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THE school year is under way across the nation, which means the college application season is beginning in earnest. With so much focus on grades, standardized test scores and extracurricular activities, the most academically ambitious high-school seniors and their parents might not realize that to get into Harvard and other elite colleges it might be preferable to be extra tall than extra smart. The reason might surprise you.

The 10 most well-known, highly selective colleges in the country — the eight members of the Ivy League plus Stanford and MIT — collectively admit a mere 15,000 American freshmen annually, fewer than 1 percent of the 2.1 million high-school graduates who pursue higher education each year.

The admissions rates at some of these highly selective schools are as low as the single digits, with Harvard and Stanford leading the way in accepting only 6 percent of their applicants. The credentials of the incoming freshman classes are remarkable, but perhaps even more astonishing are the kids who don’t get in, such as valedictorians and candidates with perfect SAT scores.

Why then is physical stature relevant? The answer is hiding in plain sight, as a careful analysis will show.

The U.S. Census Bureau surveys the distribution of the population by height, and does not report information beyond 6 feet 6 inches tall. According to the census, 100 percent of the population, rounded to the nearest full percentage point, is shorter than an NBA small forward. Yet the Ivy League schools routinely field basketball teams with toweringly tall players. Harvard had nine members last year on their men’s basketball team above 6 feet 6 inches tall. Yale had seven, as did Columbia.

Assuming that brainpower is evenly distributed by height, then the odds someone would be both uncommonly tall and in the top 1 percent as measured by traditional scholastic criteria are astronomical, about as unlikely as Mick Jagger retiring.

To understand why this relates to admissions, it’s worth realizing the Ivy League was formed in 1954 as a sports conference. Everyone has a competitive streak, especially the high achievers who run leading schools. They don’t only play, they play to win. The official Harvard Athletics website boasts the following impressive information: The university fields 42 athletic teams, more than any Division I school in the nation; 20 percent of its undergraduates participate in intercollegiate athletics; it has won 27 NCAA or national championships in the last 29 years, and 374 Ivy League championships across all sports since the league’s inception. The Winklevoss twins, Harvard classmates of Mark Zuckerberg who sued him for allegedly stealing the idea for Facebook, also happened to be world-class rowers who competed in the Beijing Olympics.

Stanford, Harvard’s West Coast rival for academic prestige, consistently fields nationally ranked football and basketball teams and has seen dozens of its gridiron competitors drafted by the NFL, including current pro football stars Andrew Luck and Richard Sherman and Hall of Famer John Elway.

Of course, the athletes at Harvard, Stanford, Princeton and the other exclusive schools are certainly outstanding students who deserve to be there strictly on academic merit. However, you don’t need a math degree from MIT to realize an all-state linebacker with a 700 SAT in math might edge out a less athletically gifted candidate with a higher score. These schools seek to assemble a “diverse” student body, and diversity comes in many flavors.

Athletic ability is not the only type of nonacademicademic factor in admissions. Prominent colleges, like American society at large, denied women and minorities inclusion for much of their history, and in the past several decades have made a determined effort to right this wrong and become more inclusive. This seems fair to me. As I replied to my adopted daughter from the indigenous Quechua region of Peru (and she doesn’t speak a single word of Spanish) when she needed to check off ethnicity on her college applications: “Yes, you’re Hispanic.”

Schools with impressive reputations also happen to sit atop impressive piles of money. Harvard possesses the largest endowment at $30.7 billion, followed by Yale ($19.2 billion), Princeton ($17.4 billion) and Stanford ($17 billion). Multibillion dollar fortunes don’t assemble themselves, and among qualified applicants, those who come from families with the potential to move the needle financially will find the field tilted in their favor.

These universities also embrace tradition. This means a preference is given to the children of alumni (legacies) and from a small universe of outstanding prep schools with a track record of sending their highest-ranked graduates to the best colleges.

So what is one to do if you aren’t a star athlete, wealthy or at the top of the class of a fancy private school? Is there any hope for an ordinary teen that simply happens to be extremely bright?

A white kid from a middle-class family at an average suburban high school (“just folks” in admissions-speak) with a high GPA and 1560 on his or her SATs might get accepted at Harvard and rejected at Stanford in a particular year, or vice versa. In private, admissions officials will concede the difference between those who are welcomed with open arms and the applicants who barely missed the cut is nearly indistinguishable.

Science has taught us we live in a seemingly orderly world governed by randomness, which is exemplified by the unpredictable nature of college admissions. At the best schools, every student who gets in deserves to be there, but many deserving candidates are rejected. Human nature being what it is, this degree of hyper-exclusivity only further reinforces the market value of the degree upon graduation. Expect the cycle to continue.

When I’m asked how to get into Harvard, I have a standard answer: Put on some muscles and grow eight inches. It’s a tall person’s world already, and nowhere is that more true than within the rarefied air of the Ivy League.

Ed Harris is co-founder of Bellevue-based PrepScholars, a company that focuses on college counseling.