How the average hides the patients it harms.

The operation went fine. That was the maddening part.

A tonsillectomy is half an hour of routine surgery, the kind children get every day, and for decades the standard prescription for the pain afterward was codeine — dosed by weight, checked twice, exactly as the pediatric textbooks said. Parents gave it as instructed. Pharmacists filled it as instructed. Nobody did anything wrong.

And then, in a small number of cases, a child went to sleep and didn’t wake up.

It took years to work out why, and the answer was worse than anyone expected: the dose wasn’t a mistake at all. Codeine itself is inert — the liver converts it to morphine, using an enzyme called CYP2D6. In most people the conversion is steady and the dose is safe. But a small genetic minority are ultra-rapid metabolizers: in them, a textbook dose becomes a flood of morphine, and breathing slows, and sometimes stops. (At the other pole, poor metabolizers get almost no relief at all — children undertreated for pain, quietly, in the same system.)

In 2013, the FDA formally warned that a correctly prescribed dose could kill a child who seemed perfectly normal; by 2017 codeine carried a boxed warning and was contraindicated for everyone under twelve. Not because the average child was in danger — the average child was fine. The drug was banned because the average dose was lethal for a patient the prescription never looked at.

The dose was right. It was right for a patient who didn’t exist.

Before going further: this is not an essay against averages. Averages are among the most useful tools our species has ever built. Seat belts, iodized salt, vaccination schedules, statins — population-scale interventions that save millions of lives, and none of them makes sense except as averages. The average is not the problem. The problem is what we do after we compute it: we stop. We treat the summary as if it were the person.

To see how deep that failure runs — and why it turns dangerous exactly at the edges of a population — it helps to start not with medicine, but with machines.

The man who never existed

In 1950, the U.S. Air Force had a mystery on its hands. Its new jets were mechanically sound, and they were crashing at rates no one could explain. The investigation reports said pilot error, over and over, in planes that had nothing wrong with them.

A young researcher named Gilbert Daniels suspected the problem was in the cockpit. It had been designed around the average pilot — height, limb length, torso, all the dimensions that decide whether a man can see over the nose and reach the rudder pedals. So Daniels and his colleagues did something almost nobody had thought to do: they measured the actual population. More than four thousand pilots, 140 dimensions each, at an Air Force laboratory in Ohio.

Then Daniels asked the question the whole aviation industry had skipped: how many of them were average?

He started with the ten dimensions that mattered most for fitting a cockpit. He defined “average” generously — anyone in the middle 30 percent on a dimension counted. Out of 4,063 pilots, the number who fit the average on all ten was zero. Even loosened to any three dimensions, fewer than 3.5 percent qualified. His conclusion, published in a 1952 technical note with a title that reads like an epitaph — The “Average Man”? — was that if you want to design for an individual human being, the average is useless.

The crashes weren’t pilot error. The cockpit was built for a man who never existed.

The Air Force’s fix became one of the quiet triumphs of engineering: not a better average, and not a custom jet for every pilot, but adjustability — seats that slide, pedals that extend, straps that cinch. Let the machine meet the person, because the person will never meet the average.

Medicine, unlike aviation, has never fully had that epiphany. And in medicine, the cockpit fits you whether you like it or not.

The dose and the target

In 2004, three researchers gave the failure a name: the trouble with averages. Writing in the Milbank Quarterly, Richard Kravitz, Naihua Duan, and Jeremy Braslow pointed out that a clinical trial’s average result is not a description of what happens to patients — it’s a census of wildly different outcomes flattened into one number. Behind an “average benefit” can sit “substantial benefits for some, little benefit for many, and harm for a few.” Apply the average to everyone and you give the first group their benefit, the second a waste of hope — and the third their harm.

Four years later, the harm arrived on schedule.

By the mid-2000s, diabetes medicine had a conviction: lower is better. Population studies showed that, on average, higher glucose meant more complications, so the field set a population target — push patients toward normal, an HbA1c below 6 percent — and built a trial to prove the obvious. ACCORD enrolled more than ten thousand middle-aged and older patients with long-standing type 2 diabetes and high cardiovascular risk, and randomized them to intensive or standard glucose control.

The intensive arm was stopped early. After three and a half years, more people were dead: 257 versus 203, a 22 percent higher risk of death from the more aggressive treatment of the same disease. The target that was correct for the population curve was lethal for a meaningful number of the individuals sitting in the chairs. To this day, no analysis has cleanly isolated exactly who was harmed — which is itself part of the lesson: the average can’t tell you which of your patients it will be.

The aftermath is telling. Not one guideline doubled down. They dropped the universal target and replaced it with individualized ones. The field had rediscovered, in the most expensive way available, that a population’s number is not a person’s goal.

These patients weren’t missed because they fell outside the system. The system worked exactly as designed — and that was the problem.

The correction that hid the disease

There is a second, subtler failure. Sometimes the average doesn’t just mistreat the outlier — it actively hides the outlier’s danger, so that no alarm ever sounds. For this, look at what may be the most consequential number in medicine: the estimate of your kidney function.

Kidney function is inferred from blood creatinine, and the equations that do the inferring carry assumptions — age, sex, and, for two decades, race. From the 1990s onward, the standard equations included a “correction” that assigned Black patients higher kidney function at the same creatinine, on the assumption of greater average muscle mass. The assumption traced to studies from the 1960s and ‘70s — potassium content and bone density in a few hundred patients — and in one of the source studies, ethnicity had been assigned, in the authors’ own words, “probably by examination of skin color.”

The correction made charts read healthier than kidneys were. In 2020, researchers at two Boston medical centers quantified it in a registry of 56,845 patients. Remove the multiplier, and a third of Black patients — 743 of 2,225 — would be reclassified into a more severe stage of kidney disease. Most consequentially, 64 patients would cross below an eGFR of 20, the territory where kidney-transplant priority begins to accrue. Of those 64 patients, exactly zero had ever been referred for a transplant evaluation. Under the default equation, nearly a fifth of patients at that threshold had been.

No one missed a form. The math ran correctly every time. The equation — validated on populations, corrected by averages, applied to individuals — wrote a healthier number on the chart in precise proportion to how far each patient’s body stood from the population the average loved. In 2021, after a national reckoning, the nephrology societies removed race from the equations altogether.

The pulse oximeter fails the same way, at the speed of light. The device clips onto a finger and passes light through it; pigmentation absorbs light, and the devices were calibrated, historically, on populations that were mostly light-skinned. In December 2020, a study in the New England Journal of Medicine examined what the reassuring number was hiding: among patients whose pulse oximeter read “normal” — 92 to 96 percent — an arterial blood gas revealed truly dangerous oxygen levels, below 88 percent, in 11.7 percent of Black patients versus 3.6 percent of white patients. A 2024 meta-analysis of 15 studies and more than 730,000 paired measurements found the hidden condition almost twice as common. The FDA warned about the devices in 2021; in January 2025 it went further, proposing that manufacturers be required to demonstrate performance across skin tones.

The number on the screen said normal, because the device was built to define normal without that body in it.

This is why the objection “so what, outliers are rare” misreads every one of these cases. These patients were not rare — they were Black Americans with kidney disease, they were every patient with dark skin and shortness of breath, they were children with one copy of a common gene variant. The harm did not fall on the fringes of a system. It fell on the center of one that had mistaken a population’s shadow for the people in it.

Not only medicine

If the pattern were only medical, it would be a tragedy of one field. It isn’t. For decades, crash testing used a single kind of body: the 50th-percentile male. The result, in the NHTSA’s own data: a belted woman in the driver’s seat or front passenger’s seat is about 17 percent more likely to die in the same frontal crash as a man — and 73 percent more likely to be seriously injured — partly because seats, belts, and airbags were geometrically built around an average body that women are not. In November 2025, the U.S. announced new crash-test standards that finally incorporate female dummies. The average body had a body count.

And in the softer register, the same default shows up as simple slowness: the roughly 30 million Americans — one in ten — with a rare disease wait four to five years on average for a diagnosis, because a system built for the common thing answers an uncommon body with a shrug.

The honest objections

Two objections to all this deserve to be answered, because they are right.

The first is the prevention paradox. In a famous 1985 essay, the epidemiologist Geoffrey Rose showed that a large number of people at small risk can produce more disease than a small number at high risk — so population strategies, shifting the entire distribution, prevent more illness than targeting outliers. This is true, and it is the greatest argument for averages ever made. It is also, notice, an argument about populations. Seat belts and iodized salt are correctly designed for the average precisely because no one is fastening a seat belt into an average body. The prevention paradox tells a government what to do. It does not tell a doctor what to do at 2 a.m. with one patient, one liver, and one number.

The second objection cuts the other way: perhaps individualization is not the cure its marketers claim. Fair. When researchers tested genotype-guided dosing of warfarin against a well-built clinical algorithm in a randomized trial, it didn’t win. And in 2020, a review in the Lancet Digital Health looked at 927 machine-learning “precision medicine” papers and found that none had yet made a genuine difference in practice. The lesson of “treat the individual, not the average” has too often been sold as a product — an algorithm, a gene panel, a subscription — rather than what the evidence actually supports.

But look again at every fix in this essay: a contraindication for children under twelve. An individualized glucose target. A corrected equation. A clip-on device made to read darker fingers. An adjustable seat. Not one of them required precision medicine. They required noticing that the average had stopped being safe, and using information that was already in the room.

The adjustable seat

Zero out of 4,063. Daniels’ number is not about pilots. It is a statement about what an average is: a summary, a starting point — the widest possible net thrown over the most possible people. It was never a person, and the moment we treat it as one, we are designing cockpits for the dead center of a dataset and blaming the people who don’t fit.

The whole record in this essay — the deaths, the hidden hypoxemia, the un-referred patients, the injured women — comes down to two questions that any practitioner can carry:

Is this patient’s variation structured or noise? If it’s structured — genotype, body, age, pigmentation, illness — the average alone is unsafe, and the specific check is the treatment.

If I’m wrong, is the cost symmetric? When missing a danger costs more than double-checking, treat the “normal” reading as provisional.

The average is a starting point, never a stopping point.

That is all the Air Force understood, seventy years ago, that we keep forgetting. They didn’t fix the crashes with a better average. They fixed them by admitting nobody was average — and building machines that could meet each pilot where he sat.

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