Friday, November 2, 2012

A football team has a 79% chance of winning when it starts the 4th quarter with a 3-point lead.  So says the redoubtable Nate Silver, and I have no reason to question the accuracy of that claim.  However, the continuation:  Obama has a 79% chance of winning, in Silver's model, so it's like Obama is a field goal ahead at the start of the 4th quarter - is wrong..

The crucial difference between the two situations is that at any given moment, we know the score of a football game.  Zut Alors!  football scores are not subject to he Heisenberg uncertainty principle. We can know the score, and know how much time is left in the game!  There's no margin of error, no press conference at the end of the game:  "well, I thought we were three points ahead, but it turns out we were one point behind."

Election polls, like modern physics, are creatures of statistical methods, and thus have some uncertainty.  Why are Barack Obama's chances of winning only 80%?  It's not because Mitt Romney has a 20% chance of marching the team down the field for the winning touchdown as time is running out.  It's because the imprecision of polling is such that he might actually be ahead - that's what the 20% represents.  

If we use the football analogy, Mitt Romney is only one great play from seizing the lead.  Football games are often won on the last play; sometimes controversial (the Seattle Seahawks' victory over the Green Bay Packers this year), sometimes comically (the Cal band play; sometimes bizarrely (the fumble recovery by Herm Edwards for the Eagles against the Giants, for which Joe Pisarcik gets unfairly blamed.  Mr Pisarcik is still in the New Jersey area, so if you ever read this sir, we hope that you have survived Sandy without too much damage).  It's where the analogy fails though.  There isn't a miracle ad that will flip a million votes at the last second to any candidate.  Yes, a small number of voters might change their mind before Tuesday.  And yes, in down ballot races where voters are less familiar with the candidates, it may be possible to mount a come from behind win.  But our uncertainty as to who will win the presidential races is not because of the possibility of a dramatic comeback but because in 2012, we have a much greater uncertainty as to who is ahead.

To really strain the football analogy:

It's not likely that Mitt Romney is down by a six points, deep in his own territory, with time left for one play,  
 and the chance to win with a touchdown.  The difference with four years ago, is that in that game, you left early to beat the traffic.  You got home in time to see McCain score a late touchdown, but you knew it didn't matter even though you didn't know the exact score because McCain was 24 points behind when you left.

This year though, you left the stadium because your kid was sick, and the last touchdown might matter.  You aren't sure:  Maybe Mitt was down six points when he scored.  Maybe he was down ten.  Of course, in modern sports production, the score is always on the screen, so you always know.

We are overjoyed when our team wins due to an incredible play at the end of the game.  People remember the  touchdown on the last play by Seattle as the "game-winner", and have already forgotten the equally necessary earlier touchdown.  We like drama, and we create it when we can.  Thus the analogy that starts this post:  Mitt is close enough to make a dramatic comeback and win.  No, he's not.  There is some possibility he is ahead right now even though the polls don't show it, due to the possibility of pollster error and the imprecision of polling,  Of course, that is the problem of modeling a presidential election, or any single event.  Obama will not win 80% of the time; Romney will not win 20% of the time.  One of those two men will once, that is to say, 100% of the time.  You can't land on a fraction, as Dennis Hopper tells us.




The Cal band play




And of course, the fumble




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