American College Admissions Doesn't Need to Be So Competitive

post by Arjun Panickssery (arjun-panickssery) · 2025-04-07T17:35:26.791Z · LW · GW · 4 comments

This is a link post for https://arjunpanickssery.substack.com/p/college-admissions-doesnt-need-to

Contents

4 comments

Spoiler: “So after removing the international students from the calculations, and using the middle-of-the-range estimates, the conclusion: The top-scoring 19,000 American students each year are competing in top-20 admissions for about 12,000 spots out of 44,000 total. Among the Ivy League + MIT + Stanford, they’re competing for about 6,500 out of 15,800 total spots.



It’s well known that

  1. Admission to top universities is very competitive in America and even top SAT scores (1550+ out of 1600) paired with a 4.0 GPA doesn’t guarantee admission to a top school.
  2. Even top universities take into account race-based affirmative action, athletic recruitment, “Dean’s Interest List”-type tracking systems for children of donors or notable persons, and legacy preference for children of alumni.

But many people are under the misconception that the resulting “rat race”—the highly competitive and strenuous admissions ordeal—is the inevitable result of the limited class sizes among top schools and the strong talent in the applicant pools, and that it isn’t merely because of the reasons listed in (2). Some even go so far as to suggest that a better system would be to run a lottery for any applicant who meets a minimum “qualification” standard—under the assumption that there would be many such qualified students.

But in reality, the top 20 schools together enroll about 49,000 students. That’s about 1.3% of the 3.8 million students who graduate high school each year in the United States. If you restrict it to the eight Ivy League schools + Stanford + MIT, those ten schools together enroll 17,500 students per year. Below I’ll argue that there isn’t a huge oversupply of talent at all for these spots, even with the limitations of current metrics, and certainly not with metrics that would be available if the SAT was made more difficult in line with historical standards.

RankSchoolFreshman Class SizeSAT 25th PercentileSAT 50th PercentileSAT 75th Percentile% Foreign
1Princeton1,4001,4501,5281,57010
2MIT1,1001,5101,5351,58010
3Harvard1,7001,4601,5281,58010
4Stanford1,7001,4201,5351,57015
5Yale1,6001,4601,5211,58010
6Caltech2501,5301,5451,58015
7Duke1,7001,5101,5331,56015
8Johns Hopkins1,3001,4801,5481,57015
9Northwestern2,1001,4301,5131,55015
10UPenn2,4001,4501,5281,57015
11Cornell3,1001,4501,5131,54010
12UChicago1,7001,5001,5331,57015
13Brown1,7001,4401,5281,57015
14Columbia1,5001,4701,5271,57015
15Dartmouth1,2001,4401,5201,56015
16UCLA6,6001,2901,4051,52010
17UC Berkeley13,7001,2901,4151,53010
18Rice1,1001,4601,5281,57010
19Notre Dame2,1001,4201,4901,56010
20Vanderbilt1,4001,4601,5301,56010

About the data:

For reference, the SAT is scored from 400 to 1600 with a mean of about 1000 and a standard deviation of about 200, though it varies from year to year and the College Board—the non-profit that produces the exams—is a bit opaque about how they norm the tests. The newer ACT (founded in 1959) has a slightly different format and gives scores from 1 to 36, with a mean of about 21 and a standard deviation of about 5. About 2 million students took the SAT in 2024 and about 1.4 million took the ACT. The variation is mostly regional: some states require one or the other (or a choice of either) to graduate high school.

ACT & SAT Graduation Requirements by State | Piqosity
ACT® vs. SAT® Test: 19 Differences to Consider | KD College Prep
 

With regard to how many students achieve high scores:

So if you suppose that the same proportion of ACT takers who score a 35 or 36 (together 0.895%) would achieve a 1540 on the SAT, then that’s roughly 34,000 students. If there’s an intermediate score threshold of 1550 or 1560 that represents the top 0.5% of students, then about 19,000 students who graduate each year meet that bar.

Both of these numbers are well below the 49,000-strong intake at top-20 schools. The idea that top students are a dime a dozen isn’t correct; the reality is that top schools admit very many students who have relatively low SAT scores. Under the percentile assumptions in the table above, we can calculate upper and lower bounds showing that top-20 schools are enrolling 16,000–28,000 students who score below 1500 and 30,000–42,000 students who score below 1560. If you restrict it to the Ivy League + Stanford + MIT, then using the data above, out of the combined 17,500 students those ten schools enroll, at least half score under a 1540, and probably closer to 60%.

So after removing the international students from the calculations, and using the middle-of-the-range estimates, the conclusion: The top-scoring 19,000 American students each year are competing in top-20 admissions for about 12,000 spots out of 44,000 total. Among the Ivy League + MIT + Stanford, they’re competing for about 6,500 out of 15,800 total spots.

So for whatever combination of reasons—affirmative action, athletic recruitment, legacy/donor preference, personal essays about running over a feral cat—top schools are accepting a lot of relatively unqualified applicants. Top students are left competing for an artificially small number of slots. The qualitative system (which has merits as well as drawbacks) makes outcomes more uncertain and “yield” considerations sometimes cause schools to reject “overqualified” applicants who are unlikely to enroll; together this leads top students to shotgun applications to many colleges without clarity about the process or outcomes.

As an example of a more functional system, Oxford and Cambridge are the top universities in the UK. Each year they together enroll about 7,000 students out of 700,000 students who finish secondary education, so also about 1% (though about 20% of Oxford undergraduates and 25% of Cambridge undergraduates are from outside the UK). Their system has a bunch of features that make it more predictable and less strenuous:

  1. Students can only apply to either Oxford or Cambridge but not both. As a result, the “yield rate” is 80% for Cambridge and 90% for Oxford. And UK students can only apply to five undergraduate institutions in total, so weaker applicants won’t apply, especially if they recognize that they won’t reach published minimum score requirements for A-Level exams, standardized content exams similar to AP exams in America.
  2. Many subjects use entrance exams. For example, if you want to study math at Oxford, you can review every past entrance exam for free online and if you score in the 80s or 90s you’ll probably be admitted (based on publicly available statistics).

Further, the SAT used to be much harder. In 1991, only nine students scored a 1600, whereas people estimate that over 500 students achieve a perfect score today. The SAT scaled scores upward in 1995 and removed the highly g-loaded analogies section in 2005. Senator Chuck Schumer’s 1600 score from 1967 is off the charts today. But there are no signs of the College Board making the test harder, and meanwhile Princeton, UPenn, and Columbia remain test-optional even now, while UC Berkeley and UCLA don’t consider SAT/ACT scores at all.

If we removed the mechanisms and practices in place that lead top schools to admit many low-scoring students, and if applicants were matched to universities using a stable-marriage system similar to the medical-residency matching system, then the chaos and confusion of the admissions process would basically go away without any more complicated intervention required.

4 comments

Comments sorted by top scores.

comment by Mis-Understandings (robert-k) · 2025-04-07T19:09:08.781Z · LW(p) · GW(p)

I think you might fundamentally misunderstand the purpose of admission systems. To be frank, admissions is set up to benefit the university and the university alone. If getting good test scores was the bottleneck, you would see shifts in strategic behaviour until the test became mostly meaningless. For instance, you can freely retake the SAT, so if you just selected based on that people would just retake till they got a good result. 

The university has strong preferences about the distribution of students in classes. They have decided that they want different things from their applicants than "just" being good at tests.

They get this exactly through account race-based affirmative action, athletic recruitment, “Dean’s Interest List”-type tracking systems for children of donors or notable persons, and legacy preference for children of alumni, and a bunch of ill articulated selection actions in admissions offices and in other various places. 

stable-marriage system would require a national system, which would require universities as distinct and competing organizations (mostly for prestige) to coordinate for the benefit of students. They obviously should do things wiht that general description, but they tend not to. 

Replies from: arjun-panickssery, robert-k
comment by Arjun Panickssery (arjun-panickssery) · 2025-04-07T19:25:00.498Z · LW(p) · GW(p)

You're phrasing this as though it's rebutting some remark I made; if so, I'm not sure what remark that is. I know that admissions offices are admitting students according to an intentional system.

Replies from: robert-k
comment by Mis-Understandings (robert-k) · 2025-04-07T19:59:06.454Z · LW(p) · GW(p)

This is about your top line claim, and your framing.

If you try to say that if you exclude the reason a system is competitive, it does not need to be competitive, this is obvious. 

The system you propose does not fufill the top line purposes of the admissions system. 

there isn’t a huge oversupply of talent at all for these spots,

Misses the fact that the complexity of the admissions process does not come from competition over talent (universities would be willing to accept most people on their waitlist if they had more slots, and slots are limited by other factors), but from highly multidimensional preference frontiers which require complicated information about applicants to get good distributions of students. 

Basically, the argument about talent is wrong directioned for talking about admission systems.

comment by Mis-Understandings (robert-k) · 2025-04-07T19:12:18.057Z · LW(p) · GW(p)

University cohorts are basically setup to maximally benefit the people who do get admitted, not to admit the most qualified. For this purpose universities would rather have students that make the school more rewarding for other students, and not the smartest possible students. This is combined with a general tendency to do prestigous/donor wanted things. And donors want to have gone to a college that is hard to get into (even though they did not like applying). The challenge of application (and with that admit rates over yield rates) is a signal.