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Sept. 16: Watching the Clock and Awaiting the Unknown

President Obama’s chances of winning the Electoral College fell slightly on Sunday in the FiveThirtyEight forecast, to 74.7 percent from 76.2 percent on Saturday.

The downtrend in Mr. Obama’s forecast has gotten a bit sharper since last week, when his re-election chances peaked at close to 80 percent in the model.

The evidence seems a bit clearer now that Mr. Obama is off his post-convention highs in the polls. In the Gallup national tracking survey, his lead declined to three points over Mitt Romney on Sunday. And in the Rasmussen Reports tracking poll, he trails Mr. Romney by one point, although that is up from a two-point deficit on Saturday.

The state-level polls we have seen over the last several days by and large fall into the category of being good but not great for Mr. Obama. The lone poll of a swing state to be published on Sunday, Public Policy Polling’s survey of Virginia, falls into this category. The poll gave Mr. Obama a five-point lead in Virginia (or a four-point lead with third-party candidates included). However, Public Policy Polling has generally had good numbers for Mr. Obama in Virginia, and also had him ahead by five in their last poll of the state, in August.

The forecast model is deliberately reading Mr. Obama’s polls a bit skeptically right now because we are still close enough to the conventions that there could be temporary effects from them.

In our “now-cast,” which does not adjust for the effects of the conventions and projects what would happen if the election were held today, Mr. Obama’s lead over Mr. Romney is 3.8 percentage points. However, the Nov. 6 forecast is our signature product and does seek to adjust for the effects of the conventions, along with other factors like economic performance. It has Mr. Obama projected to win by a smaller margin, 3.1 percentage points.

All of this leaves us in something of a waiting game. For the next week or two, we’re mostly going to be watching to see whether Mr. Obama’s numbers hold in their current position as memories of the conventions fade. If they do, that would qualify as a positive for him by the model’s logic, since it would then be safer to assume that the gains he made were permanent rather than temporary.

But these forecasts are published each day, and so it’s our duty to also give you our best estimates in real time about how things will eventually play out.

Right now, the best guess is that Mr. Obama will emerge with something like a 3-point national lead once the noise from the conventions dies down — meaning that he gained a point or so during this period, since he led by about two points before the conventions.

Assuming that Mr. Obama holds some sort of lead a week or two from today — whether it’s one point, three points, or five points — a lot of our focus will then be on watching Mr. Romney’s clock.

Each day that Mr. Romney fails to make gains in the polls will count as an opportunity lost for him. And with each passing day, the model will become slightly more confident that a small lead in the polls will translate into an Electoral College victory for Mr. Obama, since the error in the polls becomes smaller as we get closer to Nov. 6.

It’s also worth tracking the number of undecided voters remaining in the race. The model assumes that overall uncertainty in the forecast is a function of the number of undecideds, in addition to the time left until Election Day.

At the same time, I would urge some caution if you come across analyses that take the form: “No candidate has won when trailing in the polls by X amount as of Y date, subject to conditions P and Q”.

These analyses may convey something of the right spirit, in that they emphasize that the polls have a history of being pretty accurate after Labor Day and the conventions. But they do it with much more specificity than is warranted. There is no magic date when polls go from being inaccurate to accurate, and no exact threshold at which a lead in the polls goes from being surmountable to insurmountable.

Rather, it all exists along a probabilistic spectrum, with a candidate’s chance of winning primarily a function of the size of his lead, the time remaining until Election Day and the number of undecideds left in the electorate.

As to exactly what the probabilities are on any given day — that’s really what the model is trying to figure out. Although forecasting a three-in-four chance of victory for Mr. Obama might seem quite confident given that the race remains close, we think very carefully about how to estimate this uncertainty.

In particular, the model’s estimates of the uncertainty is based in part on the historical performance of models that combine both polling and economic data, as ours does. They are intended to represent a reasonably realistic portrayal of the uncertainties that exist in the real world, rather than the uncertainty conditional upon a number of assumptions being true.

We deliberately add some uncertainty to the presidential forecast, as compared with the model’s internal calculations of it, because statistical models based on a small number of data points — in this case, the eleven presidential elections since 1968, which is when the polling data becomes more robust — tend to underestimate real-world uncertainties because of a problem known as “overfitting.”

This is much less of a problem for something like Senate races, because the historical data is much more robust: about 35 races contested once every other year, as opposed to just one every four years.

Although Senate races are not completely independent from one another — there are cycles, like 1994, 2006 or 2010, in which most of the close races tend to break in the same direction — we are nevertheless much closer to knowing exactly how much uncertainty there is, in the sense that we might know exactly what a baseball team’s probability of winning is given that leads by a given number of runs with a given number of innings left to play.

In presidential forecasting, by contrast, there is a considerable amount of uncertainty about exactly how much uncertainty there is. Thus, it shouldn’t be surprising that various formal and informal means of estimating it come up with different numbers.

Interestingly enough, however, we’re seeing more of a consensus between the FiveThirtyEight model — where Mr. Obama’s win probability has fallen over the past several days — and at bookmakers and betting markets, where it has continued to

The average bookmaker now makes Mr. Obama about a 75 percent favorite to win re-election, almost exactly as the FiveThirtyEight forecast now does.

Mr. Obama’s odds of victory are 72 percent at the betting market Betfair, although they are lower than that, 66 percent, at another betting market, Intrade. (I have no idea why the Betfair and Intrade estimates diverge so much, which shouldn’t happen if the markets are reasonably efficient.)

One last question to consider is whether there is less uncertainty in the presidential race because the polls have been very steady throughout the election cycle. This is a reasonably intuitive hypothesis: if voters are locked in and the numbers are hard to move, that makes a small lead more likely to hold up.

The FiveThirtyEight forecast compromises on this hypothesis somewhat. The model allows for the possibility of a “uniform swing” that would affect the vote in about the same way in all states, but the magnitude of the potential swing is calculated solely as a function of the number of undecideds in the race and the remaining number of days until the election, and not past volatility in the polls.

However, the model also provides for the possibility that there will be variance in the outcome at the state level, independent of the national trend. We do assume — since this shows up quite clearly in the historical state-level data — that we are better able to peg the relative position of states in which the polling data has been more consistent. They are less likely to veer off in their own direction in a surprising way, independently of the national trends.

Whatever assumptions that you eventually make, it is these kind of questions that should be most pertinent to you if you are actually considering placing a bet on Mr. Obama or Mr. Romney. And they are intrinsically difficult questions given the paucity of data in presidential elections.

Personally, if I were actually making bets in these markets (I don’t), I’d first be looking toward cases where the amount of uncertainly is a little more knowable. For example, as of late Sunday night, Intrade gave Representative Connie Mack of Florida, the Republican candidate for Senate, a 30 percent chance of winning the seat.

That’s an unjustifiably high number, given that Mr. Mack’s opponent, Senator Bill Nelson, holds a lead of about eight points in the polling average. If you go back to past Senate races and look up the dozens and dozens of cases where a candidate trailed by about eight points a month and a half before the election, you’ll find that they came back to win nowhere near 30 percent of the time; somewhere in the ballpark of 10 percent is a more realistic estimate of Mr. Mack’s chances.

But, again, we don’t have that luxury for presidential elections, particularly when it comes to estimating the uncertainty in the national popular vote. Instead, we’re making inferences about it based on a mere handful of cases.

That doesn’t mean that all inferences are equally good, or that all assumptions are equally valid. And there is almost certainly a lot of value in trying to come up with some mathematical way to estimate the uncertainty. In politics and other fields, our off-the-cuff estimates of uncertainty are routinely quite terrible, and line up poorly with the objective probabilities in cases where they have been tested.

Under different conditions, we may either overestimate or underestimate the amount of uncertainty in a prediction — or even oscillate back and forth between these, never getting the answer quite right.

Before the conventions, the presidential race was routinely described with formulations like “tossup” or “too close to call” or “could go either way”. Personally, I prefer to use those phrases when the probabilities really are quite close to 50-50. I don’t think they were appropriate in the presidential race this year, when Mr. Obama held a small but quite persistent lead that made him the favorite.

Now, however, we seem to have gone full circle, with some news organizations already writing obituaries for Mr. Romney’s campaign:

Romney adviser Stuart Stevens “has become the leading staff scapegoat for a campaign that suddenly is behind in a race that had been expected to stay neck and neck through Nov. 6.”

I would see a little more justification for that if Mr. Obama had continued to hold at something like a six-point lead in the national race after this convention, as seemed possible when he was getting some very strong numbers in the polls early last week. To a slightly lesser extent, I’d see a justification for it if Mr. Obama’s numbers hold at their present levels for another two weeks or so.

For the time being, however, Mr. Obama’s bounce seems to have tapered off a bit, and it may taper off somewhat further, so I’m not sure there’s all that much news. Mr. Romney has gone from a modest underdog in the presidential race to a modestly larger underdog, which isn’t good news for him. However, it isn’t a particularly sudden or night-and-day difference. Whatever problems he is having convincing voters about his candidacy, they are probably mostly the same ones that he has had all year. But the race is not over, by any means.

Nate Silver founded and was the editor in chief of FiveThirtyEight.


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