What are the Odds?

Evan Manvel

What are the Odds?

Photo courtesy Wikipedia

Paul the Octopus is the world’s most famous cephalopod. Unfortunately, the media haven’t paid much attention to Leon the porcupine, Anton the tamarin, or Mani the parakeet (they didn’t do so well in soothsaying). Nor did the media talk about Paul’s missed Euro 2008 predictions, or the problems with the design of the choice system.

This morning The Oregonian ran an AP story about a four-time lottery winner with the headline “What are the odds?” and lede “The odds that Joan Ginther would hit four Texas Lottery jackpots for a combined nearly $21 million are astronomical. Mathematicians say the chances are as slim as 1 in 18 septillion-that's 18 and 24 zeros.“ Near the end of the story, the reporter finally fessed up, “If Ginther's winning tickets were the only four she ever bought, the odds would be one in 18 septillion… a habitual player winning four times over a 17-year span is much less far-fetched.”

Taken as diversion, such stories are fun. Yet they also add to our collective innumeracy, which can lead to bad personal financial decisions and bad policy decisions. The main problem here is selection bias – we remember the times things worked, and forget the times they didn’t, leading us to draw conclusions based on the wrong data set.

Such bias contributed to the home mortgage meltdown - “home prices always go up!” - and contributes to stock market fluctuations. Many legislative actions are based on selection bias; elected officials or voters pass laws in response to an anecdotal story, without fully understanding broader implications. And it’s hard to forget Nancy Reagan consulting an astrologer to help plan the President’s schedule, affecting how the Iran-Contra scandal played out and other decisions.

Our collective innumeracy may bring in money for critical public services, as people are playing the lottery more often (some understand the odds and play for fun, but some suffer from selection bias). But it also impedes the public's willingness to pay for public services, as many voters remember an anecdote of government waste and draw overbroad conclusions.

To improve our policy decisions, it is critical the media play their role as ongoing educators, while also providing entertaining and interesting stories. The Oregonian could run with their lottery story by leading with the end of the story, getting people interested in the intriguing ways odds change when we consider all the data – “To some, she’s the luckiest woman on earth. To mathematicians, she’s a not unlikely outcome of a game that’s played hundreds of millions of times.”

Raise a glass to Paul the Octopus. But remember Leon the porcupine, who predicted Australia would win the World Cup.

UPDATE: A friend sent me a link to a clever Radiolab show about stochasticity and perception.

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    Hmmm... "a habitual player winning four times over a 17-year span is much less far-fetched."

    It's still pretty amazing. I'm a habitual PowerBall player for well over a decade now, and I've never gotten so many as four of six numbers right. Of course, I buy a total of $20 of tickets every year - so not much. (Mostly for the brief respite that comes with daydreaming about how I'd spend a $100 million jackpot.)

    But four jackpots in 17 years -- either something's screwy, or she's been buying tens of thousands of number combinations.

    I'm reminded of the guys back in the early 90s that tried to make a logical bet on the lottery by buying up thousands of individual number combinations. For the PowerBall, that would become possible once the jackpot exceeds $196 million (lump sum) - since the odds of winning are 1 in 195.2 million, though I don't believe PowerBall has ever gone that high. (It would half to be an advertised 29-year jackpot of some $400 million.)

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    The sentence from the article is correct, in that the odds of specific woman X winning specific lottery Y four times are high.

    However, the odds of someone, somewhere in the world, winning some lottery four times are quite different. It would be a great follow-up article.

    It's like that old party trick - if you have 24 people in a room, odds are better than 50% that two of them will share a birthday. And if you have 57 people in the room, odds are 99%. Whereas the odds that someone will have your specific birthday are about one in 365.

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      I still remember my high school physics teacher (Stampa) trying to convince us that if 57 people in a room meant 99% odds of two people sharing a birthday, then 60 people in a room meant 100% odds of two people sharing a birthday. That memory still pisses me off.

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    I'd be happy if they could just remind us of the history of the top marginal tax rate.

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