The End of Average: How We Succeed in a World That Values Sameness - Todd Rose (2016)



Peter Molenaar spent the early part of his long and acclaimed career as an averagarian scientist, building an international reputation through research on psychological development that relied heavily on average-based norms. He was so confident of the value of averagarian thinking that, on occasion, Molenaar needled colleagues who suggested that behavioral scientists might be relying too heavily on averages to understand individuals.1

Molenaar’s confidence seemed justified. After all, he had spent a lifetime immersed in mathematics. In high school, he had been selected to compete in the Dutch Mathematical Olympiad. His dissertation for his doctorate in developmental psychology consisted of a mathematical tour de force describing “a dynamic factors model derived from a constrained spectral decomposition of the lagged covariance function into a singular and a nonsingular component.” Molenaar’s subsequent psychology publications were often so crammed full of equations and proofs that a lay reader might wonder if there was any psychology to be found at all.2

He rode his math talent and commitment to averagarianism to the very pinnacle of academic success in the Netherlands. In 2003, Molenaar was an H1 professor, the highest possible rank in the Dutch educational system, and served as the chairman of the Department of Psychological Methods at the prestigious University of Amsterdam. But in the Netherlands, the academic pinnacle has a shelf life. Dutch law mandates that all H1 professors must step back from their duties at the age of sixty-two to make way for their replacements, and then retire completely at age sixty-five. In 2003, Molenaar was fifty-nine, and he wasn’t quite sure if he was ready to step down, but at least he was expecting to ride off into the academic sunset at the top of his game—until an unexpected request was laid at his feet.

With just three years to go as an active professor, he was somewhat annoyingly asked to take over a fall semester course after a colleague was abruptly sidelined. The class was a seminar on the theory and methods of mental testing. Trust me, the course is just as boring as it sounds. Much of test theory was codified into its modern form in a 1968 textbook often regarded as “the Bible of Testing,” Statistical Theories of Mental Test Scores, authored by two psychometricians named Frederic Lord and Melvin Novick.3 To this day it remains required reading for anybody who wants to design, administer, or understand standardized tests; I had to read Lord and Novick myself in grad school. It is the kind of book you gloss over as quickly as you can because the text is about as interesting as the instructions to a tax form. The tome is so dull, in fact, that nobody had ever noticed that its sleep-inducing pages concealed the thread that would unravel averagarianism.

To prepare for his stint as a substitute teacher, Molenaar opened his copy of Lord and Novick. That’s when he experienced what he calls his aha-erlebnis, the German word for “epiphany.” It was a moment that would change the direction of his life—and shake the foundations of the social sciences. In the book’s introduction, Lord and Novick observed, rather drily, that any mental test attempted to discern the test taker’s “true score” on some feature of interest. This made sense; isn’t the reason we give someone an intelligence test, personality test, or college admissions test because we want to know their true intelligence ranking, true personality type, or true aptitude percentile?

Next, Lord and Novick observed that according to the leading theory of testing at the time—classical test theory4—the only way of determining a person’s true score was by administering the same test to the same person, over and over again, many times.5 The reason it was necessary to test someone repeatedly on, say, a math aptitude test, was because it was presumed that some amount of error would always occur in each test session (maybe the test taker was distracted or hungry; maybe she misread a question or two; maybe she guessed well). But if you took a person’s average score across a large number of test sessions, this average score would converge onto the individual’s true score.

The problem, as Lord and Novick fully acknowledged, was that it was impossible as a practical matter to test the same person multiple times, because human beings learn and therefore anyone who took, say, a math test, would inevitably perform differently as a result of seeing the same test again, foiling the possibility of obtaining many independent test scores.6 But rather than admit defeat, Lord and Novick proposed an alternate way to derive someone’s true score: instead of testing one person many times, they recommended testing many people one time.7 According to classical test theory, it was valid to substitute a group distribution of scores for an individual’s distribution of scores.

Adolphe Quetelet performed the same conceptual maneuver almost a century ago when he used the “Statue of the Gladiator” metaphor to define the meaning of a human average for the first time. He declared that taking the average size of 1,000 copies of a single soldier statue was equivalent to taking the average size of 1,000 different living soldiers. In essence, both Quetelet and Lord and Novick assumed that measuring one person many times was interchangeable with measuring many people one time.

This was Molenaar’s moment of aha-erlebnis. He instantly recognized that Lord and Novick’s peculiar assumption did not merely impact testing—the same assumption served as the basis for research in every field of science that studies individuals. It called into question the validity of an immense range of supposedly sturdy scientific tools: admissions tests for private schools and colleges; selection processes for gifted programs and special needs programs; diagnostic tests evaluating physical health, mental health, and disease risks; brain models; weight gain models; domestic violence models; voting behavior models; depression treatments; insulin administration for diabetics; hiring policies and employee evaluation, salary, and promotion policies; and basic methods of grading in schools and universities.

The strange assumption that a group’s distribution of measurements could safely be substituted for an individual’s distribution of measurements was implicitly accepted by almost every scientist who studied individuals, though most of the time they were hardly conscious of it. But after a lifetime of mathematical psychology, when Molenaar unexpectedly saw this unjustifiable assumption spelled out in black and white, he knew exactly what he was looking at: an irrefutable error at the very heart of averagarianism.


Molenaar recognized that the fatal flaw of averagarianism was its paradoxical assumption that you could understand individuals by ignoring their individuality. He gave a name to this error: “the ergodic switch.” The term is drawn from a branch of mathematics that grew out of the very first scientific debate about the relationship between groups and individuals, a field known as ergodic theory.8 If we wish to understand exactly why our schools, businesses, and human sciences have all fallen prey to a misguided way of thinking, then we must learn a little about how the ergodic switch works.

In the late 1800s, physicists were studying the behavior of gases. At the time, physicists could measure the collective qualities of gas molecules, such as the volume, pressure, and temperature of a canister of gas, but they had no idea what an individual gas molecule looked like or how it behaved. They wanted to know if they could use the average behavior of a group of gas molecules to predict the average behavior of a single gas molecule. To answer this question, physicists worked out a set of mathematical principles known as ergodic theory that specified exactly when you could use information about a group to draw conclusions about individual members of the group.9

The rules are fairly straightforward. According to ergodic theory, you are allowed to use a group average to make predictions about individuals if two conditions are true: (1) every member of the group is identical, and (2) every member of the group will remain the same in the future.10 If a particular group of entities fulfills these two conditions, the group is considered to be “ergodic,” in which case it is fine to use the average behavior of the group to make predictions about an individual. Unfortunately for nineteenth-century physicists, it turned out that the majority of gas molecules, despite their apparent simplicity, are not actually ergodic.11

Of course, you don’t need to be a scientist to see that people are not ergodic, either. “Using a group average to evaluate individuals would only be valid if human beings were frozen clones, identical and unchanging,” Molenaar explained to me.12 “But, obviously, human beings are not frozen clones.” Yet, even the most basic averagarian methods like ranking and typing all assumed that people were frozen clones. This was why Molenaar called this assumption the ergodic switch: it takes something nonergodic and pretends it is ergodic. We might think of the ergodic switch as a kind of intellectual “bait and switch” where the lure of averagarianism dupes scientists, educators, business leaders, hiring managers, and physicians into believing that they are learning something meaningful about an individual by comparing her to an average, when they are really ignoring everything important about her.

An example might help illustrate the practical consequences of the ergodic switch. Imagine you want to reduce the number of errors you make when you are typing on a keyboard by changing the speed at which you type. The averagarian approach to this problem would be to evaluate the typing skills of many different people, then compare the average typing speed to the average number of errors. If you do this, you will find that faster typing speeds are associated with fewer errors, on average. This is where the ergodic switch comes in: an averagarian would conclude that if you wanted to reduce the number of errors in your typing, then you should type faster. In reality, people who type faster tend to be more proficient at typing in general, and therefore make fewer errors. But this is a “group level” conclusion. If you instead model the relationship between speed and errors at the level of the individual—for instance, by measuring how many errors you make when typing at different speeds—then you will find that typing faster actually leads to more errors. When you perform the ergodic switch—substituting knowledge about the group for knowledge about the individual—you get the exact wrong answer.

Molenaar’s epiphany also reveals the original sin of averagarianism, the mistake that occurred at the founding moment of the Age of Average: Quetelet’s interpretation of the average size of Scottish soldiers. When Quetelet declared that his measurement of the average chest circumference actually represented the chest size of the “true” Scottish soldier, justifying this interpretation using the “Statue of the Gladiator,” he performed the very first ergodic switch. This ergodic switch led him to believe in the existence of the Average Man and, even more important, was used to justify his assumption that the average represents the ideal, and the individual represents error.

A century and a half of applied science has been predicated on Quetelet’s primal misconception.13 That’s how we ended up with a statue of Norma that matches no woman’s body, brain models that match no person’s brain, standardized medical therapies that target nobody’s physiology, financial credit policies that penalize creditworthy individuals, college admission strategies that filter out promising students, and hiring policies that overlook exceptional talent.

In 2004, Peter Molenaar spelled out the consequences of the ergodic switch for the study of individuals in a paper entitled, “A Manifesto on Psychology as Idiographic Science: Bringing the Person Back into Scientific Psychology, This Time Forever.”14 After a scientific career devoted to averagarian thinking, his manifesto now declared that averagarianism was irredeemably wrong.

“I guess you could say I was like the biblical Paul,” Molenaar told me with a smile. “At first, I was persecuting the Christians, all my colleagues who declared the average was wrong and the individual was the way. Then I had my ‘road to Damascus’ moment, and now I’m the biggest proselytizer of them all when it comes to the gospel of the individual.”


Just because you’re bringing the gospel to the gentiles doesn’t mean they’re going to listen. When I asked Molenaar about the initial reaction to his ideas, he replied, “As with most attempts to supplant or even slightly alter the ordained approaches, the arguments often fall on somewhat deaf ears. The more radical efforts can take on a Sisyphean character.”15

Shortly after publishing his individuality manifesto, Molenaar gave a talk at a university about its details that included a call to move past averagarianism. One psychologist shook his head in response and declared, “What you are proposing is anarchy!”16 This sentiment was perhaps the most common reaction among psychometricians and social scientists whenever Molenaar showcased the irreconcilable error at the heart of averagarianism. Nobody disputed Molenaar’s math. In truth, it’s fair to say that many of the scientists and educators whose professional lives were affected by the ergodic switch did not follow all the details of ergodic theory. But even those who understood the math and recognized that Molenaar’s conclusions were sound still expressed the same shared concern: If you could not use averages to evaluate, model, and select individuals, well then … what could you use?

This practical retort underscores the reason that averagarianism has endured for so long and become so deeply ingrained throughout society, and why it has been so eagerly embraced by businesses, universities, governments, and militaries: because averagarianism worked better than anything else that was available. After all, types, ranks, and average-based norms are very convenient. It takes little effort to say things like “She is smarter than average,” or “He was ranked second in his graduating class,” or “She is an introvert,” concise statements that seem true because they appear to be based on forthright mathematics. That is why averagarianism was a perfect philosophy for the industrial age, an era when managers—whether in businesses or schools—needed an efficient way to sift through large numbers of people and put them in their proper slots in a standardized, stratified system. Averages provide a stable, transparent, and streamlined process for making decisions quickly, and even if university administrators and human resource executives paid lip service to the problems associated with ranking students and employees, no manager was ever going to lose her job because she compared an individual to an average.

After hearing his colleagues react to his individuality manifesto by asking, quite reasonably, what they were supposed to use if they could not use averages, Molenaar realized it was not enough to prove averagarianism was wrong through some complex mathematical proof. If he truly wanted to overthrow the tyranny of the average once and for all, he needed to offer an alternative to averagarianism—some practical way to understand individuals that provided better results than ranking or typing.

Molenaar sat down with his boss, the dean of the graduate school at the University of Amsterdam, and excitedly informed her of his plans to develop a new scientific framework for studying and assessing individuals. He laid out ideas for several new projects, including an international conference on individuality, then asked for funding for these initiatives.

“You know I can’t give you any new resources,” the dean reluctantly replied. “You’re stepping down in three years. I’m very sorry, Peter, you know the rules of the system, and there’s nothing I can do.”17

Molenaar was abruptly forced to look at himself in the mirror. Here he was, at the age of sixty, convinced he could make a profound contribution to science, one that could very possibly change the basic fabric of society. But launching revolutions was a young man’s game, and the Dutch university system wasn’t going to provide him with any support for his grand aspirations. He asked himself, Did he really want to fight for this?

Molenaar considered bowing to the inevitable—after all, he was on the tail end of a very successful career, and even if he did decide to become the leader of a game-changing scientific movement, it would demand not only years of research, but countless battles with scientists and institutions. But he didn’t consider this too long. “When you realize what’s at stake—how many parts of society are affected by all this,” Molenaar told me, “I just had to try to find a way.”18

He began seeking out new opportunities outside of the University of Amsterdam that would enable him to pursue his vision of building an alternative to averagarianism. In 2005, one materialized. On the other side of the Atlantic, Penn State University offered him a tenured position on their faculty, and shortly after that, appointed him the founding director of the Quantitative Developmental Systems Methodology core unit of the Social Science Research Institute, an entire research group he could shape as he wished. At Penn State, he gathered around himself a group of top-flight scientists and graduate students from around the world who shared his vision and who soon came to affectionately refer to Molenaar as “Maestro.” Together, they began to lay the foundation for an actionable alternative to averagarianism: an interdisciplinary science of the individual.

Recall that the two defining assumptions of the Age of Average are Quetelet’s conviction that the average is the ideal, and the individual is error, and Galton’s conviction that if someone is Eminent at one thing they are likely Eminent at most things. In contrast, the main assumption of the science of the individual is that individuality matters19—the individual is not error, and on the human qualities that matter most (like talent, intelligence, personality, and character) individuals cannot be reduced to a single score.

Building on this new assumption, Molenaar and his colleagues began to develop new tools that enable scientists, physicians, educators, and businesses to improve the way they evaluate individuals. These tools often draw upon a very different kind of math than that used by averagarians. The mathematics of averagarianism is known as statistics because it is a math of static values—unchanging, stable, fixed values. But Molenaar and his colleagues argue that to accurately understand individuals one should turn to a very different kind of math known as dynamic systems—the math of changing, nonlinear, dynamic values.20

Since the assumptions and mathematics of the science of the individual are so different than those of averagarianism, it should be no surprise that the science of the individual also turns the method of studying people on its head.


The primary research method of averagarianism is aggregate, then analyze: First, combine many people together and look for patterns in the group. Then, use these group patterns (such as averages and other statistics) to analyze and model individuals.21 The science of the individual instead instructs scientists to analyze, then aggregate: First, look for patterns within each individual. Then, look for ways to combine these individual patterns into collective insight. One example from developmental psychology illustrates how switching to an “individual first” approach to studying people can overturn long-standing convictions about human nature.

From the 1930s through the 1980s, scientists who studied infant development wrestled with a puzzling mystery known as the stepping reflex. When a newborn is held upright, she begins moving her legs in an up-and-down motion that closely resembles walking. For a long time, scientists suggested this stepping reflex pointed to the presence of an inborn walking instinct. But the reason this reflex was so mystifying was that at around two months of age, the reflex disappeared. When you hold up an older baby, her legs remain mostly motionless. But then, shortly before the infant begins to walk, the stepping reflex magically returns. What causes this reflex to appear, disappear, then appear again?

Scientists first attempted to solve the mystery of the stepping reflex using the traditional method of averagarianism: aggregate, then analyze. Since everybody presumed that the stepping reflex was associated with neural development, scientists examined a large number of infants, calculated the average age that the stepping reflex appeared and disappeared, then compared these average ages with the average age of various milestones of neural development. Scientists discovered that one neural process seemed to correspond with the appearance and disappearance of the stepping reflex: myelination, the physiological process whereby neurons grow a protective sheathing. So scientists proposed the “myelination theory”: each baby is born with the stepping reflex, but as the motor control center of the brain begins to myelinate, the reflex vanishes. Then, after the motor control center of the brain develops further, the baby regains conscious control of the reflex.22

By the early 1960s, myelination theory had become the standard medical explanation of the stepping reflex. It even served as the basis for the diagnosis of neural disorders: if a baby’s stepping reflex did not disappear on time, physicians and neurologists warned the parents that their child might have some kind of neurological disability.23 Many pediatricians and child psychologists even asserted it was bad for parents to try to encourage their child’s stepping reflex, arguing it could delay normal development and cause neuromuscular abnormalities.

The curious and unwieldy myelination theory held sway over American pediatrics for several decades and might have even lasted into the twenty-first century, if not for a young scientist named Ester Thelen.24 While studying animals early in her career, Thelen discovered that many instinctive behaviors that biologists insisted were fixed and rigid were actually highly variable, depending in large part on the unique quirks of each individual animal. These formative professional experiences drove her to study the mathematics of dynamic systems, and eventually she decided to reexamine the human stepping reflex by focusing on the individuality of each child.

Thelen studied forty babies over a period of two years. Every day she took a photo of each baby, examining their individual physical development. She held them over treadmills and placed them in different positions to analyze the individual mechanics of each baby’s motions. Eventually, she formulated a new hypothesis about what was causing the disappearance of the stepping reflex: chubby thighs.

She noticed that the babies who gained weight at the slowest rate tended to move their legs the most and for the longest period of time. The babies who gained weight at the fastest rate tended to lose their stepping reflex the earliest, because their leg muscles were simply not strong enough to lift up their legs. It was not the absolute chubbiness of the thighs that was the key factor, but rather the rate of physical growth, since what mattered was the amount of body fat relative to the development of muscle strength.25 That is why previous scientists who had simply compared average ages to average weights had never discovered anything. The aggregate, then analyze approach disguised each child’s individual pattern of development. Thelen’s analyze, then aggregate approach revealed it.

Needless to say, chubby thighs had never before appeared in any scientific account of the stepping reflex, so many researchers rejected the idea out of hand. But in a series of ingenious experiments, Thelen proved beyond a doubt that her theory of chubby thighs was correct. She placed babies in water and voilà—the stepping reflex reemerged, even in those babies with the fattest legs. She added different weights to babies’ legs and was able to predict which babies would lose the stepping reflex.26

When Esther Thelen studied the individuality of each baby, she arrived at an explanation that had eluded generations of averagarian researchers who had informed parents that there might be something wrong with their infant’s brain when the real cause of their concerns was their infant’s flabby thighs.

At Penn State, Peter Molenaar and his department have demonstrated a number of similar findings where an individual-first approach leads to superior results compared to relying only on group averages. There is one difficulty presented by this individual-first approach: it requires a great deal of data, far more data than averagarian approaches. In most fields that study human beings, we didn’t have the tools one hundred, fifty, or even twenty-five years ago to acquire and manage the extensive data necessary to effectively analyze, then aggregate. During the industrial age, averagarian methods were state of the art, and individual-first methods were often mere fantasy. But now we live in the digital age, and over the past decade the ability to acquire, store, and manipulate massive amounts of individual data has become convenient and commonplace.

All that’s missing is the mindset to use it.


When Lieutenant Gilbert Daniels first suggested that cockpits needed to fit every pilot instead of the average pilot, it seemed an impossible task. Today, the same companies that once said it could not be done tout the flexibility of their cockpits as a selling point.27 Similarly, when Esther Thelen decided to challenge the deeply entrenched myelination theory by studying the individuality of babies, it seemed a difficult undertaking at the very least, and possibly a pointless one. But it did not take long for her to notice the overlooked role of chubby thighs.

Averagarianism forces our thinking into incredibly limiting patterns—patterns that we are largely unaware of, because the opinions we arrive at seem to be so self-evident and rational. We live in a world that encourages—no, demands—that we measure ourselves against a horde of averages and supplies us with no end of justification for doing so. We should compare our salary to the average salary to judge our professional success. We should compare our GPA to the average GPA to judge our academic success. We should compare our own age to the average age that people get married to judge whether we are marrying too late, or too early. But once you free yourself from averagarian thinking, what previously seemed impossible will start to become intuitive, and then obvious.

It’s easy to have sympathy for the psychologist who informed Molenaar, “What you are proposing is anarchy!” Letting go of the average seems unnatural. It’s venturing beyond the known shores, a proposition that seems particularly foolhardy when the entire world around you remains firmly on the terra firma of averagarianism. But there’s no need to grope blindly in the dark. In the next part of the book, I will share three principles drawn from the science of the individual that can replace your reliance on the average: the jaggedness principle, the context principle, and the pathways principle. These principles will allow you to evaluate, select, and understand individuals in a whole new way. They will allow you to discard types and ranks and discover instead the true patterns of individuality in your own life. They will help you eliminate the unchallenged authority of the average once and for all.