William “Rick” Singer leaves federal court in Boston on March 12 after he pleaded guilty to charges in a nationwide college admissions bribery scandal. (Steven Senne/AP)

Last week, the Justice Department announced it was prosecuting a handful of wealthy parents who allegedly paid enormous sums to fraudulently get their children admitted to elite colleges. The idea that wealth can buy slots in the “meritocracy” offended many. But behind that overt cheating is a plethora of less obvious ways the college admissions system unfairly favors the children of the well-off. Most notably, college athletics scholarships are rigged in favor of kids from wealthy backgrounds — even if they don’t cheat.

Athletics and extracurricular activities strongly influence college admissions

Here are some rough facts: Approximately two million high school graduates apply to college each year. A handful of institutions — namely the Ivy League schools of Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, Princeton University, the University of Pennsylvania and Yale University, as well as Caltech, Stanford University, MIT, University of Chicago, Duke University and Northwestern University — are the most elite gatekeepers for the meritocracy. They collectively accept a little over 20,000 students. Thus, about 1 percent of the nation’s students attend these most elite private schools.

These schools accept a substantial number of athletes. Princeton has 990 varsity athletes, nearly as many as the University of Michigan with 1,011 — even though Princeton’s student population is five times smaller. Harvard, with a student population of 6,800, has 1,200 athletes. Demonstrated achievement in athletics, therefore, provides a significant route into elite schools and so do exceptional talent in music, theater and science. Participation in international piano competitions, winning a national science competition or captaining a champion debate team makes an applicant more desirable to elite schools.

It’s obvious why elite schools want high achievers. These schools want students who will remake and improve the world. Past achievement is likely a good predictor of future success. A young man who can run a mile in 4 minutes and 10 seconds, or a young woman who can row 2,000 meters on a rowing machine in 6 minutes 45 seconds demonstrates a combination of natural ability and willingness to work hard. The same can be said of a champion juggler or Rubik’s cube solver. If those applicants scored 1500 on the SAT, they become attractive candidates for admission.

Prizing exceptionalism helps kids from some schools – but not others

However, wealthy school districts — private and public — offer far more sports and extracurricular activities than do poorer schools. Consider New Trier, an elite public school north of Chicago, which offers 18 varsity sports — including fencing and bass fishing — along with more than 150 clubs. Students at New Trier can take dance, compete in forensics, row on a crew team or participate in model U.N. Similarly, Harvard-Westlake, a private prep school in a wealthy area of Los Angeles, offers 15 sports and more than 50 clubs. In contrast, students at Romulus High School in the Detroit metropolitan area choose from among only nine sports and fewer than 20 extracurricular activities. New Trier High is located in Winnetka, which has a per capita income of $105,000 and a median home price of just under $2 million. Romulus has a per capital income of less than $45,000 and a median home value of just over $100,000.

With these extra opportunities, students from elite schools have a far higher chance of showing exceptional abilities than students from poorer schools. That’s not because the students from elite schools have more talent; rather, they have more opportunities to exhibit and develop their talents.

And this influences their chances of getting into a highly selective college.

Here’s how we did our research

In a recent working paper, Uma Jayakumar and I identify three causes of bias in favor of students in well-off areas. First, a student who tries four times as many sports and activities will be four times as likely to show exceptional results. We call that an “opportunity effect”: more opportunities increase the likelihood of success. Thus, the New Trier student or Harvard Westlake student, who has the opportunity to try more sports, has a higher likelihood of showing exceptional abilities.

Second, students at wealthy schools have the chance to try elite sports — which results in a “specialization effect.” Becoming a college-level water polo player requires having the opportunity to play water polo — which is available to approximately 22,000 high school boys. By comparison, more than a million boys play football; more than a half million play basketball; and another half-million run track. If Princeton has roughly the same numbers of admissions slots for each sport, then the water polo player is more than 40 times more as likely to become a Princeton athlete.

Third, students at elite schools have access to better coaching, better facilities and more family support — which offers them what we call a “support effect.” With more support, they are more likely to excel.

These three effects combine to produce a substantial advantage. Our crude initial estimate suggests that kids from advantaged schools may be 10 to 20 times more likely to show the exceptional talent desired by elite colleges. Once we undertake a more nuanced and careful analysis, that range will probably tighten. We expect to find huge advantages in particular sports like fencing, skiing, and crew.

Yes, William Singer — the college admissions adviser at the center of the current fraud scandal — claims to have altered the test scores of potentially hundreds of students per year. But that focus on overt cheating and fraud may distract attention away from a much broader bias toward wealthy families: the emphasis on exceptionalism in elite college admissions.

Wealth cannot purchase innate talent. But it can provide access to elite — and less competitive — sports and activities like fencing, water polo, crew, classical music, debate and dance. It can provide better coaching, counseling, stronger familial support. As a result, students from wealthy families are much more likely to get into elite colleges — not through cheating, but through the selective back door available primarily to those from wealth.

Scott E. Page (@Scott_E_Page), author of “The Model Thinker” (Basic Books, 2018), is the Leonid Hurwicz Collegiate Professor of Complex Systems, Political Science, and Economics at The University of Michigan and an external faculty member of the Santa Fe Institute.