The Woman Who Won Twice
In October 1985, Evelyn Adams won the New Jersey lottery. Three point nine million dollars. Four months later, in February 1986, she won it again. Another one point four million. The newspapers did the math and gasped. The odds of one woman hitting two jackpots like that were one in seventeen trillion. A miracle. Lightning finding the same lucky woman twice.
Then a pair of statisticians ran a different number, and the miracle quietly fell apart.
They didn't ask the odds of Evelyn Adams winning those two exact draws. They asked a bigger question. Across all the people buying tickets, in all the states, week after week, year after year, what are the odds that somebody, somewhere, wins twice? The answer wasn't one in seventeen trillion. Over a few years it was better than a coin flip. Not a miracle. Closer to a scheduled event. Someone was going to be the two-time winner. It just happened to be her.
Here is what the headline got wrong. One in seventeen trillion is a number sitting on top of a fraction with nothing written underneath it. And a number on top means nothing until you ask what is on the bottom. Out of how many chances?
Call it the missing denominator. The impossible-sounding odds, divided by all the times the dice actually got rolled.
Once you start looking for the missing denominator, the world stops feeling quite so magical, in the best way.
You run into a college friend in an airport in a country neither of you lives in. What are the odds. It feels like fate. But count the bottom of the fraction. Every person you would recognize, every trip you take, every crowd you stand in, every year you are alive. Out of all of that, a stunning coincidence is not a long shot. One of them was always going to land. This time it landed on you.
A fund manager beats the market ten years running and the magazines call him a genius. But picture ten thousand managers who do nothing but flip coins. After ten years, pure chance leaves a handful of them still on a perfect streak. They look like wizards. They are the coins that kept landing heads. The streak was the bottom of the fraction the whole time.
A test for a rare disease comes back positive and your stomach drops. But the disease is rare, which means the denominator, all the healthy people, is enormous, and no test is perfect. So most of the alarms it sets off are false ones. The frightening number on top barely means anything until you weigh it against how rare the thing actually is.
This is not just a parlor trick. The same missing denominator has put innocent people in prison, when a courtroom hears "one in a million" and nobody stops to ask how many millions of people there were.
So when a number shows up dressed as a miracle or a disaster, don't gasp at the top of the fraction.
Ask what is on the bottom.