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Approval Ratings and Re-Election Odds

Earlier this month, we posted the simple version of a finding, based on the historical record, that is worth keeping in mind when you read articles about how Barack Obama’s presidency has (or has not been) been revitalized: It’s just too soon for his approval ratings to tell us very much about his re-election prospects for 2012.

This is an overdue follow-up to that article — what you might think of as the slightly-more-complicated version.

While it’s true that approval ratings aren’t of much use now, it’s also the case that, by the time we get close to the election, they will have become a very reliable predictor of Mr. Obama’s chances of winning another term.

Based on Gallup polling, here is what I estimate that the incumbent president’s approval rating was on Election Day in almost every election since 1940. (There is no data for 1944 because Gallup went on wartime hiatus.) There are a few tricks I had to employ to derive these numbers; I’d ask you to take them on faith for a few moments, and then we’ll explain everything later on.

At first glance, the relationship seems nearly perfect: every incumbent with an approval rating of 49 percent or higher won re-election, while every candidate with a rating of 48 percent or lower lost.

In practice, things probably don’t work quite that crisply. For example, Harry Truman, whom we estimate had a 50 percent approval rating on Election Day 1948, won by 4.5 points, and 114 electoral votes, over Thomas E. Dewey, which suggests that he had some margin to spare. And candidate quality clearly makes a difference. Although Robert Dole is sometimes considered a weak Republican nominee, Bill Clinton beat him in 1996 by just 8.5 points, despite Mr. Clinton’s 55 percent approval rating. By contrast, in 1972, Richard Nixon, with an approval rating only a couple of points higher (57 percent), trounced a very weak Democratic nominee, George McGovern, by more than 23 points.

Still, the approval rating at which an incumbent candidate goes from being an underdog to a favorite for re-election is somewhere in the high 40s.

The reason the threshold is probably slightly below 50 percent rather than right at 50 percent is that in any approval survey, some people (typically 5 to 10 percent) say they are undecided about the president’s performance. For instance, at this writing, Barack Obama’s Gallup approval rating is 49 percent but his disapproval rating is just 42 percent, a net margin of +7. If those were the figures on Election Day, he would be a favorite to win unless nearly everybody who was undecided about his performance cast their ballots against him, something that is possible in theory but usually doesn’t occur in practice.

Now, then, how did we come up with these numbers? As I said, it’s not quite so straightforward.

Gallup has approval ratings data going back to 1937. The problem is that, until fairly recently, they had a habit of stopping their approval ratings polling several months before a presidential election. For instance, in 1956, their last poll of Dwight Eisenhower’s public approval was in early August; they did not survey him again until late November, after he had already defeated Adlai Stevenson.

However, we can extrapolate what Mr. Eisenhower’s rating would have been on Election Day 1956 by drawing a smoothed regression line — known in the business as a Loess curve — using the data points before and after that date. The one hitch is that incumbent presidents, whether they win, lose, or don’t run at all, almost always receive a “bounce” in their approval rating after the election, as people either rally around a winner or feel sympathy for the lame duck. The average magnitude of this post-election bounce is 4 points. So, before I fitted the curves, I subtracted 4 points from approval rating polls conducted after Election Day.

By applying this process of bounce-adjustment and curve-fitting, we are able to estimate an incumbent president’s Gallup approval rating on Election Day itself or on any day before it, as shown in this nifty-looking graphic:

I haven’t labeled the curves by the candidate’s name in the chart, because that which create too much clutter. But I have distinguished those who eventually won re-election (blue lines) from those who lost (red).

A couple of cases are worth attention. The red line that you see briefly extending above 80 percent is for George H.W. Bush. His approval ratings, which were already pretty good, shot up following the start of Operation Desert Storm in 1991, when American-led forces drove Iraqi troops back from their occupation of Kuwait. Politically, that made Mr. Bush look like an extremely formidable candidate for re-election: Saturday Night Live ran a sketch later that year entitled “Campaign ’92: The Race To Avoid Being The Guy Who Loses To Bush,” with Democratic candidates at a debate all trying to lose so they would not have to run against him. But Mr. Bush’s approval ratings fell precipitously throughout late 1991 and early 1992, and were below 40 percent by Election Day.

If Mr. Bush is the precedent that challengers will cite when their campaign seems to be flailing, the opposite example is the original Comeback Kid, Harry Truman. He’s the blue line that you still see down around 40 percent approval with just five months to go before the election of 1948.

It’s hard to know exactly where Mr. Truman’s approval numbers were on Election Day. When Gallup surveyed in late June, he had just 39 percent approval; in January, 1949, after he had beaten Thomas E. Dewey, he was up to 69 percent; and then he reverted back to 50 percent just a couple months later. Our Loess curve estimates that Mr. Truman’s approval rating was probably around 50 percent on Election Day, but this is just a guess. What’s clear is that Mr. Truman was at some point an extremely unpopular president, and he nevertheless — to the great surprise of the Chicago Daily Tribune — defeated Mr. Dewey.

Another thing to take from the graphic is how the red and blue lines gradually untangle themselves as the relationship between approval ratings and re-election becomes stronger over time. We can see this a bit more clearly by taking the average approval rating for the 8 winning candidates and the 3 losing ones and tracking them over the two years leading up to the election:

I would resist the idea that there is any one magical date when approval ratings go from meaningless to meaningful as predictors of re-election. In the chart, the first time the winners and the losers begin to separate themselves is about 19 months before the election — which would correspond roughly to March of the prior year — but the split would have come a bit earlier if not for Mr. Bush’s Gulf War bounce. There’s also increasing differentiation in the period roughly 10 to 5 months before the election, corresponding with primary season. Still, for the most part, the separation occurs gradually.

I’ve also tried to play around with various sorts of logistic regression models that attempt to predict a president’s chances at re-election based solely on his Gallup approval rating and the number of days until the election. Don’t take this terribly seriously — it’s hard to do anything very rigorous based on so few data points (just 11 presidents in the sample), and I can imagine better model designs than the one that I’ve used. But it does yield some ballpark estimates of what this data implies.

For example, a year in advance of the election, the model figures that a president with a 60 percent approval rating is about 90 percent likely to win re-election, whereas a 40 percent rating translates into a win probability of a bit below 40 percent. So by that point the differences have become fairly meaningful:

What does this mean for Barack Obama? Right now, we’re still in the period where the most useful number for estimating his re-election chances is not his approval rating but rather the historical track record of incumbent presidents. As I wrote on Wednesday, since the Civil War, 73 percent of incumbent presidents who sought another term won, as have 70 percent since World War II. Plugging Mr. Obama’s current numbers into the regression model that I described above yields a 65 percent likelihood of re-election — but again, this is a really rough guess, based mostly on the high historical batting average for incumbents rather than anything to do with Mr. Obama himself.

What we can say is important is the range in which Mr. Obama’s approval ratings have been varying in recent months: between about 45 and about 50 percent. If Mr. Obama’s approval rating is at the top of that range, 50 percent, on Nov. 6, 2012 — about where it is now — the model figures that his chances of winning re-election will be greater than 80 percent. But if his approval rating is at the bottom of the range instead, at 45 percent, his chances for a second term will be only about one in three, and he’ll have to hope that the Republican nominee is a weak one.

Much will change between now and then, of course. But Mr. Obama would probably win an election held next Tuesday — and that would not have been true a couple of months ago.

Nate Silver is the founder and editor in chief of FiveThirtyEight.