Bias · Statistics
Survivorship bias
88 bombers came back, and these are their bullet holes. Where would you add armour?
| Part | Holes on survivors | Fatal hits on the lost |
|---|---|---|
| Engines | 9 | ? |
| Cockpit | 0 | ? |
| Fuselage | 64 | ? |
| Wings | 135 | ? |
| Tail | 38 | ? |
Drag the bomber to turn it.
What you are looking at
A bomber, marked with every bullet hole found on the aircraft that made it back from a raid. Wings and fuselage are peppered. Engines and cockpit are almost clean.
Armour is heavy, so you can only add a little. Where does it go? Nearly everyone answers: where the holes are.
Show the lost planes
Press Show the lost planes. The orange marks are the hits that brought down the aircraft that never returned, the ones nobody could inspect. They sit exactly where the survivors are clean.
Enemy fire did not avoid the engines. Hits landed all over the aircraft, in proportion to its size. A bomber hit in the wing flew home and was counted. A bomber hit in an engine did not, and its holes went to the bottom of the sea with it. The clean patches are not where planes are safe. They are where planes do not survive being hit.
Send more waves and the pattern only sharpens.
Not a paradox, strictly
Nothing here contradicts anything else. This is a bias: a reliable way of drawing the wrong conclusion from true facts. Every hole on the model is real. The mistake is treating the planes on the runway as if they were all the planes that took off.
It belongs here because it feels like a paradox the moment the answer is revealed: the right place for the armour is where the evidence shows no damage at all.
Where else it hides
- Success stories. Founders who dropped out of university and got rich are easy to list. The far larger number who dropped out and did not are in no magazine.
- “They built things to last.” The old buildings still standing are the ones that were built well. The rest fell down long ago and left no impression.
- Investment funds. Funds that perform badly are closed or merged, so the average record of the funds that exist today flatters the industry.
- Medical advice from the lucky. “My grandfather smoked all his life and lived to 95” is a report from a survivor.
The question to ask is always the same: what would I be seeing if things had gone the other way, and would it have reached me at all?
Where it comes from
The story is about Abraham Wald, a mathematician who had fled Vienna and worked during the Second World War for the Statistical Research Group at Columbia University. In 1943 he wrote a series of memoranda on how to estimate an aircraft’s vulnerability from the damage on those that returned, making the missing planes part of the calculation instead of ignoring them.
The image of a plane dotted with holes, which travels with the story everywhere, is an illustration of the idea and not Wald’s own data. So is the bomber on this page: its numbers are simulated.