What are the Odds?

Evan Manvel

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.

By Evan Manvel July 14, 2010