Where the line is
A gull on a harbor post with fishing line around one leg, a statistician in wartime New York, and what the ones who came back can and cannot tell us.
Clovelly, north Devon, on an August evening. A herring gull was standing on a wooden post, and I crept toward it to take a photo. I managed a few shots just before it took off.
Back home, looking through the photos, I noticed a length of fishing line knotted around one of its legs, just above the foot. My first reaction was pity. The sea is full of line, and here was one more bird caught in it.
But look at it another way and the photo is saying something else entirely. It teaches a trick of thinking that comes in handy more often than you'd expect.
The one that came back
This gull is not a victim. It is a survivor. Line catches birds in all sorts of places: around the beak, around the neck, through a wing. With line around its beak a gull cannot feed; with a bound wing it cannot fly. Those birds are not standing on posts in the evening light. The ones you get to photograph are the ones whose bad luck landed somewhere they could live with, and a leg, it turns out, is such a place. The knot is not a sample of what the sea does to gulls. It is a sample of what a gull can survive.
Archaeologists ran into the same thing with bones. Famine and disease leave marks on a skeleton, but only if the person lives long enough for the bone to change. The frailest die before anything is written into them. So a cemetery full of clean skeletons can belong to a sicker people than one full of scarred ones; the scars belong to those who held on. They call it the osteological paradox. A scar is evidence of survival, not of suffering.
The usual name for all this is survivorship bias: drawing conclusions from what made it through a filter, while forgetting that the filter was there. The best-known story about it comes from World War II.
Holes in the wrong places
In 1943, in an apartment building at 401 West 118th Street, near Columbia University in New York, a group of mathematicians called the Statistical Research Group worked on questions for the American war effort.
Here is the kind of problem that came their way. Bombers return from their missions full of holes, and the holes are not spread evenly: many on the wings and the fuselage, far fewer on the engines. Armor would help, but armor is heavy, so it has to go where it helps most. Where would you put it? Try it yourself.
In the usual telling, the officers wanted to armor the planes where the holes were. If you did the same, you saw what happens: hardly any more planes come home than with no plates at all.
One of the group's mathematicians, Abraham Wald, asked a different question: were the clean parts really clean? Put the armor where the holes aren't, he said.
Born in 1902 in Kolozsvár, now Cluj in Romania, into a Jewish family, Wald did his mathematics in Vienna, where as a Jew and a foreigner he could never get a university post. He left Austria in 1938, after the Nazis took it. In 1944 almost all of the family he had left behind in Cluj were deported and murdered at Auschwitz.
Born in 1902 in Kolozsvár, now Cluj in Romania, into a Jewish family, Wald did his mathematics in Vienna, where as a Jew and a foreigner he could never get a university post. He left Austria in 1938, after the Nazis took it. In 1944 almost all of the family he had left behind in Cluj were deported and murdered at Auschwitz.
The guns weren't aiming anywhere in particular, so every part of a plane was hit about as often as its size would suggest. A plane hit in the engines doesn't come back to be counted. The missing holes are on the missing planes. Plate those parts, and nearly the whole squadron comes home.
It is a perfect story, and like most perfect stories it has been polished. What survives of Wald's work is a set of eight memoranda from 1943: more than a hundred pages of careful, dry mathematics about estimating how vulnerable each part of a plane is from the damage on the ones that return. The examples in them are all made up, and no aircraft is named.
There is no record of the skeptical officers or the dramatic reversal. The mathematician Bill Casselman, who went back to the sources, calls most of the popular version plausible reconstruction, and the two statisticians who studied the memos most closely wrote in 1984 that they did not know whether the method was used during the war at all.
The memos themselves nearly went missing. When the group closed in 1946, its director took home a box of loose papers. Around 1980, moving house, he handed the box to a colleague at the Center for Naval Analyses, who decided that most of it was not worth keeping. He kept the bundle of Wald's memos and published it. "Recorded history hangs by thin threads," Casselman writes.
Even the famous picture, the gray plane covered in red dots that you have almost certainly seen, is not from the war. A designer named Cameron Moll drew the first version for a talk around 2005, putting made-up dots on an airliner. In 2016 a Wikipedia editor traced it again over a US Navy patrol bomber, and from there it went everywhere.
In 2026 Wald's son Robert, a physicist, told a Brazilian magazine that his father's work goes much further than the bomber story, and that it saddens him to see it oversimplified and distorted. Robert was three when his parents died, in December 1950, when the plane taking them to a lecture tour in India flew into a hillside in the Nilgiri mountains.
There is an irony here: the most famous story about survivorship bias is itself a survivor. The tidy version outlived the messy one because it was easier to retell.
The dead leave a count
There is a detail in the real story that the legend drops, and it is the most interesting part. Wald could reason about the planes that didn't come back because he knew how many didn't come back. Whoever sent the bombers knew how many left and how many landed. In a worked example built on his method, 400 planes go out and 380 return; from how many of the returning planes took one hit, two hits, three, you can work out how likely a plane is to survive a hit at all. Wald even imagined the same battle fought with dummy bullets, a ghost fleet in which every plane comes home, and compared it with the real one. The dead left no holes to study, but they left a number, and a number was enough.
Most of the time we don't get that number. Nobody counts the restaurants that closed, the bands that split up after one gig, the start-ups that ran out of money in a spare room. They don't leave a gap in the record; they leave no record. That is when survivorship bias does real damage, because there is nothing on the page to tell you something is missing.
Investment funds are the cleanest example, because there people did eventually go back and count. Of the 3,000 or so American equity funds that were open at the start of 2006, only 45% still existed twenty years later, and only 12% had both survived and beaten their benchmark, according to a 2026 count by Dimensional. A fund that does badly for a few years is usually closed or quietly merged into a better one, and its record goes with it. In 1997 the Wall Street Journal noticed that the average 1986 return of American stock funds, first reported as 13.39%, had become 14.65%: someone had recalculated it using only the funds still alive. Nothing about 1986 had changed. The past had gotten better because the losers had been deleted.
Nassim Nicholas Taleb ran the numbers on this in Fooled by Randomness. Take ten thousand fund managers with no skill at all, give each an even chance of a good year, and drop anyone who has a bad one. After five years, 313 of them have a perfect record, by pure luck. Here is the experiment.
And we have a winner! Ten years or so without a single losing year, a bestseller, the publishers on the phone. However, half of the managers closed in the first year, a quarter in the second, and so on, each year halving what was left, until one was standing.
They all followed the same method, more or less, and tossed the same coin. No one writes books about them, and they don't appear in any fund list today. The arithmetic guarantees a winner; it doesn't care who.
Warren Buffett, who has every reason to believe in skill, made the fair counterpoint in 1984. If you had millions of orangutans flip coins, some would win twenty times in a row, and that alone proves nothing. But if a suspicious number of those winners turned out to come from the same zoo in Omaha, you would want to know what they were being fed.
Skill doesn't show itself by existing among the survivors. It shows itself by turning up more often than luck would allow.
The crowd that vanished
If you take photos, as I do, you may have noticed that every picture is a survivor: it shows only what was in the frame at that moment, and only if it made the cut afterwards. The first photographs made this almost literal.
In 1838 Louis Daguerre pointed his camera out of a window at the Boulevard du Temple, one of the busiest streets in Paris. The exposure took minutes, so every carriage and every walker moved through the frame too fast to leave a trace. The street looks deserted. The only people in it are a man who stood still to have his boots polished, and the man polishing them. It is usually called the first photograph of a human being, and it shows a crowd reduced to the two who stayed.
Every archive works a little like that exposure. Three quarters of American silent feature films are lost. When people say the silent era was magical, they mean the quarter that someone bothered to keep. Sophocles wrote over a hundred plays and we have seven, largely the ones Byzantine teachers chose for their reading lists. When we say they don't build them like they used to, we are standing in front of the cathedrals that stayed up.
The photograph of the gull is a survivor too. I took several frames that evening and kept this one, because of the knot and the light. You are seeing my filter as well as the harbor's.
When survivors tell the truth
It would be easy to turn all this into a reflex, and shout "survivorship bias!" at every success story. That is its own mistake. Looking at survivors is fine when the question is about survivors, or when what decided who survived has nothing to do with what you are measuring. If bombers had been lost to bad weather at random, the holes on the ones that came back would have told the truth.
The writer Samuel Hughes made the point well about old buildings. If old streets look beautiful only because the ugly buildings were knocked down, then old photographs should be full of ugly buildings that are gone now, and mostly they aren't. A filter is a claim to be checked, not a trump card.
So the useful question is never just "who is missing?" It is three questions. Did whatever removed the missing ones depend on the thing I care about? Do I know how many are missing? And if not, can I find out? Wald could answer all three, which is why he could say something about planes he never saw.
The sailors who drowned
Two thousand years ago, according to Cicero, someone showed the philosopher Diagoras a shrine hung with paintings left by sailors who had prayed in a storm and come home safe. Surely that proved the gods listened? Diagoras asked where the paintings were of the sailors who had prayed and drowned.
Taleb opens the chapter of The Black Swan on what he calls silent evidence with this same story. The drowned, he points out, would have found it hard to tell theirs from the bottom of the sea.
Wald was after the same kind of knowledge: not what happened to everyone, but what the ones who made it can tell you about the ones who didn't, if you remember to ask.