In South Dakota, Only the Farm Trumps Conservatism

With no major city, few minorities and few union members, South Dakota is rough terrain for Democratic presidential candidates. The last Democrat to carry the state was Lyndon Johnson in 1964.

Aug. 23: Seven Ways to Evaluate a Poll

By NATE SILVER

Each night before I run our presidential forecast model, I make a guess at what it will say based on my impressionistic take on the data from that day.

I figured that Thursday would be something of a push. Barack Obama held the lead in a number of state polls. But the numbers were not necessarily better for him than the prior renditions of the same surveys. Also, Mitt Romney got a strong number in the Fox News national survey - and the stock market declined fairly significantly, which lowered the model's economic index.

The conclusion of the model was less equivocal. It evaluated the state polls as being quite strong for Mr. Obama, and they outweighed the other factors. His chances of winning the Electoral College rose to 68.6 percent in the forecast from 66.7 percent on Wednesday.

Mr. Obama saw the most improvement to his forecast in Ohio, where his winning chances improved to 70 percent from 64 percent. In that s tate, there was a new survey from Quinnipiac, which was conducted in conjunction with the New York Times and CBS News. It gave Mr. Obama a 6-point lead there. There was also a survey from the University of Cincinnati, which put him ahead by three points.

Let's focus on that Quinnipiac poll, however. It showed Mr. Obama with a six-point lead. But Mr. Obama had a lead by the same margin in its July poll. So why does the model evaluate it as a significant positive for him?

The reason is that looking at changes in poll numbers is a useful habit, but hardly the only comparison you should be making.

Instead, there are at least seven ways that you might evaluate a poll as being strong or weak for a candidate. In the case of the Ohio poll, the comparison to the July survey showed no net change toward either candidate - but the poll was nevertheless strong for Mr. Obama by several of these measures.

1. How does the poll compare to other recent surveys of the s tate? This is a simple one, and in the Quinnipiac poll, this comparison was favorable for Mr. Obama. He led by six points, better than his average lead of one point in the other Ohio surveys conducted so far in August.

2. How does the poll compare to the polling firm's previous surveys in the state? Note my usage of the plural, surveys. You should be looking at how a new poll compares to the prior one that a survey firm released in a state - but also in comparison to its entire body of work there.

For example, suppose that a polling firm conducts a survey of Virginia every month. In February, March, April, May and June, the survey shows a small but consistent lead for Mr. Romney of between one and three percentage points.

Then, suddenly, Mr. Romney's lead increases to 10 points in the July poll.

What would qualify as a good number for Mr. Romney when the firm releases its August survey?

If the August poll put Mr. Romney eight points ahead, that would still count as a very strong number for him. It's down a bit from the July poll, but much better than he'd gotten in the other months of the year.

When a poll initially appears to be an outlier, you should expect there to be some reversion to the mean the next time the firm takes the temperature of the state. In these cases, just holding steady in a poll can count as a big “win” for a candidate, since what once looked like an outlier now looks like more of a trend. Even falling by a point or two can be a pretty decent result under some circumstances.

The July Quinnipiac poll in Ohio, which gave Mr. Obama a six-point lead, was not quite an outlier; Mr. Obama has periodically gotten numbers like that in Ohio throughout the campaign. Still, it was better for Mr. Obama than the surveys that Quinnipiac had conducted in Ohio prior to July, which put him up by an average of three points. (Moreover, the polls Quinnipiac conducted prior to July had been conduct ed among registered voters rather than likely voters. Usually, the shift to likely voters harms the Democratic candidate - but in this poll Mr. Obama's numbers have improved instead.)

3. How does the survey compare with the polling firm's surveys in other states? A related question is whether the polling has a strong “house effect.” That is, does it consistently show greater numbers for a particular candidate, no matter where it polls? If so, then it's not really a big deal when it ventures into a new state and print another one.

Or, does it show strong numbers for a candidate in some states, but not others? This is more of the case with Quinnipiac. It has had good numbers for Mr. Obama in Ohio, Florida and Pennsylvania recently - but not as much in the other swing states that it polls, or in noncompetitive states like New York or in its national surveys. In fact, the model calculates Quinnipiac's house effect as being just a tiny bit Republican-leaning on ba lance. That makes its poll showing a solid lead for Mr. Obama in Ohio more meaningful.

4. How does the poll compare with the national trend? This is the trickiest of the seven concepts, but one of the more important ones. When comparing a poll with prior surveys of the state, it's important to look at exactly when each survey was conducted, and what the national environment looked like at the time.

Say a polling firm comes out with a new survey in Michigan, showing Mr. Obama seven points ahead there. The firm's lone prior poll of the state had been in February, when it also had Mr. Obama seven points up.

This would count as a favorable development for Mr. Obama. Why? Because February was a very strong month for Mr. Obama in the polls. (At the time, Mr. Romney's numbers were really suffering because of his problems in the Republican primaries.) You'd have anticipated some decline for Mr. Obama since then; if his numbers held steady instead, that would defy your expectations and would be a constitute a positive sign for him.

Likewise, the last couple weeks have shown stronger numbers for Mr. Romney than he got in July. (Perhaps this was because of a small bounce for Mr. Romney following the selection of Representative Paul D. Ryan as his running mate.) That is priced into the model at this point. When a new survey comes out, its expectation is that the numbers will be a point or so stronger for Mr. Romney than they were a month ago - and it will be disappointed in Mr. Romney if he does not match them.

The state polls that Mr. Romney got on Thursday were not terrible by any means. But they looked more like the numbers we were seeing in June and July - when Mr. Obama led in the vast majority of swing state polls - and less like what we were seeing over the past few weeks, when Mr. Romney was leading in almost half of the polls in states like these.

A side note: Be careful of making comparisons to polls conducted immediately after the party conventions, when the candidates can experience significant (but short-lived) bounces. Say that Mr. Romney holds a seven-point lead in a North Carolina poll conducted in the immediate aftermath of next week's Republican National Convention, a time when Mr. Romney might be enjoying a significant bounce in the polls. The polling firm surveys the state again in late September, and Mr. Romney's lead is down to one point.

When something like this happens, you'll see blogs with headlines like “Romney Collapsing in North Carolina!” You should avoid taking these very seriously. All that happened is that you are comparing a poll conducted in the midst of Mr. Romney's convention bounce to one that wasn't. It is unlikely that the change tells you anything about North Carolina in particular.

5. How does the poll compare with the historical trend in a state? A state poll can be used to make an inference about where the national race stands. Oh io, for example, is typically very slightly Republican-leaning relative to the country as a whole. So when Mr. Obama gets a poll showing him 6 points ahead there, that speaks favorably to his position in the national race.

A related point is that the states often revert to the mean over the course of an election cycle. If a candidate seems to be overperforming in a particular state - as Mr. Obama has been in Ohio - there can be downward pressure on his numbers as the state's partisan gravity kicks in.

Our forecast model accounts for this property. It is designed to be a little skeptical that, for instance, Mr. Obama is actually leading by a larger margin in Ohio (by about three points in the polls) than in the national numbers (where he leads by about two points). However, the longer a candidate is able to defy gravity, the more confidence we might have that there is something different about the state this year.

6. How does the poll relate to the electora l calendar? Any time that a candidate is leading in a state, and he simply maintains that lead, that counts as a modest positive for him because time is running off his opponent's clock. A three-point deficit in April is very easy to overcome. In August? Still plenty of time, but there's room for a touch of concern. On election eve? Oops - it's probably too late.

There's no need for Mr. Romney to panic yet, especially since he has gotten his share of decent state polls recently. But if Mr. Obama still holds a three-point lead in Ohio after the party conventions, it's going to qualify as a negative for Mr. Romney every time that he fails to reduce the gap.

7. How does the number of undecided voters compare with prior renditions of the survey? In general, I focus on the margin between the candidates (“Mr. Obama's up by three points”) rather than their absolute numbers (“Mr. Obama 47 percent, Mr. Romney 44 percent”), or the number of undecided voters in the state.

This is partly because there are a lot of myths about how undecided voters behave, and I don't want to encourage those.

But the main reason is that, just as there are house effects related to whether a polling firm leans Republican or Democratic, different polling firms also consistently show more or fewer undecided voters, depending on how much the survey questions “push” voters toward a candidate choice. Our model actually adjusts for this, but it's something that can escape your attention unless you're being super detail-oriented.

Nevertheless, there is some useful information in the number of undecided voters in a race - especially when you are making comparisons to the prior editions of the same survey.

As a rule, the fewer undecided voters in a state, the less uncertainty there is about the eventual outcome. Thus, the candidate who is leading in a state should be pleased when the number of undecided voters falls, as this can make a s mall lead more robust. A 49-47 deficit is harder to overcome than 45-43, even though the margin between the candidates is two points in each instance.

***

Isn't this an awful lot to keep track of? It certainly is, and that's why a computer program can come in handy. The model can and does evaluate all this context when it considers a poll, and sometimes it concludes that a set of survey results are stronger or weaker for a candidate than they might appear on the surface.

Then again, the story of Thursday's polls wasn't all that complicated: Mr. Obama held leads in all six of the polls released of voters in Ohio, Florida, Pennsylvania, Wisconsin and Michigan - and Mr. Romney will need to win at least two of those states, and possibly three, to have much of a chance in the Electoral College. Mr. Romney has had some strong polling days recently, but this was not one of his better ones.

Republican Voters Could Sit Out Missouri Senate Race

By NATE SILVER

So far, we've had two polls of the Missouri Senate race since Representative Todd Akin made his remarks about rape on Sunday. The first survey, conducted by Public Policy Polling on Monday night, had Mr. Akin holding onto a one-point advantage in the race. But a second poll, conducted Wednesday night by Rasmussen Reports, had his opponent, the Democratic incumbent Claire McCaskill, up by 10 percentage points instead.

My view is that the Rasmussen Reports poll represents a more-realistic portrayal of the race as it stands now. It postdates the Public Policy Polling survey by 48 hours: potentially relevant as many Republicans denounced Mr. Akin and tried to coax him out of the race on Tuesday and Wednesday.

And the news of Mr. Akin's interview on Sunday may have taken some time to sink in with voters. Not every Missourian follows the habits of the typical Beltway reporter, checking Twitter every few minutes and reacting in stantaneously to each news event. There is reasonably sound empirical evidence that controversies of this magnitude can be quite harmful to candidates in the end.

There was one element, however, that the polls had in common. Both showed a large number of Republicans who were not willing to declare their support for either Mr. Akin or Ms. McCaskill.

In the Rasmussen Reports poll, 13 percent of Republican voters said they planned to vote for “some other candidate.” Another 8 percent said they weren't sure whom to support.

By contrast, just 1 percent of Democrats said they weren't sure whom they'd vote for, and almost none preferred a third-party option. Instead, 96 percent said they'd vote for Ms. McCaskill.

The Public Policy Polling survey did not provide a third-party option, but an unusually high fraction of their Republican respondents - 19 percent - said they were undecided in the race. Just 4 percent of Democratic voters did the same.

What's going to happen to these Republicans? That may determine whether Mr. Akin still has a shot of winning.

The most optimistic interpretation for Republicans is that some of these voters will grudgingly vote for Mr. Akin in the end. Perhaps, even, the high number of undecided Republicans reflects social desirability bias. (Some of these Republicans are prepared to cast a ballot for Mr. Akin, but they're not willing to tell a pollster that when it might be politically incorrect to do so.)

However, both the Public Policy Polling and the Rasmussen Reports polls were automated surveys: voters were pushing buttons on their phones rather than talking to another human being. Although automated surveys can introduce other problems, reducing social desirability bias may be one of their benefits, since voters may feel as though their answers are more anonymous.

So it's important to keep in mind that these undecided Republicans do have so me other options. They don't have to pick between two unacceptable alternatives if they don't want to.

First, there is, in fact, a third candidate on the Missouri ballot: Jonathan Dine of the Libertarian Party.

Second, Republicans could deliberately undervote the Senate race, skipping it while voting for the presidency and other contests.

Or third, they could simply not turn out to vote at all. In polls, “I'm undecided” can sometimes be code for “I'm sitting this one out.”

Reduced Republican turnout would hurt Mitt Romney in Missouri, but I don't think this should be a major concern for Republicans. He holds a large enough lead there to have some cushion in the event of reduced turnout. And although he could lose the state, it would probably be only in cases where he was having problems elsewhere on the map, and President Obama was already well on his way to 270 electoral votes and a second term.

The Senate race is another matter.

The parade of Republicans who denounced Mr. Akin were making a sensible move, in the hope that they might persuade him to abandon the race, or failing that, to minimize the damage to the national Republican brand.

But when high-profile Republican leaders from Mr. Romney to Sean Hannity conveyed the idea that Mr. Akin was an unacceptable choice, Republican voters may have gotten the message. It seems unlikely that many of them will vote for Ms. McCaskill. But if 20 percent of Republicans vote Libertarian instead, or just skip the race, she'll be a heavy favorite.

Aug. 22: Keeping Score on a Busy Polling Day

By NATE SILVER

Wednesday was among the busiest polling days of the year; we added 14 new surveys to our database, including some from rarely polled states like Montana and New Mexico.

Although the pace of polling still lags well behind that of 2008, we're going to start seeing days like this more often once we get past the party conventions. The simplest way to keep track of things on a day like this is probably just as follows. Sort the polls into three piles: those that showed better numbers for Mitt Romney than our previous impression of a state did; those that showed better numbers for President Obama; and those where the poll was pretty much in line with what we understood about the state already.

There were a few polls in each category on Wednesday.

Good Polls for Mitt Romney

An Associated Press poll showed President Obama with a one-point lead in the national race, but, really, this is a better poll for Mr. Romney than for Mr. Obama. The Associated Press's previous polls had shown a larger advantage for Mr. Obama - by three points, for instance, in their survey in June. And the poll was conducted among registered rather than likely voters, which typically underestimate the standing of Republican candidates by about two percentage points.

A poll from Gravis Marketing gave Mr. Romney a small lead in Florida: by two points if the Libertarian candidate Gary Johnson is listed as an option, and by three points if he isn't. I don't know much about the polling firm, which also released a poll showing Mr. Romney up in Colorado earlier this week. But it conducts automated surveys (“robopolls”), and typically those are a bit Republican-leaning - partly because they exclude voters relying on their cellphones, who fall into more Democratic demographics. Still, this is the fourth poll out of four to show Mr. Romney with a lead in Florida since Representative Paul D. Ryan was selected as his running mate. All of those were automated surveys; The New York Times, CBS News and Quinnipiac University will be releasing a live-telephone poll of Florida tomorrow.

A poll from Rasmussen Reports gave Mr. Romney a huge, 17-point lead in Montana, a state that sometimes was described as a swing state in 2008 but that has had little attention from the campaigns and the pollsters this year. It certainly does not look like a place where Mr. Obama is going to make any headway, although it deserves more polling with the competitive Senate race there.

Polls in Line With Expectations

A Marquette University poll of Wisconsin gave Mr. Obama a three-point lead among likely voters. This survey is something of a wash: it has the race tightening from a five-point lead for Mr. Obama previously. But it still has him ahead in the state, and the gain for Mr. Romney is pretty consistent with other polls to show a “bounce” in Wisconsin since his pick of Mr. Ryan. Our forecast now gives Mr. Romney a 29 percent chance of winning Wisconsin, up considerably from before his vice-presidential selection, when those chances had fallen below 15 percent.

There were two new polls of Nevada - one from SurveyUSA, which gave Mr. Obama a two-point lead, and another from the Democratic polling firm Garin Hart Yang, which has him up by five. SurveyUSA has generally shown decent results in other states for Mr. Obama, and you'd naturally expect Garin Hart Yang to show pretty good numbers for him as well. Still, all 11 polls of Nevada in our database have shown Mr. Obama with a lead there, and Mr. Romney's electoral calculus is more complicated so long as its six electoral votes remain in the “lean Democrat” column.

Good Polls for President Obama

A Rasmussen Reports poll of New Mexico gives Mr. Obama a 14-point lead there. This is the fir st poll of any kind in New Mexico in about a month. The prior Rasmussen Reports poll of New Mexico had also given Mr. Obama a big lead there - 16 points - but it was conducted in April, when Mr. Obama's numbers had been stronger across the board. New Mexico just does not look like a competitive state this year; our model estimates that Mr. Romney is no more likely to win it than New Jersey.

A poll of Georgia from the firm 20/20 Insight LLC shows a surprisingly tight race there, with Mr. Obama trailing Mr. Romney by just three points among likely voters. Since this is the first horse-race poll that the firm has released in Georgia or any other state so far this year, it is hard to put the survey in context, and the model is designed to treat polls skeptically under those conditions; it gives Mr. Obama only about a 3 percent chance of winning Georgia in November. But the state is another that could use more polling; this is the first Georgia poll of any kind since May .

So Wednesday was not a knockout polling day for either of the candidates. The New Mexico poll was good for Mr. Obama, but he had already been heavily favored to win there. The Florida poll had a good headline number for Mr. Romney, but we're not lacking for robopolls that came to the same conclusion, and a number of polls of middling quality aren't necessarily the best substitute for a good one. The Georgia poll had a better-than-expected result for Mr. Obama and the Montana poll a worse-than-expected one, but neither state is very important in the electoral calculus.

That leaves the Associated Press national poll as the standout number of the day, showing a positive trend for Mr. Romney. The forecast model now gives Mr. Romney almost exactly a one-in-three chance (33.3 percent) of winning the Electoral College. That is little changed from Tuesday, but it nevertheless is his highest figure in our Electoral College forecast since July 29 and is con sistent with a trend toward improved polling for Mr. Romney of late.

Aug. 21: Romney Showing Improved Results in Swing State Polls

By NATE SILVER

We can get pretty detail-oriented in our analysis of the polls here at FiveThirtyEight. But sometimes there is also value in applying a simpler approach.

One simple thing I've noticed is this: Mitt Romney has held the lead recently in quite a few swing state polls. That wasn't the case in June or July, when Barack Obama held leads in those polls far more often than Mr. Romney did.

Right now, our forecast model classifies the 10 most important states in the Electoral College as follows, and in the following order: Ohio, Virginia, Wisconsin, Colorado, Pennsylvania, Florida, Iowa, Nevada, New Hampshire and North Carolina.

If you simply count the scientific polls that have been conducted in those states since Aug. 1, Mr. Obama has led in 13 of them, Mr. Romney has led in 11, and there have been two exact ties.

This marks a contrast from June and July, when Mr. Obama held leads in polls of the top 10 states about four times as often as Mr. Romney did.

If you read the fine print on the polls, then things don't look quite as good for Mr. Romney. In the polls where Mr. Obama has held a lead, it has generally been by a somewhat larger margin than when Mr. Romney does. And the polling firms that have been most active in the states recently have been a bit Republican-leaning on balance - and a few of the polls have been outright weird.

It's also plausible that this is partially a statistical fluke, since we really haven't gotten all that much data. So far in August, we've logged 35 state polls in our database, counting both swing states and noncompetitive ones. That puts us well behind the pace from four years ago, when there were more than one hundred state polls conducted in the month of August.

But our forecasting model, which makes an effort to account for these sorts of factors, nevertheless finds that Mr. Romney has made up some distance in the swing states.

A few weeks ago, we were starting to see a gap between the popular vote and the Electoral College. Generally speaking, our model was giving Mr. Obama about a two-in-three chance (67 percent) of winning the popular vote, but slightly better than a 70 percent chance of winning the Electoral College.

Now? Our popular vote forecast really hasn't changed very much. As of Tuesday night, our model gave Mr. Obama a 66.9 percent chance of winning the popular vote.

But the gap between the Electoral College and the popular vote has pretty much dissipated. Mr. Obama was given a 67 percent chance of winning the Electoral College in Tuesday's model - almost exactly the same odds as in the popular vote forecast.

Perhaps a more important qualification is that many of these polls were conducted shortly after Mr. Romney named Representative Paul D. Ryan as his running ma de. Candidates typically get a temporary bounce in the polls after naming their vice-presidential nominee, but it usually dissipates soon and their polling may be slightly inflated in the interim. This is not something that our model adjusts for.

Even so, I don't think we should totally write off the idea that Mr. Romney has made up some ground in the swing states. Apart from his selection of Mr. Ryan, there are other things going on in the campaign. For example, Mr. Romney's advertising advantage in swing states could be starting to pay dividends.

In Missouri\'s Move to the Right, a Question of How Far

By MICAH COHEN

We continue our Presidential Geography series, a one-by-one examination of the peculiarities that drive the politics in all 50 states and the District of Columbia. Here, a look at Missouri, the Show Me State. FiveThirtyEight spoke with David Robertson, a professor in the political science department at the University of Missouri-St. Louis, and Brian R. Calfano, an associate professor of political science at Missouri State University.

Like the Four Corners Monument - which sits at the intersection of four states - Missouri sits at a regional crossroads.

Depending on your perspective, Missouri is either the southernmost northern state, it reaches farther south than any state in the Midwest, or the northernmost southern state, it was a slave state in the 1850s.

Missouri is also where the eastern United States meets the frontier West.

Missouri “has the western most industrial city and the eastern most cowtown, ” Mr. Robertson said.

For nearly a century of presidential elections, Missouri lived up to its regional representativeness, backing every winning presidential candidate but one from 1904 through 2004. But beginning in 1996, Missouri's bellwether status began to show cracks. The state began to consistently vote more Republican than the nation, and in 2008, Missouri backed the Electoral College runner-up. It was the only battleground state carried by Senator John McCain.

In this year's race, despite the slight edge that President Obama has nationally according to the current FiveThirtyEight forecast, Mitt Romney seems a solid favorite in Missouri. Instead, the state's United States Senate contest, which was thrust into the news this week because of the Republican candidate Todd Akin's statement on rape and abortion, may provide a better test of just how far Missouri has moved to the right, a shift caused by a number of factors.

First, white, culturally conservative, working-class voters in rural Missouri, following a trend (PDF) evident in Deep South states like Georgia, began leaving the Democratic Party. The exodus was slower and more subtle in Missouri than in the Deep South, Mr. Calfano said, but it has made a difference.

In Missouri's northern neighbor, Iowa, Democrats still win a fair number of rural counties. But in Missouri, the farming counties in the north and the relatively poor southeast, around the boot heel, now reliably vote Republican.

Rural “counties that voted for Bill Clinton probably aren't going to vote for a Democrat for a good number of years to come,” Mr. Robertson said.

In addition to the Republican rise in rural Missouri, the state has also been moved to the right by population growth in its traditional Republican strongholds, which have been gaining population at a faster rate than Missouri's Democratic-leaning areas. Southwestern Missouri, a longti me Republican bastion with a strong evangelical Christian culture, and the suburbs and exurbs of St. Louis, which are home to traditional, more fiscally focused Republicans, have both gained residents (PDF) over the last decade. Missouri's main Democratic vote centers, on the other hand, grew slowly or not at all.

Kansas City and St. Louis are still overwhelmingly Democratic, with large, mostly black minority populations. But Kansas City, Missouri's largest metropolis, grew by just 6 percent (PDF) from 2000 to 2007, and metro St. Louis actually lost 1 percent (PDF) of its population over that period, as many of its residents left for the suburbs.

Thanks partly to retirees settling around Branson, Springfield and the Lake of the Ozarks region, southwestern Missouri grew 9 percent (PDF) from 2000 to 2007. And over the same period, as the city emptied out, the St. Louis suburbs grew by 15 percent (PDF). More votes are now cast in St. Charles County, a heavily Republ ican suburban and exurban county, than in the city of St. Louis.

The Bellwether: Clay County

For an early clue as to how Missouri might vote on Nov. 6, look to Clay County, which includes Kansas City suburbs as well as part of the city itself. Clay County exactly matched the statewide presidential vote in 2008 and 2004. In 2000, it was off by only 2 percentage points.

The Bottom Line

The FiveThirtyEight model currently makes Mr. Romney a 79 percent favorite in Missouri, and the state is not likely to play a decisive role electorally; Missouri is not among FiveThirtyEight's top 15 tipping point states.

Rather, it is the Senate race in Missouri that has received the bulk of political attention, even before Representative Akin - a Republican seeking to unseat the Democratic senator, Claire McCaskill - made his comments on rape and abortion.

So the Senate race may provide a good measurement of Missouri's current political landscape. Missouri's shift to the right is evidenced in the viability of Mr. Akin, a deeply conservative Republican congressman, who was leading Ms. McCaskill in most polls before his comments led to calls for him to withdraw.

Since his comments, however, Mr. Akin's advantage is more tenuous. A Public Policy Polling survey, taken after the issue became a national debate, shows the race as a tossup. Has Missouri moved far enough to the right to save Mr. Akin?

“While it's safe to say that Missouri is likely a center-right state now,” Mr. Calfano said, “the Akin controversy might be an indicator of an upper bound on how much the state electorate will tolerate right-wing rhetoric.”

In fact, Ms. McCaskill is vulnerable not so much because she is a Democrat - Jay Nixon, Missouri's Democratic governor is expected to win re-election relatively easily - but because she aligned herself so closely with President Obama, who is unpopular there, Mr. Calfano said.

That might be reassuring to Missouri Democrats, who can still win races if they hew to the ideological center. But the fact that Ms. McCaskill's ties with Mr. Obama are such a liability in Missouri shows the steep hill he would have to climb to win the state's 10 electoral votes.

“If Romney is putting money in here and competing for it in October,” Mr. Robertson said, “he's in real big trouble.”

Akin Comments Could Swing Missouri Senate Race

By NATE SILVER

In my review of Senate races last week, I classified Representative Todd Akin of Missouri, who won the Republican primary earlier this month, as a very slight favorite over the Democratic incumbent in the state, Claire McCaskill.

Although some Democrats were pleased that Mr. Akin was the nominee, he nevertheless held a small lead over Ms. McCaskill in the polls, which averaged five percentage points across four surveys conducted in July and August.

But that was before Mr. Akin's controversial remarks about rape in an interview with a St. Louis television station that was broadcast on Sunday morning. The comments, and Mr. Akin's subsequent explanation of them, drew overwhelmingly negative sentiment at social networking platforms, including on Mr. Akin's Facebook page.

No two controversies are alike, and we'll have to wait for polling data to see what impact this has on the race. But based on some loose historical pr ecedents, the remarks could be enough to swing the polls to Ms. McCaskill.

In August 2006, Senator George Allen, then the Republican incumbent in Virginia, was videotaped using the term “macaca” at a rally, which was interpreted by some as a racial epithet against a staff member for his Democratic opponent, James Webb.

The polls quickly shifted against Mr. Allen. He had led by an average of 12 points in the three polls conducted just before his comments. But his lead was whittled down to just two points in the three polls conducted just after the remark, and Mr. Allen eventually lost the race by about 10,000 votes.

Last February, in another instance of apparent racial insensitivity, the Republican candidate Pete Hoekstra of Michigan, a former United States representative, released an attack ad against the Democratic incumbent, Debbie Stabenow, that was deemed offensive by Asian-American groups. Mr. Hoekstra's standing also declined in the polls. He had trailed Ms. Stabenow by an average of eight percentage points in three polls conducted in late 2011, before the ad's release. But the gap averaged 18 points in two polls taken just after the commercial was released, although it has recovered some since.

These episodes in Virginia and Michigan, which produced a net swing of about 10 percentage points in the polls against the candidate involved in the controversy, appear as though they may represent fairly typical cases.

A paper by Nicholas Chad Long of St. Edward's University examined the performance of Senate candidates running for re-election between 1974 and 2008 who were involved in various types of controversy.

Mr. Long identified 21 cases in which the controversy surrounded a public statement the candidate had made. He found that, on average, these candidates received about 5  percent less of the vote than they otherwise would have on Election Day, controlling for other factors. Since most Senate race s are two-way contests, losing five percentage points also implies that the opponent gains five percentage points, meaning that the net swing is equal to 10 points.

If Mr. Akin lost a net of 10 points in the polls to Ms. McCaskill because of the remark, he would be trailing her by five points in surveys rather than leading her by about that margin.

It can be easy to overrate the importance of scandals in the first few days after they occur. Many voters will vote along party lines almost no matter what, and others will decide based on factors like the economy or an incumbent senator's voting record.

Nevertheless, my view is that insensitive comments concerning rape are especially likely to be deemed inexcusable by voters, and that the swing against Mr. Akin could be larger than the average of 10 percentage points from similar events.

Some Republican activists on social media platforms, perhaps going through a similar calculation, are calling on Mr. Aki n to withdraw from the race. An effort to replace a candidate on the ballot would create controversy of its own, potentially including legal challenges. But if the swing against Mr. Akin in the polls is 10 percentage points or more, it might be an avenue Republicans would need to consider if they want to maximize their chances of taking over the seat.