For several weeks now, I’ve been bandying about various election projections that some readers no doubt regarded as far too favorable to President Obama.
Well, take heart, you skeptics. Readers who are hoping that Mitt Romney wins next week’s election will want to pay close attention to today’s lesson on the difference between election probabilities and poll percentages. They ain’t the same thing.
Let’s begin our little tutorial with the latest projection from polling analyst Nate Silver. He sees a 77-percent likelihood that President Obama will win re-election next week. For our purposes here, let’s just say that he sees — at this point in time, on the basis of his reading of all the polls in the various states — only one chance in four that Romney will win.
There’s a tendency, I suspect, that some people misread Silver’s projection. He’s not saying that Obama has an overall lead of 3-1 in the polls. If that were the case, Obama would be a prohibitive favorite. But he’s not. Romney still has a fair chance of winning. Not a really great chance, mind you, but a fair chance.
Andrew Gelman offered THIS EXPLANATION in a column that ran yesterday in The New York Times:
I can simultaneously (a) accept that Obama has a 72 percent chance of winning and (b) say the election is too close to call. What if the weatherman told you there was a 30 percent chance of rain — would you be shocked if it rained that day? No. To put it another way, suppose Mitt Romney pulls out 51 percent of the popular vote and wins the election. That doesn’t mean that [analyst] Nate Silver skews the polls… Romney winning the election with 51 percent of the vote is well within the margin of error, as Silver clearly indicates. That’s what too close to call is all about…
[P]eople aren’t so good at thinking about probability and uncertainty. I struggle with this every day, and I can only imagine how difficult this sort of thing is for non-statisticians. An example from my own life: every semester I find myself surprised that some students who perform well on the midterm fall down on the final exam, while others who struggle at first end up performing very well. As a statistician, I know that a midterm exam is a noisy signal — but as a human, it’s hard for me to avoid falling into the trap of thinking of measurements as perfect.
[F]ootball analyst Brian Burke…suggests that if you’re up by a touchdown with five minutes left, you have something like a 90 percent chance of winning. Even if you’re only up by a field goal, your chance of winning appears to be something like 80 percent… Another analyst gives an 80 percent chance of winning if you’re ahead by a touchdown at the end of the third quarter…According to yet another site… a team that’s leading by 2 points with 5 minutes to go has a 65 percent chance of winning. So I think it’s more accurate to say that Obama is up by 2 points, not by a touchdown, in this final stretch.
Perhaps now you conservative critics of Nate Silver understand that his probability projections are not as outlandish as you previously thought.
HERE‘s more for you to chew on from Silver’s post of this morning:
Mitt Romney and President Obama remain roughly tied in national polls, while state polls are suggestive of a lead for Mr. Obama in the Electoral College. Most people take this to mean that there is a fairly good chance of a split outcome between the Electoral College and the popular vote, as we had in 2000. But the story may not be so simple.
For both the swing state polls and the national polls to be right, something else has to give to make the math work. If Mr. Obama is performing well in swing states, but is only tied in the popular vote nationally, that means he must be underperforming in noncompetitive states.
High-population red states like these, Texas and Georgia, are just the sort of places where Mr. Obama would need to lose a lot of ground in order to increase the likelihood of his winning the Electoral College while losing the popular vote.
Perhaps Mr. Obama is underperforming in deeply blue states rather than deeply red ones? Sometimes you’ll get numbers that check out with this assumption: Mr. Obama did get some mediocre polling in Oregon on Tuesday, for instance. But he also got a poll showing him ahead by 23 points in California. Another survey on Tuesday gave him a 31-point lead in Massachusetts.
Read the whole thing. It’s chock full of fascinating data.
Meanwhile, over at the Princeton Election Consortium, analyst Sam Wang’s probablity projection makes Silver’s look downright conservative. He says the chances of Obama winning range from 95 percent to 99 percent. And he projects, on the basis of current data, that Obama will get 318 electoral votes while Romney gets 220.
Wang’s latest post is HERE.
UPDATE: HERE‘s a whole batch of new state polls, most of which are at least fairly good news for Obama.
UPDATE II: Here’s what the Intrade market betting charts looked like shortly before noon today, with Obama leading Romney 65 percent to 35 percent.