When FiveThirtyEight last issued a U.S. Senate forecast — way back in July — we concluded the race for Senate control was a toss-up. That was a little ahead of the conventional wisdom at the time, which characterized the Democrats as vulnerable but more likely than not to retain the chamber.

Our new forecast goes a half-step further: We think the Republicans are now slight favorites to win at least six seats and capture the chamber. The Democrats’ position has deteriorated somewhat since last summer, with President Obama’s approval ratings down to 42 or 43 percent from an average of about 45 percent before. Furthermore, as compared with 2010 or 2012, the GOP has done a better job of recruiting credible candidates, with some exceptions.

As always, we encourage you to read this analysis with some caution. Republicans have great opportunities in a number of states, but only in West Virginia, South Dakota, Montana and Arkansas do we rate the races as clearly leaning their way. Republicans will also have to win at least two toss-up races, perhaps in Alaska, North Carolina or Michigan, or to convert states such as New Hampshire into that category. And they’ll have to avoid taking losses of their own in Georgia and Kentucky, where the fundamentals favor them but recent polls show extremely competitive races.

Since a number of you may be new to FiveThirtyEight, I’m going to go into slightly more detail than usual in explaining how we make these forecasts. You’re welcome to skip past this next section if you’re more interested in the forecasts than in how we came to them.

An overview of our methodology

In contrast to the forecasts we’ll begin issuing sometime this summer, which are strictly algorithmic based on our senate forecast model, these are done by hand. However, they’re based on an assessment of the same basic factors our algorithm uses:

The national environment. The single best measure of the national political environment, in our view, is the generic congressional ballot. Right now, it shows a rough tie between Democrats and Republicans. That stalemate likely reflects voters’ dislike for both Obama and the Republican Party.

A tie on the generic ballot might not sound so bad for Democrats. But it’s a misleading signal, for two reasons. First, most of the generic ballot polls were conducted among registered voters. Those do not reflect the turnout advantage the GOP is likely to have in November. Especially in recent years, Democrats have come to rely on groups such as racial minorities and young voters that turn out much more reliably in presidential years than for the midterms. In 2010, the Republican turnout advantage amounted to the equivalent of 6 percentage points, meaning a tie on the generic ballot among registered voters translated into a six-point Republican lead among likely voters. The GOP’s edge hadn’t been quite that large in past years. But if the “enthusiasm gap” is as large this year as it was in 2010, Democrats will have a difficult time keeping the Senate.

Democrats’ other problem is one of basic constitutional mathematics. Senators are elected in six-year cycles, so the seats in play this year were last contested in 2008, an extraordinarily strong year for Democrats. Even a strictly neutral political environment, or one that slightly favored Democrats, would produce a drop-off relative to that baseline. And Democrats’ losses will grow this year if voters go from modestly favoring Republicans to strongly favoring them.

Incidentally, we prefer to look at aggregate measures of the national environment, like the generic ballot and Obama’s approval ratings, instead of piecemeal ones such as voters’ views of Obamacare. Certainly the unpopularity of the Affordable Care Act — and its clumsy roll-out late last year — contributes to Democrats’ problems. But it’s hard to tell where Obamacare’s unpopularity ends and President Obama’s overall unpopularity begins. Voters’ views of the economy also have ambiguous effects in midterm years, especially when control of government is already divided.

Candidate quality. The notion of “candidate quality” might sound awfully subjective, but there are sound statistical ways to assess it. Fundraising totals, especially individual contributions, are a good indication of a candidate’s organizational strength. Various systems rate a candidate’s ideology on a left-right scale, based on her voting record or public issue statements, and we can compare those ratings against those of voters in her state. And candidates who have previously held elected office tend to outperform inexperienced ones, controlling for other factors.

State partisanship. As Dan Hopkins wrote at FiveThirtyEight last week, races of all kinds have become more and more correlated with presidential results in recent years. So the Partisan Voting Index (PVI), which compares how a state voted in the past two presidential years against the national popular vote, is also a useful tool for congressional races. At this early point in the cycle, there’s reason to be skeptical of races where the polls are out of step with how the state usually votes; states often revert to their partisan mean once more voters engage with the campaign.

Incumbency. Incumbents may be unpopular in the abstract, but they still win the overwhelming majority of races. Incumbency still represents an advantage in most cases, and sometimes a significant one. We can spot the potential exceptions by looking at an incumbent’s approval or favorability ratings.

Head-to-head polls. Head-to-head polls at this point in the cycle have some predictive power if evaluated carefully. That means taking care to see whether the poll was conducted among registered or likely voters, and putting less emphasis on polls when one or both candidates lack widespread name recognition. However, as my colleague Harry Enten has lamented, many of the more important Senate races have rarely been polled this year. Furthermore, much of the polling comes from firms such as Rasmussen Reports and Public Policy Polling, which have poor track records, employ dubious methodologies, or both. So the most appropriate use of polls at this stage is to see whether they roughly match our assessment of the race based on the fundamentals. Where there is a mismatch, it could indicate that the polls are missing something, that our view of the fundamentals is incorrect, or some of both — and it means there is more uncertainty in the outlook for the state.

Overall forecast

In consideration of these factors, we assess the probability of the Democratic or Republican candidate winning each seat. Where the choice of candidates is uncertain — for instance, in a race where a Democrat will face either a moderate, six-term incumbent U.S. representative or a poorly-financed tea party upstart, depending on the outcome of the Republican primary — the probabilities are meant to reflect a weighted combination of the plausible match-ups. Our assessment of the 36 races up for grabs this November is as follows:

One advantage of looking at the races on a probabilistic basis is that we can simply sum the probabilities to come up with a projection of how the new Senate will look. That method projects that Republicans will finish with 51 seats, a net gain of six from Democrats, and exactly as many as they need to win control of the chamber. (Democrats will hold the Senate in the event of a 50-50 split because of the tiebreaking vote of Vice President Joe Biden.)

That represents an edge for Republicans, but not much of one — and there are any number of paths by which they might get to 51 seats, or fail to do so. It might help to break the 36 races down into six categories, based on the party which holds the seat now and its likelihood of flipping to the other party.

Democrat-held seats likely to be picked up by Republicans (4): West Virginia, South Dakota, Montana, Arkansas

You’ll find that our characterization of the 36 races in most cases is very close to that issued by such forecasters as the Cook Political Report and Rothenberg Political Report. We’re looking at the same sort of information they are, and they have strong track records, so it’s natural there should be similarities.

One point of difference is that we’re much more pessimistic about the Democrats’ chances in West Virginia, South Dakota and Montana. These races have a lot in common, taking place in three red states where longtime Democratic incumbents have retired.

We’re bullish on Republican chances in these states for simple reasons. First, they’re red states. Second, we think the national political environment modestly favors Republicans. Third, we think the Republicans are poised to nominate equal or superior candidates in each state. Fourth, our research suggests there is little or no carry-over effect from incumbency once the incumbent himself retires. In West Virginia, for instance, the retirement of Democrat Jay Rockefeller provides little information about how the race will turn out in November.

We give Republicans a 90 percent chance of winning West Virginia, in fact. The state’s politics are a little more complicated than might be apparent from presidential voting — Obama is extraordinarily unpopular there, but a slim majority of the state’s voters are still registered as Democrats, and Democrats hold the governorship and both branches of the state legislature. But Republicans are poised to nominate an excellent candidate in Rep. Shelley Moore Capito, and she has held leads of 6 to 17 percentage points in polls against the likely Democratic nominee, Secretary of State Natalie Tennant.

We also give Republicans a 90 percent chance of winning South Dakota. It’s a more straightforward case, except that the presumptive Republican nominee, Gov. Mike Rounds, has been caught up in a controversy over the state’s participation in the EB-5 immigration visa program. To have much of a chance, Democrats will either need Rounds to lose the Republican primary or be significantly damaged by it.

Montana is slightly different in that Democrats technically do have an incumbent, John E. Walsh, running for re-election there. However, Walsh was appointed, not elected (he replaced Max Baucus in February when Baucus was named United States Ambassador to China). Appointed senators have a poor historical track record; from a predictive standpoint, it’s best to think of their races as open seats, rather than incumbent defenses. Walsh trails the likely Republican nominee, Rep. Steve Daines, by double digits in polling so far. The race is likely to tighten; Montana is somewhere between a purple state and a red one, and Walsh, who was elected as Montana’s lieutenant governor in 2012, is a credible candidate. Still, we give Republicans an 80 percent chance of flipping it.

The final race in this category is Arkansas, where Democrats have a true incumbent, Sen. Mark Pryor, running. Pryor was once so popular that he won without Republican opposition in 2008. But Arkansas has become redder and redder, and Democratic Sen. Blanche Lincoln’s 21-point loss to Republican John Boozman in 2010 demonstrates that past popularity is no guarantee of future success for a Democrat there. Furthermore, Republicans have a strong candidate in Rep. Tom Cotton, who is ahead by an average of about five points in recent polls. Pryor will be able to fight for his seat — he had $4.2 million in cash on hand as of Dec. 31, compared to $2.2 million for Cotton. The polling has returned inconsistent answers about Pryor’s approval and favorability ratings, so it’s hard to say how deep a reservoir of personal goodwill he will have to draw from. But the evidence points toward him being the underdog.

Democrat-held seats that are toss-ups (4): Louisiana, North Carolina, Alaska, Michigan

For Republicans, the path of least resistance to a Senate majority is winning West Virginia, South Dakota, Montana and Arkansas, and then two of the four states in this category.

Louisiana, where the Democratic incumbent Mary Landrieu is running, may be the easiest opportunity. Landrieu’s fundamentals are similar in most respects to Pryor’s: Her fundraising has been fine, but otherwise she’s running against the tide in what has become a very red state, and her moderate overall voting record may be undermined by her role in passing the Affordable Care Act in 2010. The difference is that Landrieu’s most likely opponent, Rep. Bill Cassidy, has yet to pull ahead in the polls, which instead show a race that’s roughly tied.

In North Carolina, Democrat Kay Hagan is an example of a candidate who could go in and out with the political tides. She was elected in 2008 over Elizabeth Dole as the Obama campaign turned out African Americans and college students throughout the state. But those are precisely the voters who don’t always show up for midterms. Still, Hagan could get a reprieve depending on Republicans’ choice of nominee. Republicans have eight declared candidates for their May 6 primary who range from Thom Tills, the speaker of the state House, to a variety of activists and political amateurs.

Alaska might be the hardest race to forecast. The polling there is often erratic. The state has voted Republican for president every year since 1968, but its independent streak sometimes translates differently in other races. The Democratic incumbent, Mark Begich, might face an establishment candidate in Daniel S. Sullivan, the former attorney general, or Mead Treadwell, the lieutenant governor — or he could face Joe Miller, the former judge and tea party activist who is unpopular beyond the Republican base.

The race in Michigan differs from the others in this group: It’s somewhere between purple and blue instead of red, and there’s no incumbent, as Democratic Sen. Carl Levin is retiring. But Republicans will have an excellent candidate in Terri Lynn Land, the former secretary of state. She comes from the old guard of moderate Michigan Republicans, instead of the tea party wing that might have preferred a candidate like Rep. Justin Amash. The likely Democratic nominee, Rep. Gary Peters, should win his primary without serious opposition, and he’s kept pace with Land in fundraising. But we take the polls that show the race as a toss-up at face value. The question is whether Michigan’s modest blue lean is enough to overcome a modestly Republican-leaning national climate.

Democrat-held seats that lean Democratic but with a plausible GOP pick-up (3): Colorado, Iowa, New Hampshire

Republicans have some backup options if they fail to win states such as North Carolina and Michigan.

The best one is Colorado. The GOP got the candidate of its choice in Rep. Cory Gardner, who declared for the race last month. That will prevent them from again nominating Ken Buck, the tea party candidate who lost a winnable race in 2010. (Buck has withdrawn from this year’s Senate race and decided to run for the U.S. House instead.) By our measures, Gardner is a decent candidate rather than a great one. He’ll start at a fundraising deficit to the Democratic incumbent, Mark Udall, who had $4.7 million in cash on hand as of Dec. 31, and he comes from a conservative district and has amassed a conservative voting record that may or may not translate well in the Denver suburbs. But Udall’s approval ratings only break even, and we give Republicans a 40 percent chance of winning his seat.

The other big recruiting news is in New Hampshire, where Scott Brown, the former Massachusetts senator, has announced he’ll seek the Republican nomination. But as Harry Enten noted, Brown isn’t terribly popular in New Hampshire, which has long had a love-hate relationship with Massachusetts. Just as important, Jeanne Shaheen, the Democratic incumbent, has enjoyed approval ratings that would be good enough to get her re-elected. The political winds in New Hampshire can shift quickly, which is why we’re not ruling out a Republican win. But we don’t think Brown improves the GOP’s chances much as compared with another credible candidate.

Iowa is also a political bellwether. Sen. Tom Harkin, the Democrat, is retiring, which might seem to give Republicans even or better odds in a Republican-leaning national environment. But Democrats have a substantial edge in candidate quality. Rep. Bruce Braley, the presumptive nominee, has a fairly moderate voting record and $2.6 million in cash on hand. Meanwhile, Republicans have yet to coalesce around one of several inexperienced candidates. Perhaps like the one in New Hampshire, therefore, this race could swing Republican if the Democrats’ national position deteriorates further; Braley would hold the seat for them in an election held today.

Democrat-held seats likely or almost certain to be retained by Democrats (10): Minnesota, Oregon, New Jersey, Virginia, Hawaii (special election), Massachusetts, Illinois, New Mexico, Delaware, Rhode Island

Minnesota might seem vulnerable for Democrats. Sen. Al Franken won his seat only after a months-long recount in 2008, and he’s amassed the liberal voting record you’d expect of him. But Franken’s approval ratings are pretty good and he raises plenty of money from liberals around the country. So far, he has deterred a credible Republican challenger from entering the race.

In Oregon, Democratic incumbent Jeff Merkley has middling approval ratings. But the state has become quite blue, and the Republican roster there is weak; in 2010, the GOP nominated inexperienced candidates in both the Senate and gubernatorial races. It doesn’t look like they’ll nominate a strong candidate this year, either. Their chances of victory depend on the electoral climate becoming catastrophic for Democrats.

The other eight races on this list are likely to hold for Democrats even in worst-case scenarios. Republicans have sometimes talked up their opportunity in Virginia, where the former chairman of the Republican National Committee, Ed Gillespie, is running. Ordinarily, we’d snark about party hacks overrating the chances of one of their brethren winning office, but Virginia just elected Terry McAuliffe as its governor. However, Democratic incumbent Mark Warner maintains high approval ratings, and he’d likely hold the seat even against a strong opponent.

Republican-held seats that lean Republican but where Democratic pick-up is possible (2): Georgia, Kentucky

Republican paths to take over the Senate are complicated slightly by their need to defend two seats of their own.

The higher-profile problem is in Kentucky, where Sen. Mitch McConnell, the Republican minority leader, has poor approval ratings, and Democrats will nominate a charismatic candidate in Alison Lundergan Grimes, the secretary of state. Grimes has run about even with McConnell in polls since she declared her candidacy in July. But McConnell will have all the financial resources he could want — he had $10.9 million as of Dec. 31 — along with Obama’s unpopularity in Kentucky to undermine Grimes. His path to survival could resemble that of the Democratic leader, Harry Reid, who prevailed in Nevada in 2010 with similarly poor approval ratings after a brutal campaign. We give McConnell a 75 percent chance of holding the seat. I’ll concede that I’m curious to see what our algorithmic forecasts do with this race once they’re up and running.

Georgia might be the slightly better opportunity for Democrats. The Republican primary, to be held May 20, has been a mess in the polling, with any of five different GOP candidates near the top of the race depending on the survey. Their prospects range from Secretary of State Karen Handel, who might be the strongest general-election nominee, to Reps. Phil Gingrey and Paul Broun, who have amassed conservative enough voting records that they might turn off swing voters even in red Georgia. Democrats are almost certain to nominate Michelle Nunn, the daughter of former U.S. Sen. Sam Nunn, who has run even with or slightly ahead of the Republicans in scant polling so far. Ordinarily, we are skeptical of candidates who lack previous experience in elected office, but those from famous political families don’t have the same name-recognition deficit to overcome and can sometimes tap into their families’ networks to raise funds and staff their campaigns.

Republican-held seats likely or almost certain to be retained by Republicans (13): Maine, Mississippi, South Carolina (regular election), Nebraska, South Carolina (special election), Texas, Tennessee, Oklahoma (special election), Kansas, Oklahoma (regular election), Wyoming, Alabama, Idaho

Thirteen other Republican-held seats will be contested in November, but none looks like a viable opportunity for Democrats. The moonshot for Democrats might be in Mississippi, where the Republican incumbent, Thad Cochran, is vulnerable to a primary challenge and Democrats have a good prospective nominee in former Rep. Travis Childers. Still, as Harry Enten explained, it’s hard for any Democrat to get to 50 percent of the vote in Mississippi.

A wide range of outcomes

We’ve sometimes seen people take our race ratings and run Monte Carlo simulations based upon them, which assume that the outcome of each race is independent from the others. But that’s a dubious assumption, especially so far out from the election. Instead, the full-fledged version of our ratings assumes that the error in the forecasts is somewhat correlated from state to state.

In plain language: sometimes one party wins most or all of the competitive races. If we had conducted this exercise at this point in the 2006, 2008 or 2012 campaigns, that party would have been the Democrats. In 2010, it would have been the Republicans. There are still more than seven months for news events to intervene and affect the national climate.

There are 10 races that each party has at least a 25 percent chance of winning, according to our ratings. If Republicans were to win all of them, they would gain a net of 11 seats from Democrats, which would give them a 56-44 majority in the new Senate. If Democrats were to sweep, they would lose a net of just one seat and hold a 54-46 majority.

So our forecast might be thought of as a Republican gain of six seats — plus or minus five. The balance has shifted slightly toward the GOP. But it wouldn’t take much for it to revert to the Democrats, nor for this year to develop into a Republican rout along the lines of 2010.