Nate Silver and the Binomial Theorem

Courtesy of thenandnow.com

There has been a lot of chatter about the meaning of Nate Silver’s current election forecast.

Unfortunately, what the commentary reveals is less about Silver and more about statistical illiteracy.  Silver’s model is complex, but the basic logic is quite simple: he runs a forecasting model based on a lot of state public opinion polls, then creates thousands and thousands of random “draws” from the predictions of that model.

Currently, approximately 3/4 of those random draws have Obama winning the electoral college.  Sounds good if you are a Democrat but keep in mind:

  • 25% of the draws have Romney winning.
  • This election is run once, not thousands of times.
  • Because the model is based on an electoral college victory, small changes in a small number of states–for instance, a 1% shift in the vote in Ohio–could have large effects on the forecast.

Andrew Gelman, a political statistician at Columbia, provides an apt metaphor.  In football, if your team is  leading by 2 points with less than 5 minutes to go, your team will win 65% of the time.

Does this mean you feel confident with a 2 point lead with 5 minutes left?  What if John Elway is the quarterback for the other team?  Maybe you don’t think Mitt Romney has a John Elway drive in his campaign, but look at his standing just a few weeks ago, and look at it now.

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