Picture a café on a good day. A hundred customers. Eighty left happy, twenty did not. That evening, four of the happy ones write a review and ten of the unhappy ones do. The review page shows fourteen reviews, ten of them bad. The café looks terrible. The day was good.
Everybody→The gate: who answers→The count
A count can only hold the people who got counted. Between the world and the number there is a gate: who answered, who turned up, who bothered. If the gate lets one kind of person through more than another, the number is about the gate, not the world.
Left happy
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Left unhappy
At the café, who is more likely to go home and write a review?
The happy ones. There were four times as many of them.
Not yet. There were more of them, and fewer of them wrote. The count on the page is who wrote, not who came, and the writing was done mostly by the twenty.
About the same share of each.
Not yet. If the gate were even, the page would show the day: four good reviews for every bad one. It showed the opposite, because the gate was not even.
The unhappy ones. A bad hour is a reason to write; a good one is not.
Right. An unhappy customer has something to say and a reason to say it. A happy one finishes their coffee. The gate opens wider for the unhappy, so the page is about the gate.
Move the control through how many of the twenty unhappy customers write a review. Happy customers write at 5 in 100 throughout. The numbers are made up and round.
Happy reviews4
Unhappy reviews1
Unhappy customers who write, in 100: 5
5 in 100 unhappy customers write a review. Tonight: 4 happy reviews and 1 unhappy one. The page shows an average of 4.2 stars, from a day where 80 in 100 left happy.
Happy reviews4
Unhappy reviews4
Unhappy customers who write, in 100: 20
20 in 100 unhappy customers write a review. Tonight: 4 happy reviews and 4 unhappy ones. The page shows an average of 3.0 stars, from a day where 80 in 100 left happy.
Happy reviews4
Unhappy reviews10
Unhappy customers who write, in 100: 50
50 in 100 unhappy customers write a review. Tonight: 4 happy reviews and 10 unhappy ones. The page shows an average of 2.1 stars, from a day where 80 in 100 left happy.
Happy reviews4
Unhappy reviews20
Unhappy customers who write, in 100: 100
100 in 100 unhappy customers write a review. Tonight: 4 happy reviews and 20 unhappy ones. The page shows an average of 1.7 stars, from a day where 80 in 100 left happy.
The gate lets through 50 in 100 of the unhappy and 5 in 100 of the happy. The day was 80 in 100 happy. What does the page show?
Mostly good reviews, because most customers were happy.
Not yet. Most customers were happy and most reviews were not. The count on the page went through a gate that favoured the unhappy ten to one.
More bad reviews than good, on a day that was mostly good.
Right. Four happy reviews against ten unhappy ones. The page is a faithful count of who wrote, and who wrote was decided by the gate, not by the coffee.
About half and half.
Not yet. Half and half would need the gate to be about even. At 50 against 5 it is ten times wider for the unhappy, and the page shows it.
Move the control.
Came backholes in wings and body
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Did not come backnever counted
The oldest version is from 1943. A statistician, Abraham Wald, studied the damage on planes that came back from wartime raids. The parts that came back undamaged, he reasoned, were where a hit was most often fatal: a plane hit there never came back to be counted. Armour, by that reasoning, belonged on the parts with no holes.
Picture the holes counted on returning planes: most on the wings, some on the tail, almost none on the engine. Tap where that reasoning says armour would do the most good.
Tap the part of the picture that answers it.
Wings60 holes in 100
Tail30 holes in 100
Engine10 holes in 100
Made up and round. Holes on planes that came back.
The engine
Right. The planes that came back were hit in the engine almost never, because a plane hit in the engine did not come back to be counted. The missing holes mark the fatal spot.
The wings
Not yet. The wings took the most holes on planes that flew home, which means a plane can take a wing hit and survive. Armour there protects against the damage that was already being survived.
The tail
Not yet. The tail is in the middle: hit sometimes, survived often. The count that matters is the one that is nearly empty, and that is not the tail.
Each is a count. Did everybody get counted, or only those who came through a gate?
One card at a time. Tap the pile it belongs to.
Card 1 of 6
A poll of people who picked up a phone call at two on a Tuesday afternoon.
A census that visits every household in the country.
A list of famous people who dropped out of school and became billionaires.
A school weighing every pupil at the start of term.
A gym's wall of before-and-after photos.
The ages of everyone at a concert, read off the ticket records.
A poll of people who picked up a phone call at two on a Tuesday afternoon. → Through a gate
Not yet. Through a gate. The gate is being at home, free and willing at two on a weekday, and it lets through some kinds of people far more than others.
A census that visits every household in the country. → Everybody
Not yet. Everybody. A census is built to have no gate, which is why it costs so much and happens so rarely.
A list of famous people who dropped out of school and became billionaires. → Through a gate
Not yet. Through a gate. The gate is became famous. The dropouts who did not become billionaires are not on anybody's list.
A school weighing every pupil at the start of term. → Everybody
Not yet. Everybody. Every pupil stands on the scale, so the average is the school's and not the gate's.
A gym's wall of before-and-after photos. → Through a gate
Not yet. Through a gate. The gate is finished the programme and liked the result. Those who stopped in week three sent no photo.
The ages of everyone at a concert, read off the ticket records. → Everybody
Not yet. Everybody who was there. Every ticket is a record, so the count holds the whole crowd and not the part that chose to answer.
3Everybody
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3Through a gate
Right. Three counts hold everybody, and three hold only the people who came through a gate. The three with a gate are the ones that get shared, because the gate is what makes them striking.
1 of 20
dropout on a list, out of twenty who dropped out
Made up and round: nineteen of twenty left no list to be on.
The ones who came through the gate are called the survivors. They are the planes that flew home, the customers who wrote, the dropouts who got rich. We see them because they are the ones left to see. The ones who did not make it left nothing behind to count.
Successful, up at fivecounted
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Who else?not counted
A post says: every successful person I know gets up at five in the morning. By this lesson, who is missing from the count?
Nobody. The writer knows a lot of people.
Not yet. Knowing a lot of people is a big count through a narrow gate. The gate is still successful, and it still leaves out everyone the claim needs.
The people in other time zones.
Not yet. Time zones do not change who got counted. The missing people are the ones who did the same thing and did not get the result, and they live next door.
The people who get up at five and are not successful, and the successful ones who sleep in.
Right. The gate is successful people I know. Nobody counted the five o'clock risers who are not successful, and they are the count that would say whether five o'clock does anything.
Lesson complete
A count holds only who got counted. The gate between the world and the number decides what the number says.