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Rumors of the Democrats’ Demise in the Senate are Slightly Exaggerated

Are Republicans favorites to take back the Senate next year?

For the time being, I’d say so. The simple fact that Democrats have 23 senators up for re-election in 2012 — compared to just 10 for the Republicans — tilts the playing field in the G.O.P.’s favor. And although both parties have had their share of retirement announcements, the Democrats’ — particularly Kent Conrad’s in North Dakota and Jeff Bingaman’s in New Mexico — have tended to come in more vulnerable seats.

But as I’ll aim to demonstrate for you, I don’t think the Republicans are terribly heavy favorites: instead just a wee bit above 50 percent.

By contrast, the political betting market Intrade gives Republicans a 66 percent chance of a takeover, which would require their winning either three seats and the presidency or four seats without it. And the buzz I’ve heard from some strategists — including some Democratic ones — is that the takeover is all but inevitable.

The mistake these strategists are making is in neglecting the degree to which the outcomes in different races are correlated with one another. If Democrats are having a good cycle in 2012 — like they did in 2006 or 2008 — they could win all or almost all of the toss-ups, as well as make inroads into a couple of seats in Republican territory. It’s entirely plausible, in fact, that Democrats could actually gain seats.

Conversely, if Republicans are having a night like the one they did in 2010, Democrats could be in grave trouble. Not only could Republicans win the majority, but it’s within the realm of possibility that they could gain a net of 13 seats, which would allow them to beat any Democratic filibuster in the next Congress.

Right now, we don’t have a good read on the mood of the country. Voters are essentially evenly divided on Barack Obama’s performance — both his approval and disapproval ratings have been hovering in a narrow range between 45 and 50 percent. There aren’t very many generic ballot polls yet, but they also come to a split verdict, with some showing a slight edge for Republicans and others for Democrats.

As the past few election cycles should demonstrate, however, there is no guarantee that voters will continue to be so equivocal. Sentiment might shift fairly dramatically toward one or another party — and the balance of power in the Senate will shift along with it.

Let’s take a technique borrowed from Harry J. Enten, which is to look at the performance of the race ratings issued by the Cook Political Report (probably a better indicator, at this early stage, than what we have of the polling).

I’ve evaluated the performance of the early Cook Political forecasts during the past four election cycles — 2004 through 2010. These were the forecasts they issued in August 2003 (the earliest they have available for that cycle) , April 2005, April 2007 and late March 2009, so about the same point in the cycle that we find ourselves in now.

Cook classifies races along a 7-point spectrum ranging from Solid Democrat to Solid Republican. Races classified as Solid Democrat or Solid Republican have been won by their respective party about 90 percent of the time — that’s not bad, obviously, but it’s not as well as Cook does later in the cycle, when their calls on races they describe as “solid” literally almost never miss. Nobody in April 2007, expected the Democrats to have a chance against the late Ted Stevens in the Alaska senate race, which they eventually won in 2008 after Mr. Stevens was convicted on corruption charges. (The charges were later thrown out, but not until after the election.) Last-minute retirements can also complicate matters.

The races that Cook classified as toss-ups were indeed won by each party about half of the time (seven by Democrats and 10 by Republicans, not a statistically significant difference given the sample size). Things got a little fuzzier in the middle two categories that Cook uses, which are “lean” and “likely.” They called the right winner in 12 of the 13 “lean” races — impressive — but just 20 of the 30 “likely” ones, which supposedly convey a greater degree of certainty. That is almost certainly a fluke of small sample sizes, but at this early stage, it is probably better to lump the “lean” and “likely” races together into the same category, which imply about a 70 percent chance of winning.

Let’s assume, then, that a party is 90 percent likely to win a race that is classified as “solid,” 70 percent likely to win one characterized as “lean” or “likely,” and 50 percent likely to win each toss-up. This allows us to develop a forecast of the number of seats they’re expected to win overall and compare it to the actual results.

In 2004, Republicans did slightly better than expected. Democrats were expected to win 17 or 18 seats based on the Cook forecasts, when instead they won 15. Still, this was a pretty decent performance; other than Tom Daschle in South Dakota (Cook classified the race as Likely Democrat) and John Breaux in Louisiana (who left the Democrats in a bind by retiring after dithering for some months), there were no gigantic surprises.

In 2006, however, almost every competitive race broke one way: in the direction of the Democrats. Not only did Democrats win all of the seats in which they were favored, and four of the five tossups, but they even won four seats (Missouri, Montana, Ohio and Virginia) that Cook had classified as Likely or Solid Republican. Overall — rather than winning about 17 seats as the early forecast implied — Democrats instead won 24.

Democrats did similarly well in 2008, winning all the seats in which they were favored, as well as seven contests that were thought to favor the G.O.P. Overall, they won 20 senate races that year, rather than 13 or 14, which would have been in accordance with early expectations.

But Republicans turned the tables in 2010, winning all 14 races in which they were favored, six of the seven toss-ups, and four races where Democrats had seemed to have the edge. Overall, they won 24 contests on election night, when the early forecast would have implied about 18 instead. (This does not count Scott Brown’s win in Massachusetts earlier in the year, by the way, which would be another notch on their belt.)

Get the picture? It’s not that the Cook forecasts do badly — frankly I’m amazed that they do as well as this so early in the cycle. In any given year, however, the errors are likely to be highly correlated with one another — all or most of the misses will be on the same side.

Now let’s consider what this means in the context of 2012. Here’s how Cook has the races categorized right now:

I could critique a couple of their individual calls — I think it’s too generous to Republicans to classify New Mexico as a toss-up, despite Mr. Bingaman’s retirement, but too generous to Democrats to say the same for North Dakota. But the overall picture looks about right. The forecast implies that Democrats will win about 19 senate contests next year, which when coupled with the 30 senators they have who are not up for re-election, would give them 49 to the Republicans’ 51. Translation: Republicans are slight favorites to take over the chamber, whether or not they win the presidency.

The issue, however, is that this is an extremely small edge relative to the margin of error. The average expectation is that Democrats will win 49 seats. But the way this forecasting method performed from 2004 through 2010, its margin of error (95 percent confidence interval) is roughly plus-or-minus 12 or 13 seats. In other words, almost anything could happen.

Specifically, assuming that the forecast error is normally distributed (which it probably isn’t exactly, but should be fine for a 30,000-foot overview like this one), this implies there is a 52 percent chance that Republicans will win an outright majority in the Senate, a 41 percent chance that Democrats will retain an outright majority, and a 6 percent chance that things will be split exactly 50:50, with control of the Senate to be determined by the vice president’s vote. That’s how I get to the notion that the G.O.P.’s chances of a takeover are somewhere in the range of 50 to 60 percent, but probably not much more than that.

These numbers also imply that there is about a one in four chance — 25 percent — that Democrats could actually gain seats in the Senate, by winning races like Nevada, Arizona, Massachusetts, Maine or Texas, while holding all or most of their own. There’s also about a 9 percent chance, however, that Republicans will win at least 13 seats, which would give them a supermajority.

It’s quite possible that this method is overestimating the variance somewhat, simply because the last few political cycles have been more volatile than normal. But even if you shave 25 percent off the margin of error, the Republicans’ chances of claiming an outright majority (not counting a 50:50 split) improve only to 53 percent from 52 percent. Even if you cut the error in half, in fact, they improve only to 55 percent. (Also — although this simple model does not account for this — in cycles that are less volatile, the incumbency advantage tends to be more powerful, so Democrats could hang on by the hairs of their chinny-chin-chins provided that they avoid further retirements.)

So breathe easy, Democrats. You’re probably going to lose the Senate. But by “probably,” I mean that in just about the most narrow sense of the term possible.

To a first approximation, in fact, it’s probably better to think of the battle for the 2013 Senate as a toss-up as we await further evidence.

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