The latest CDS shows very different numbers:
Michigan 25th – 660/670; Princeton 25th – 710/720
Michigan 75th – 730/780, Princeton 75th – 780/790
The latest CDS also lists different numbers for Stanford:
Harvard 25th – 730/730, Stanford 25th – 700/720
The CDS does not list a 800 on verbal for yale, but more importatantly, if 25% of students received a 800 on math and 25% of students received an 800 on verbal, it does not mean 25% of students received a 1600. Most of those students probably received 800 on one section, but not the other. ~40% of matriculating students did not report the SAT at all. I expect many of this not reporting group scored less than 1600 as well.
For colleges like HYPSM, SAT score percentiles is not a particularly good indicator of how much score is valued because the colleges primarily admit on non-score criteria that has some degree of correlation with score. MIT’s website explains this more eloquently than I can in the quote below
***"Now, I and others are on the record as saying that we admit people, not test scores, and that in any case there is really not a difference in our process between someone who scores, say, a 740 on the SAT math, and someone who scores an 800 on the SAT math. So why, as the commentor asks, is there such a difference in the admit rate? Aha! Clearly we DO prefer higher SAT scores!
Well no, we don’t. What we prefer are things which may coincide with higher SAT scores. For example, a student who receives a gold medal at the IMO is probably more likely to score an 800 on the math SAT than a 740. But if we take an IMO medalist (with an 800) over random applicant X (with a 740), does that mean we preferred an 800 to a 740? No. It means we preferred the IMO medalist, who also happened to get an 800!"***
If a HYPSM type college did not consider scores at all in their application process, they’d still have a very high score range due a high scoring applicant pool and selecting for characteristics that are correlated with score (high GPA, high course rigor, stellar LORs, impressive out of classroom achievements, etc.). However, there would be a larger number of anomalies at the low end, so I’d expect the 25th percentile to have more notable decreases. We see this effect in test optional colleges. For example, a comparison of score ranges for Bowdoin (test optional) to other top ranked LACs is below. I used ACT instead of SAT for simplicity. Note that Bowdoin has all matriculating students take either SAT or ACT and reports all students, even though it is not considered in application process for non-submitters. The gap is larger in 25th percentile than 75th, when tests are not considered for a large portion of applicants.
Bowdoin – 30-34
Amherst – 31-34
Swarthmore – 31-34
A similar effect occurs when a large portion of applicants are given strong preference, such as strong hooks. Hooks have more impact on the 25th percentile score than the 75th percentile score, so a lower 25th also can have implications on hook preferences.
If you want to guess at how much score impacts admissions by score ranges, you might look for colleges that having higher/lower score ranges than suggested by their selectivity and/or give scholarships for high stats or NMS. Vanderbilt is a good example. An ACT comparison is below. Vanderbilt has a higher score range than HYPS (and all the LACs listed above), even though most would consider Vanderbilt less selective than HYPS. Both the 25th and 75th percentile scores seem higher than expected. You can confirm by reviewing Naviance and similar scattergrams. Scattergram decisions for Vanderbilt seem to better follow scores than HYPS, particularly for the 75th percentile.
Vanderbilt – 33-35
Harvard – 32-35
Yale – 32-35
Princeton – 31-35
Stanford – 32-35