We last issued a U.S. Senate forecast in mid-March. Not a lot has changed since then.

The Senate playing field remains fairly broad. There are 10 races where we give each party at least a 20 percent chance of winning, so there is a fairly wide range of possible outcomes. But all but two of those highly competitive races (the two exceptions are Georgia and Kentucky) are in states that are currently held by Democrats. Furthermore, there are three states — South Dakota, West Virginia, and Montana — where Democratic incumbents are retiring, and where Republicans have better than an 80 percent chance of making a pickup, in our view.

So it’s almost certain that Republicans are going to gain seats. The question is whether they’ll net the six pickups necessary to win control of the Senate. If the Republicans win only five seats, the Senate would be split 50-50 but Democrats would continue to control it because of the tie-breaking vote of Vice President Joseph Biden.

Our March forecast projected a Republicans gain of 5.8 seats. You’ll no doubt notice the decimal place; how can a party win a fraction of a Senate seat? It can’t, but our forecasts are probabilistic; a gain of 5.8 seats is the total you get by summing the probabilities from each individual race. Because 5.8 seats is closer to six (a Republican takeover) than five (not quite), we characterized the GOP as a slight favorite to win the Senate.

The new forecast is for a Republican gain of 5.7 seats. So it’s shifted ever so slightly — by one-tenth of a seat — toward being a toss-up. Still, if asked to place a bet at even odds, we’d take a Republican Senate.

Of course, it can be silly to worry about distinctions that amount to a tenth of a seat, or a couple of percentage points. Nobody cares all that much about the difference between 77 percent and 80 percent and 83 percent. But this race is very close. When you say something has a 47 percent chance of happening, people interpret that a lot differently than if you say 50 percent or 53 percent — even though they really shouldn’t.

It’s important to clarify that these forecasts are not the results of a formal model or statistical algorithm — although it’s based on an assessment of the same major factors that our algorithm uses. (Our

tradition is to switch over to fully automated and algorithmic Senate forecasts at some point during the summer.)

The political landscape

We usually begin these forecast updates with a broad view of the political landscape. Not all that much has changed over the past couple of months.

If the macro environment hasn’t changed much, what about the environment in individual states and races? There have been a few shifts since March, but they mostly offset one another. We’ll start with the races where Democratic prospects look brighter than before.

Races where Democratic chances have improved

In March, we gave Arkansas Sen. Mark Pryor just a 30 percent chance of holding his seat for Democrats. But five of the seven polls since then have put Pryor ahead of his Republican opponent, Rep. Tom Cotton.

Does that mean Pryor should be thought of as the favorite instead? Not quite, in our view. Most of the polls showing him ahead are among registered voters. Also, it’s not necessarily wise to dismiss earlier polling, most of which showed Cotton with the lead. There can sometimes be temporary fluctuations in the polling, as candidates, for example, buy a large amount of advertising but then revert to the mean. Pryor is also running for re-election in a state where Barack Obama’s approval rating is somewhere in the mid-30s. However, it seems clear that Pryor has done a better job of separating himself from the national environment than former Sen. Blanche Lincoln did four years ago, and we now have his chances at 45 percent.

Michigan is the other state where there’s been a clear improvement in Democratic prospects. That race looked like a toss-up in March, but the Democratic candidate, Rep. Gary Peters, has held a lead of about five percentage points in several polls since then. Our guess is that the race will tighten some; the GOP has a pretty good candidate in Terri Lynn Land, the former secretary of state. Furthermore, while Michigan is somewhat blue-leaning, that’s offset by a slightly GOP-leaning national environment. Still, we now have Peters’ odds at 65 percent, up from 55 percent previously.

The other changes are minor. In New Hampshire, we’ve never thought there was too much reason for Republicans to be optimistic about the opportunity for former Massachusetts Sen. Scott Brown. The problem is not with Brown so much as with his Democratic opponent, Sen. Jeanne Shaheen, who retains fairly high approval ratings. Shaheen has held a lead of between three and 12 points in polls since March, although the polls are a mixed bag in terms of quality. Because New Hampshire polling can be volatile, and because Brown’s relative moderation could potentially offset some of Shaheen’s popularity , we don’t think it’s safe to say she has the race in the bag (two other models give Shaheen a 98 percent chance of victory). But we do put her chances at 80 percent, up slightly from 75 percent before.

In two other states, poor Republican candidates may help Democrats, although both states were on the fringes of being competitive to begin with. One case is Oregon, where Republicans nominated Monica Wehby, a pediatric neurosurgeon, despite accusations that she had stalked and harassed her ex-husband and ex-boyfriend. Wehby wasn’t a great candidate to begin with — her fundraising has been mediocre, and candidates without prior experience in elected office don’t tend to hold up as well over the course of a Senate campaign (even if they have impressive accomplishments in other domains). The harassment allegations are another complication for a candidate who needed a lot of things to break in her direction. Thus, we have the Democratic Sen. Jeff Merkley with a 95 percent chance of surviving, up from 90 percent in March.

How about Mississippi, where the incumbent Sen. Thad Cochran was forced into a runoff by his conservative Republican opponent, Chris McDaniel? Democrats have a reasonably good and moderate candidate there in former Rep. Travis Childers.

Real Clear Politics’ elections analyst Sean Trende has a good rundown of the difficulties that Childers might face. First, let’s assume for a moment that McDaniel wins the runoff. While he might be “too” conservative for some states, Mississippi is very conservative itself. McDaniel would probably also have to make gaffes or misstatements on the campaign trail, as Richard Mourdock did for the Republicans in Indiana in 2012, or create trouble for himself. Second, Mississippi is not just conservative but highly “inelastic”, meaning that there are few swing voters there and it can be hard for any Democrat to cobble together a 50 percent coalition. Third, McDaniel still has to win the runoff for Childers to even have a chance at winning, and that might not happen.

The race could badly use some better polling: all we have on the McDaniel-Childers matchup is a Rasmussen poll from March and a Public Policy Polling survey from November (not two of our favorite polling companies). For now, we have Childers’ chances at 10 percent in Mississippi, up from 5 percent before, on the assumption that he’d have perhaps a 20 percent chance against McDaniel but almost none against Cochran.

Races where Republican chances have improved

These favorable developments for Democrats have been offset by other cases in which Republican odds now look somewhat better.

The most notable case is in Iowa, where we had previously given the Democratic Rep. Bruce Braley a 75 percent chance of being elected. That was before a tape was released showing Braley referring to Iowa Sen. Chuck Grassley as a “farmer from Iowa who never went to law school” — not a smart statement in a state that relies heavily on agriculture. Meanwhile, Republicans got their preferred candidate in state senator Joni Ernst, who won the Republican primary last week.

Braley had held onto his lead in several polls since the “farmer” comments, but two released last week after Ernst’s primary victory had her ahead instead. There’s some reason to be skeptical of these polls: one was from Rasmussen Reports, and the other was from Loras College, which has not previously done much public polling. Furthermore, candidates sometimes get a temporary bounce from the favorable publicity surrounding a primary win, which then fades. (A case in point is the Democrat Creigh Deeds in the 2009 gubernatorial race in Virginia.) We now put Braley’s chances at 60 percent.

The other Republican gains reflect minor adjustments. In Alaska, it now looks unlikely that Republicans will nominate Joe Miller, who won his 2010 primary against Lisa Murkowski but lost to her when she ran as a write-in candidate in the general election. Miller is very unpopular with the general electorate and might have given the incumbent Democratic Sen. Mark Begich a free pass. Instead, Begich will likely now face either lieutenant governor Mead Treadwell or former Alaska attorney general Daniel S. Sullivan. We give Begich a 50 percent chance of surviving that contest, down from 55 percent before.

In Kentucky, incumbent Sen. Mitch McConnell won his primary and is seeing his head-to-head polling improve ever so slightly against Alison Lundegran Grimes, the Democrat. Grimes is fighting an uphill battle against Kentucky’s Republican-leaning partisan gravity and against McConnell’s financial advantages, so the slight uptick in McConnell’s polling puts the race somewhat more in line with the fundamentals of the state, as we see them. We have Grimes’ chances down slightly to 20 percent from 25 percent.

Montana is one state where statistical models and qualitative forecasters disagree. Whereas groups like Cook Political Report characterize the race as merely leaning toward the Republican, Rep. Steve Daines, the polling-driven models have him as almost certain to win.

The case for the Democrat, the appointed incumbent Sen. John Walsh, would rely on citing Montana’s recent political history (Democrats have performed well and closed well in non-presidential races there) and Walsh’s political pedigree (he is Montana’s former lieutenant governor). It seems like a stretch to us (and may result partly from the erroneous assumption that all incumbents are equal, when in fact appointed incumbents like Walsh run far worse than elected ones do). In any event, Walsh will need to make up a lot of ground in the polling. We have Walsh’s chances at 15 percent for now, down from 20 percent in March. He and Daines just won their primaries, and if Walsh doesn’t see some improvement in his polling soon, Democrats may need to write the race off.

Finally, in South Dakota, the former Republican Gov. Mike Rounds won his primary last week. He’s the far stronger candidate than the Democrat, Rick Weiland, who lost election attempts to the U.S. House in 1996 and 2002. Plus, South Dakota is a red state. We give Republicans a 95 percent chance of victory, up from 90 percent before.

Incidentally, there’s one race where Republicans are absolutely certain to win. That’s Alabama, where the Republican Sen. Jeff Sessions won his primary unopposed last week — and is also unopposed in the general election. Congratulations to him on a fourth term in the Senate.