Where should the extra armor go?
World War II: engineers studied the bullet holes on bombers that made it home.
Armor is heavy, so it can go in only a few places. Where?
Why are there so few holes on the engines?
Statistician Abraham Wald said to armor where the holes aren’t. Predict why.
The planes in the study
Which could the engineers inspect?
Engine holes on returning planes
Why were there so few?
The missing holes were on the planes that never came back.
Left: what the engineers saw. Right: every hit, including planes that were lost.
Every plane the engineers inspected had survived its damage. A hole in a wing showed a bomber could be hit there and still fly home.
Illustrative drawing, not historical counts. Source: Abraham Wald, Statistical Research Group, Columbia University (1943).
Change how dangerous an engine or cockpit hit is.
The same hits every time. Only the returning planes get inspected.
The more dangerous a spot is, the fewer holes you find there on the planes that made it home.
STILL STANDING
GONE
Were buildings from 100 years ago built better?
You can’t tell. Time already removed the weak ones.
Only the sturdiest, best-loved buildings made it. Before judging a group, ask who dropped out before you looked.
A DIFFERENT QUESTION
THE SURVIVORS
Can the survivors answer this question?
Yes. A survivor proves that something can survive.
Like the wing holes, survivors are good evidence of what can be lived through. They mislead only when you ask about what’s missing. Match the question to the data you have.