I won’t believe that a populist Republican can lose in Alabama until I see it with my own eyes, no matter how many polls tell me it’s possible.

But there are a lot of polls right now telling me it’s possible.

A new one from Gravis has Doug Jones leading Moore by five points:

Democrat G. Douglas Jones has taken a five-point lead over Republican Roy S. Moore, 47 percent to 42 percent, as the two men vie for the Senate seat to be decided in the Dec. 12 special election, according to the lasted Big League-Gravis poll of 628 likely Alabama voters conducted Nov. 14 through Nov. 15…

In the Nov. 10 Big League-Gravis poll, Moore held his lead over Jones: 48 percent for Moore and 46 percent for Jones.

“There is a 7-point swing, but it’s more dramatic,” he said. “The amount of undecideds has basically doubled.”

Moore’s lost six points in a week due to the barrage of accusations against him. Of the last six polls taken, Jones has led in four, including the three most recent — and two of those three haven’t been particularly close, with Moore trailing by five in Gravis’s data and by eight in the Fox News poll published last night:

Much less ambiguity about the polling trend in Alabama now. Things have gotten worse for Moore since the allegations first came out. pic.twitter.com/1cPt1jzvos

— Nate Silver (@NateSilver538) November 17, 2017

Against all odds, Jones now leads in the RCP poll average by the slightest of margins. For the moment, he’s a favorite to win.

Isn’t it possible, wonders Jake Tapper, that some Alabamans embarrassed by the Moore allegations are telling pollsters they won’t vote for him when secretly they plan to? That theory came up often during the presidential election to explain Hillary’s steady lead too. It’s a sort of “Bradley effect” at work: Some people, when asked a question by a pollster, may give that pollster what they think the “appropriate” response is rather than what their honest opinion is. Moore’s been accused repeatedly of having been a lech with teenaged girls over the past week so go figure that some Republicans who still plan to pull the lever for him wouldn’t be eager to tell a pollster that right now. And if that’s true then the polls are understating Moore’s actual support. One showing Jones ahead narrowly may actually point to a Moore upset.

I think that’s possible but there are wrinkles to it. First, evidence of a Bradley effect in Trump’s victory last November is ambiguous. Right, he pulled an upset in a race he was expected to lose, but the popular vote result didn’t diverge much from the poll average. The polls predicted Clinton to finish 3.2 points ahead of Trump; in reality she finished 2.1 points ahead. It could be that there was a small but very significant Bradley effect given how tight the race was in key states like Florida and Michigan; maybe one or two percent in those places told pollsters they’d support Clinton because they were embarrassed about the “Access Hollywood” tape and then went out and voted for Trump anyway, making the difference between victory and defeat. It’s conceivable but there’s no way to know and the popular vote cuts against it.

There’s another reason to doubt a “Bradley effect” in Moore’s case, though:

I posted this last night… but EVERY pollster who polled before/after allegations saw shift to Jones. Fox News is only live interviewer in bunch. Rest are automated phone. So folks would be lying to a machine. pic.twitter.com/4Mf8h7fYoZ

— (((Harry Enten))) (@ForecasterEnten) November 17, 2017

Not all of these polls involve talking to a live person. The idea behind the Bradley effect is that a person doesn’t want to be judged negatively by a pollster during a live interview if he or she gives an embarrassing answer. If you’re talking to a machine, though, that fear should be reduced or eliminated entirely. Realistically, I think the best pro-Moore spin on the polls right now is that there’s still nearly a month to go before Election Day and it’s better that this dirt got flung at him now than three weeks from now. If he doesn’t get hit again after Thanksgiving, it’s possible people’s memories will be short and he’ll squeak through to victory.

Here’s Brian Kilmeade, co-host of the president’s favorite TV show and a longstanding Fox News presence, telling Oklahoma Sen. James Lankford that if Moore had called one of his daughters at high school for a date, as he’s alleged to have done with one woman in the 1970s, “I would kick his head in.”