Many people have a theory about admissions to ultra-selective colleges.

They think: You have to have stratospheric SAT or ACT scores. You have to be the class valedictorian. You have to take 15 Advanced Placement courses and pass all the tests with top marks. You also have to be an all-state athlete or musician, preferably both, and volunteer in 20 ways to help the disadvantaged.

Or they think: You have to have two or three generations of alumni in your family, preferably some of them major donors. You have to come from the right demographic (factoring in your school, city, state, gender, ethnicity, race, family income level, etc.).

Here is Stuart Schmill’s theory: “Quality over quantity.”

His theory matters more than others because he is dean of admissions at the Massachusetts Institute of Technology.

MIT just admitted 1,548 applicants from a pool of 18,989. That’s a rate of about 8 percent, one of the lowest in the nation. On Monday, The Post reported on how high school seniors cope with the stress of such low admission rates at highly desirable schools. It also published a selection of acceptance and denial letters from MIT and other schools.

Schmill, like other deans, said there is no formula to getting in. But he has certain priorities. Obviously, a demonstrated interest in — and appreciation of — math and science helps at his school. Here are some other thoughts.

“I think many students sign up for more things than they ought to,” he said. “We don't need a four-page resume that’s filled with all kinds of things students do. What we see too much of is students who feel like they need to cover every base.”

Schmill said he is looking for students who show initiative. He is interested in those who have gone beyond the norm, or “done something because it’s what they wanted to do. In contrast to students who just sort of follow along what’s handed to them.”

But he adds: “We temper our expectations. We don’t expect high school students to be superhuman.”

Schmill, an MIT graduate who has led the admissions office since 2007, acknowledged that applicants are often bewildered when they are turned down.

“The college admissions process is for many students the first time in their lives when they have done all the right things and not gotten the reward they expected,” he said. “We adults know this happens all the time. What we realize is, we just keep at it.”

Schmill said MIT has cut back on its outreach expenditures about 40 percent in the past five years in an effort to ensure that the applicant pool is not filled with students who have a low probability of admission. But he said he has intensified efforts to find excellent students regardless of family income. “We really are trying to find those gems from low-income backgrounds,” he said.

The new movie “Admission,” a fictional account of admissions at Princeton University , shows officers behind closed doors reading and debating applications. The movie, hilariously, depicts individual applicants standing before the admissions officers as they are judged. Those who are rejected vanish through a trap door at the moment of decision.

For the college-bound public, Schmill said, there is a challenge inherent in a system that for the most part does not explain exactly how and why a given student is admitted or denied. “The admissions process generally is very much a black box,” he said. Schmill figures the only way to address that “is to communicate as well and as accurately as we can.”