math sections of SAT/ACT/SAT II the least bit difficult.