For someone not from the US: From the second point I understand that the SAT is not the only thing used to decide who gets in? So, it's not "we have 100 slots this year, the 100 best get in"? What else is used?
I think each school has their own culture/brand they're going for and they want to find the best fit for that brand. Just having the best test takers doesn't match.
Harvard probably wants a mix of people who have a history of going to Harvard, elites, with high performers and others. If it's only elites, then the academic quality goes down. Only best academic performers, elites will go to another school to call home, etc.
elites == upper class, for those not from the US... Of course that being the reason test scores are considered primary in other countries and not the US. American universities have a need to recruit upper class students for various purposes including keeping the influence of the upper class on government, media, etc going.
To add to the other answers: at top universities, you can also have very unusual applicants. At Caltech we'd sometimes have (standard age) freshman come in with research publications, for example.
If you have the resources to review applicants individually, sometimes there are people who clearly stand out for reasons unrelated to test scores. I expect that in most cases, if they've taken tests, they have good scores, and it can make sense to generally have a threshold, but if you simply rank by top scores they are likely not the absolute best, as they would have been spending more time and attention on things other than studying for them.
It's actually super common to have research publications on undergrad applications now, so much so that I've heard that having such a publication is "table stakes" to be competitive at top schools.
Simultaneously, I've also heard that it's easier to get your name on a paper as a high schooler than as an undergrad working in the same lab. Some of this is because professors are incentivized to put random high schoolers on their papers -- when applying for grants, they're often asked what K-12 outreach they've done (https://new.nsf.gov/funding/learn/broader-impacts). "Look at this paper where there's a random high schooler on it" checks the box if a bit inappropriately. Incentives at work!
That funny, at the time I left academia, I found almost the entire opposite attitude. The faculty openly lobbied against having high school and sometimes even undergrads in the lab. This was in fairly heavy duty experimental life sciences, where we did small animal research, so I guess it depends on field/university/department.
But in my lab at least, we did have the odd high schooler/undergrad, whom I had a part in mentoring. For the high schoolers, my PI at least privately admitted it was because their parents had "means" and it was about at least the potential for grant money.
High school grades/class rank. And then (at least this is how MIT used to do it although I'm sure most schools have some variant of the process) you have all the qualitative stuff on the other axis: letters of recommendation, interview, high school activities, sports, other types of projects, etc.
I expect very few schools just mechanically admit based on SATs.
The goal of elite university admissions is not to maximize academic success, it's to maximize career success and prestige. Organized athletics at the highest level require high levels of teamwork and grit which translate very well to the work force. Grit and teamwork might actually be the most important attributes for having a successful career so it really surprise me when people dont understand why athletes get some preference in admissions.
Aside from scholarships for sufficiently talented, it certain places it sometimes viewed as demonstrating leadership and/or social skills. Especially if you have some type of leadership role (captain, etc.). And especially military academies.
Good schools get enough applicants such that the top X are more or less indistinguishable from one another via quantifiable metrics. It's hard to define the 100 "best" when you're looking >100 kids with the same scores.
Harvard might not have this problem, but some, even some good, schools have to put some thought into if the student is actually going to accept the offer as well. Some states require a certain percent of students to be from the state in state funded schools.
> So, it's not "we have 100 slots this year, the 100 best get in"?
I think most schools would claim it is that, they just reject that testing is the end all be all of who is the best. These schools are looking for the next generation of leaders, theres a lot that goes into being a leader that isnt counted on standardized tests. Standardized tests really just tell you who has the highest IQ. Useful, but it misses lots of other attributes.
>So, it's not "we have 100 slots this year, the 100 best get in"?
If a university's mission goes beyond just collecting already-top-performing students from the best (usually wealthiest) school districts, you can't just do a straight rank on a single signal. There's a lot of variance in educational opportunity across the US, ranging from highly selective specialty public high schools [1], to places where they can only afford 4 days of schooling a week [2].
Multiple components are considered: SAT scores, high school grades, application essay questions, in-person interview (optional, but suggested), participation in extracurricular activities, recommendations from former teachers or influential people, and sometimes, a specific, highly-desired skill or talent (usually athletics, music, arts)