Caroline Sacks’s decision to evaluate herself, then, by looking around her organic chemistry classroom was not some strange and irrational behavior. It is what human beings do. We compare ourselves to those in the same situation as ourselves, which means that students in an elite school—except, perhaps, those at the very top of the class—are going to face a burden that they would not face in a less competitive atmosphere. Citizens of happy countries have higher suicide rates than citizens of unhappy countries, because they look at the smiling faces around them and the contrast is too great. Students at “great” schools look at the brilliant students around them, and how do you think they feel?
The phenomenon of relative deprivation applied to education is called—appropriately enough—the “Big Fish–Little Pond Effect.” The more elite an educational institution is, the worse students feel about their own academic abilities. Students who would be at the top of their class at a good school can easily fall to the bottom of a really good school. Students who would feel that they have mastered a subject at a good school can have the feeling that they are falling farther and farther behind in a really good school. And that feeling—as subjective and ridiculous and irrational as it may be—matters. How you feel about your abilities—your academic “self-concept”—in the context of your classroom shapes your willingness to tackle challenges and finish difficult tasks. It’s a crucial element in your motivation and confidence.
The Big Fish–Little Pond theory was pioneered by the psychologist Herbert Marsh, and to Marsh, most parents and students make their school choices for the wrong reasons. “A lot of people think that going to an academically selective school is going to be good,” he said. “That’s just not true. The reality is that it is going to be mixed.” He went on: “When I was living in Sydney, there were a small number of selective public schools that were even more prestigious than the elite private schools. The tests to get into them were incredibly competitive. So the Sydney Morning Herald—the big newspaper there—would always call me up whenever they were holding their entrance examinations. It would happen every year, and there was always this pressure to say something new. So finally I just said—and maybe I shouldn’t have—well, if you want to see the positive effects of elite schools on self-concept, you are measuring the wrong person. You should be measuring the parents.”
6.
What happened to Caroline Sacks is all too common. More than half of all American students who start out in science, technology, and math programs (or STEM, as they are known) drop out after their first or second year. Even though a science degree is just about the most valuable asset a young person can have in the modern economy, large numbers of would-be STEM majors end up switching into the arts, where academic standards are less demanding and the coursework less competitive. That’s the major reason that there is such a shortage of qualified American-educated scientists and engineers in the United States.
To get a sense of who is dropping out—and why—let’s take a look at the science enrollment of a school in upstate New York called Hartwick College. It’s a small liberal arts college of the sort that is common in the American Northeast.
Here are all the Hartwick STEM majors divided into three groups—top third, middle third, and bottom third—according to their test scores in mathematics. The scores are from the SAT, the exam used by many American colleges as an admissions test. The mathematics section of the test is out of 800 points.3
STEM majors Top Third Middle Third Bottom Third
Math SAT 569 472 407
If we take the SAT as a guide, there’s a pretty big difference in raw math ability between the best and the poorest students at Hartwick.
Now let’s look at the portion of all science degrees at Hartwick that are earned by each of those three groups.
STEM degrees Top Third Middle Third Bottom Third
Percent 55.0 27.1 17.8
The students in the top third at Hartwick earn well over half of the school’s science degrees. The bottom third end up earning only 17.8 percent of Hartwick’s science degrees. The students who come into Hartwick with the poorest levels of math ability are dropping out of math and science in droves. This much seems like common sense. Learning the advanced mathematics and physics necessary to become an engineer or scientist is really hard—and only a small number of students clustered at the top of the class are smart enough to handle the material.
Now let’s do the same analysis for Harvard, one of the most prestigious universities in the world.
STEM majors Top Third Middle Third Bottom Third
Math SAT 753 674 581
Harvard students, not surprisingly, score far higher on the math SAT than their counterparts at Hartwick. In fact, the students in Harvard’s bottom third have higher scores than the best students at Hartwick. If getting a science degree is about how smart you are, then virtually everyone at Harvard should end up with a degree—right? At least on paper, there is no one at Harvard who lacks the intellectual firepower to master the coursework. Well, let’s take a look at the portion of degrees that are earned by each group.
STEM degrees Top Third Middle Third Bottom Third
Percent 53.4 31.2 15.4
Isn’t that strange? The students in the bottom third of the Harvard class drop out of math and science just as much as their counterparts in upstate New York. Harvard has the same distribution of science degrees as Hartwick.
Think about this for a moment. We have a group of high achievers at Hartwick. Let’s call them the Hartwick All-Stars. And we’ve got another group of lower achievers at Harvard. Let’s call them the Harvard Dregs. Each is studying the same textbooks and wrestling with the same concepts and trying to master the same problem sets in courses like advanced calculus and organic chemistry, and according to test scores, they are of roughly equal academic ability. But the overwhelming majority of Hartwick All-Stars get what they want and end up as engineers or biologists. Meanwhile, the Harvard Dregs—who go to the far more prestigious school—are so demoralized by their experience that many of them drop out of science entirely and transfer to some nonscience major. The Harvard Dregs are Little Fish in a Very Big and Scary Pond. The Hartwick All-Stars are Big Fish in a Very Welcoming Small Pond. What matters, in determining the likelihood of getting a science degree, is not just how smart you are. It’s how smart you feel relative to the other people in your classroom.
By the way, this pattern holds true for virtually any school you look at—regardless of its academic quality. The sociologists Rogers Elliott and Christopher Strenta ran these same numbers for eleven different liberal arts colleges across the United States. Take a look for yourself:
School Top Third Math SAT Middle Third Math SAT Bottom Third Math SAT
1. Harvard University 53.4% 753 31.2% 674 15.4% 581
2. Dartmouth College 57.3% 729 29.8% 656 12.9% 546
3. Williams College 45.6% 697 34.7% 631 19.7% 547
4. Colgate University 53.6% 697 31.4% 626 15.0% 534
5. University of Richmond 51.0% 696 34.7% 624 14.4% 534
6. Bucknell University 57.3% 688 24.0% 601 18.8% 494
7. Kenyon College 62.1% 678 22.6% 583 15.4% 485
8. Occidental College 49.0% 663 32.4% 573 18.6% 492
9. Kalamazoo College 51.8% 633 27.3% 551 20.8% 479
10. Ohio Wesleyan 54.9% 591 33.9% 514 11.2% 431
11. Hartwick College 55.0% 569 27.1% 472 17.8% 407
Let’s go back, then, and reconstruct what Caroline Sacks’s thinking should have been when faced with the choice between Brown and the University of Maryland. By going to Brown, she would benefit from the prestige of the university. She might have more interesting and wealthier peers. The connections she made at school and the brand value of Brown on her diploma might give her a leg up on the job market. These are all classic Big Pond advantages. Brown is the Salon.
But she would be taking a risk. She would dramatically increase her chances of dropping out of science entirely. How larg
e was that risk? According to research done by Mitchell Chang of the University of California, the likelihood of someone completing a STEM degree—all things being equal—rises by 2 percentage points for every 10-point decrease in the university’s average SAT score.4 The smarter your peers, the dumber you feel; the dumber you feel, the more likely you are to drop out of science. Since there is roughly a 150-point gap between the average SAT scores of students attending the University of Maryland and Brown, the “penalty” Sacks paid by choosing a great school over a good school is that she reduced her chances of graduating with a science degree by 30 percent. Thirty percent! At a time when students with liberal arts degrees struggle to find jobs, students with STEM degrees are almost assured of good careers. Jobs for people with science and engineering degrees are plentiful and highly paid. That’s a very large risk to take for the prestige of an Ivy League school.
Let me give you one more example of the Big Pond in action. It might be even more striking. Suppose you are a university looking to hire the best young academics coming out of graduate school. What should your hiring strategy be? Should you hire only graduates from the most elite graduate schools? Or should you hire students who finished at the top of their class, regardless of what school they went to?
Most universities follow the first strategy. They even make a boast out of it: We hire only graduates of the very top schools. But I hope that by this point you are at least a little bit skeptical of that position. Shouldn’t a Big Fish at a Little Pond be worth at least a second look before a Little Fish at a Big Pond is chosen?
Luckily there is a very simple way to compare those two strategies. It comes from the work of John Conley and Ali Sina Önder on the graduates of PhD programs in economics. In academic economics, there are a handful of economics journals that everyone in the field reads and respects. The top journals accept only the best and most creative research and economists rate one another according to—for the most part—how many research articles they have published in those elite journals. To figure out the best hiring strategy, then, Conley and Önder argue that all we have to do is compare the number of papers published by Big Fish in Little Ponds with the number published by Little Fish in Big Ponds. So what did they find? That the best students from mediocre schools were almost always a better bet than good students from the very best schools.
I realize that this is a deeply counterintuitive fact. The idea that it might not be a good idea for universities to hire from Harvard and MIT seems crazy. But Conley and Önder’s analysis is hard to refute.
Let’s start with the top economics PhD programs in North America—all of which are among the very top programs in the world: Harvard, MIT, Yale, Princeton, Columbia, Stanford, and the University of Chicago. Conley and Önder divided up the graduates of each of those programs according to where they ranked in their class, and then counted up the number of times each PhD graduate was published in the first six years of his or her academic career.
99th 95th 90th 85th 80th 75th 70th 65th 60th 55th
Harvard 4.31 2.36 1.47 1.04 0.71 0.41 0.30 0.21 0.12 0.07
MIT 4.73 2.87 1.66 1.24 0.83 0.64 0.48 0.33 0.20 0.12
Yale 3.78 2.15 1.22 0.83 0.57 0.39 0.19 0.12 0.08 0.05
Princeton 4.10 2.17 1.79 1.23 1.01 0.82 0.60 0.45 0.36 0.28
Columbia 2.90 1.15 0.62 0.34 0.17 0.10 0.06 0.02 0.01 0.01
Stanford 3.43 1.58 1.02 0.67 0.50 0.33 0.23 0.14 0.08 0.05
Chicago 2.88 1.71 1.04 0.72 0.51 0.33 0.19 0.10 0.06 0.03
I realize that this is a lot of numbers. But just look at the left-hand side—the students who finish in the 99th percentile of their class. To publish three or four papers in the most prestigious journals at the beginning of your career is quite an accomplishment. These people are really good. That much makes sense. To be the top economics graduate student at MIT or Stanford is an extraordinary achievement.
But then the puzzles start. Look at the 80th percentile column. Schools like MIT and Stanford and Harvard accept somewhere around two dozen PhD students a year, so if you are in the 80th percentile, you are roughly fifth or sixth in your class. These are also extraordinary students. But look at how few papers the 80th percentile publishes! A fraction of the number of the very best students. And by the way, look at the last column—the 55th percentile, the students who are just above average. They are brilliant enough to make it into one of the most competitive graduate programs in the world, and to finish their studies in the top half of their class. And yet they barely publish anything at all. As professional economists, they can only be considered disappointments.
Next let’s look at the graduates of mediocre schools. I say “mediocre” only because that’s what someone from one of those seven elite schools would call them. In the annual U.S. News & World Report rankings of graduate schools, these are the institutions that are buried somewhere near the bottom of the list. I’ve selected three for comparison purposes. The first is my own alma mater, the University of Toronto (out of a sense of school spirit!). The second is Boston University. The third is what Conley and Önder call “non–top 30,” which is simply an average of all the schools at the very, very bottom of the list.
99th 95th 90th 85th 80th 75th 70th 65th 60th 55th
Univ. of Toronto 3.13 1.85 0.80 0.61 0.29 0.19 0.15 0.10 0.07 0.05
Boston Univ. 1.59 0.49 0.21 0.08 0.05 0.02 0.02 0.01 0.00 0.00
Non–top 30 1.05 0.31 0.12 0.06 0.04 0.02 0.01 0.01 0.00 0.00
Do you see what is so fascinating? The very best students at a non–top 30 school—that is, a school so far down the list that someone from the Ivy League would grimace at the thought of even setting foot there—have a publication number of 1.05, substantially better than everyone except the very best students at Harvard, MIT, Yale, Princeton, Columbia, Stanford, and Chicago. Are you better off hiring a Big Fish from a Tiny, Tiny Pond than even a Middle-Sized Fish from a Big Pond? Absolutely.
Conley and Önder struggle to explain their own findings.5 “To get to Harvard,” they write,
an applicant has to have great grades, perfect test scores, strong and credible recommendations, and know how to package all this to stand out to the admissions committee. Thus, successful candidates must be hardworking, intelligent, well-trained as undergraduates, savvy and ambitious. Why is it that the majority of these successful applicants, who were winners and did all the right things up to the time they applied to graduate school, become so unimpressive after they are trained? Are we failing the students, or are the students failing us?
The answer, of course, is neither. No one is failing anyone. It’s just that the very thing that makes elite schools such wonderful places for those at the top makes them very difficult places for everyone else. This is just another version of what happened to Caroline Sacks. The Big Pond takes really bright students and demoralizes them.
By the way, do you know what elite institution has recognized this very fact about the dangers of the Big Pond for nearly fifty years? Harvard! In the 1960s, Fred Glimp took over as director of admissions and instituted what was known as the “happy-bottom-quarter” policy. In one of his first memos after taking office, he wrote: “Any class, no matter how able, will always have a bottom quarter. What are the effects of the psychology of feeling average, even in a very able group? Are there identifiable types with the psychological or what-not tolerance to be ‘happy’ or to make the most of education while in the bottom quarter?” He knew exactly how demoralizing the Big Pond was to everyone but the best. To Glimp’s mind, his job was to find students who were tough enough and had enough achievements outside the classroom to be able to survive the stress of being Very Small Fish in Harvard’s Very Large Pond. Thus did Harvard begin the practice (which continues to this day) of letting in substantial numbers of gifted athletes who have academic qualifications well below the rest of their classmates. If someone is going to be cannon fodder in the classroom, the theory goes, it’s probably best if that person has an alternative avenue of fulfi
llment on the football field.
Exactly the same logic applies to the debate over affirmative action. In the United States, there is an enormous controversy over whether colleges and professional schools should have lower admissions standards for disadvantaged minorities. Supporters of affirmative action say helping minorities get into selective schools is justified given the long history of discrimination. Opponents say that access to selective schools is so important that it ought to be done purely on academic merit. A group in the middle says that using race as the basis for preference is a mistake—and what we really should be doing is giving preference to people who are poor. What all three groups take for granted is that being able to get into a great school is such an important advantage that the small number of spaces at the top are worth fighting over. But why on earth are people convinced that places at the top are so valuable that they are worth fighting over?
Affirmative action is practiced most aggressively in law schools, where black students are routinely offered positions in schools one tier higher than they would otherwise be able to attend. The result? According to the law professor Richard Sander, more than half of all African-American law students in the United States—51.6 percent—are in the bottom 10 percent of their law school class and almost three-quarters fall in the bottom 20 percent.6 After reading about how hard it is to get a science degree if you’re at the bottom of your class, you’ll probably agree that those statistics are terrifying. Remember what Caroline Sacks said? Wow, other people are mastering this, even people who were as clueless as I was in the beginning, and I just can’t seem to learn to think in this manner. Sacks isn’t stupid. She’s really, really smart. But Brown University made her feel stupid—and if she truly wanted to graduate with a science degree, the best thing for her to do would have been to go down a notch to Maryland. No sane person would say that the solution to her problems would be for her to go to an even more competitive school like Stanford or MIT. Yet when it comes to affirmative action, that’s exactly what we do. We take promising students like Caroline Sacks—but who happen to be black—and offer to bump them up a notch. And why do we do that? Because we think we’re helping them.