The bullet-hole planes
Where would you add armour?
Phase 1 of 3 · Planes coming home
Your bombers keep coming back shot up.
You have 3 armour plates. Where do you put them?
Every hole you see is from a plane that made it home. Armour is heavy, so you can't cover everything.
Phase 2 of 3 · Place your armour
Pick 3 zones to armour.
Tap the plane or the buttons. Tap again to take a plate off.
Phase 3 of 3 · The reveal
Result
The holes you saw show where a plane can be hit and still fly home. Armour goes where the survivors have no holes.
The planes that didn't come back
Hit in the engines and the cockpit. These are the holes you never got to see, because these planes never landed.
What's going on
In the Second World War, the Statistical Research Group at Columbia University worked on military problems for the US. One of its statisticians, Abraham Wald, studied the damage on bombers returning from missions. The holes clustered on the wings, fuselage and tail. The obvious move is to armour those. Wald's point was that the sample only contains planes that survived. A hole on a returning plane marks a place where a plane can be hit and still get home. The places with no holes, like the engines and cockpit, are where hits brought planes down, so that is where the armour should go.
An honest note: the popular version of this story is simplified and dramatised. Wald's real work was a set of technical memos with careful maths for estimating how vulnerable each part of a plane was from the damage on survivors. There is little evidence for the scene of officers pointing at a chart, and the famous dotted-plane picture is a modern illustration, not something from his reports. The lesson holds up all the same.
This is survivorship bias: drawing conclusions from what made it through a filter while the failures stay invisible. It is why studying only successful companies, bestselling authors, or the patients who stayed in a study can teach you the wrong lesson.