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A friend asked me the other day whether there’s anything preventing Hillary Clinton from rising further in our forecast, beyond what have generally been very good polls for her. Clinton’s chances are up a bit — she’s hit 88 percent in our polls-only forecast, up slightly from 86 percent on Friday and 83 percent a week ago. In the polls-plus forecast, Clinton’s chances are 85 percent, up from 80 percent a week earlier.
But there’s some truth to the notion that she’s encountering diminishing returns. And that’s for a simple reason: 88 percent and 85 percent are already fairly high probabilities. Our model is going to be stingy about assigning those last 10 or 15 percentage points of probability to Clinton as she moves from the steep, middle part of the probability distribution to the flatter part.
Before this turns into too much of a math lesson, a quick review of Monday’s polls. As has often been the case in recent days, they were a mix of catastrophic-seeming results for Trump, mixed in with others that showed a race that remains competitive.
On the not-so-bad side for Trump were a set of polls from CNN that showed him leading by 4 percentage points in Ohio, and trailing Clinton by 2 points in Nevada and 1 point in North Carolina. These polls weren’t great for Trump: None of these are must-win states for Clinton and she was winning two out of three of them despite that. Also, CNN’s polls have been somewhat Republican-leaning this year relative to the polling average. But CNN’s results were consistent with a race in which Trump is trailing by perhaps 3 to 4 points nationally and is still within striking distance.
By contrast, a trio of new national polls were fairly awful for Trump, with Monmouth University showing him trailing Clinton by 12 percentage points, CBS News putting him down by 9 points, and George Washington University — whose polls have historically been Republican-leaning — having him 8 points back. As I wrote earlier today, there were also new polls in Utah (yes, Utah) showing a competitive three-way race between Trump, Clinton and independent Evan McMullin. And another poll this afternoon showed Clinton with a narrow lead in Arizona.
Overall, the results are most consistent with a race in which Clinton leads by about 7 percentage points nationally. States in the Midwest and the Northeast for the most part look as they did in 2012, when President Obama beat Mitt Romney by just under 4 points nationally. But, in the West and in the South, where demographic shifts are unfavorable for Trump, Clinton is poised to have the best Democratic performance since at least 1996, if the polls are correct.
And Clinton is possibly still gaining on Trump. Some of Trump’s worst results came in the most recent polls; Monmouth’s national poll, for instance, was conducted Friday through Sunday, while the CNN state polls went into the field last Monday, before a number of women came forward to accuse Trump of sexual assault.
But even if Clinton continues to gain ground on Trump, her probability of winning the election won’t increase all that much. Below is a chart depicting Clinton’s lead in the popular vote and her probability of winning the popular vote on Nov. 8, according to our polls-only model:
Given the uncertainty in the forecast, a 1-percentage-point lead for Clinton — about where she was at her lowest moments in mid-September — translates into only a 58 percent chance of winning the popular vote. After the first debate, Clinton emerged with a lead of about 4 points, giving her a 79 percent popular-vote win probability — a huge difference. Moving from a 4-point lead to the 7-point lead has also had a noticeable effect, with Clinton’s chances of winning the popular vote moving up to 92 percent.
But she’s now begun to reach the point of diminishing returns. Gaining another 3 points on Trump, to bring her to 10-point lead, would improve her chances of winning the popular vote to “only” 97 percent, for instance.
There are some other complications, of course. The Electoral College adds complexity to the outcome as compared with the popular vote. Also, the width of the probability distribution narrows as the election approaches, so Clinton will gain a little bit of ground each day just by holding steady as time runs off of Trump’s clock. And the distributions are sensitive to the number of undecided voters — more undecideds mean more uncertainty. Clinton currently leads Trump by a margin of about 46 percent to 39 percent in national polls. If each candidate were to gain 4 points, so that Clinton led Trump 50 to 43, our model would become yet more confident in her chances. So be on the lookout for national polls and polls of key swing states that show Clinton in the high 40s, or even above 50 percent. She’ll need more of those for her win probability to cross the 90 percent threshold.
As an aside, FiveThirtyEight’s forecast models use a t-distribution rather than the more common normal distribution. The t-distribution has wider and fatter tails and is appropriate in cases like presidential elections where you have smaller sample sizes. Since our model is trained based on only 11 elections (1972 through 2012), we can’t say all that confidently what the chance might be of, say, a 10-percentage-point polling error. The t-distribution makes more conservative assumptions about this than the normal distribution does. If Trump wins the election despite trailing by 10 points, do I think we’re going to get a lot of credit for having given him a 3 percent chance to do so, when everyone else had his chances at 0.3 percent or something instead? No, probably not — but we still think it’s the mathematically correct approach.
With Clinton having this large a lead, individual polls won’t swing the overall popular vote or Electoral College win probabilities quite as much, and so the model won’t be as jittery as it was a few weeks ago when the race was closer.