A Trump collapse could give Democrats back the House. Here’s the math.

It’s too early to say with any certainty how Donald Trump’s “grab ‘em by the pussy” comments will hurt him in the polls.

But it certainly seems likely to leave a mark. When Trump suffered his worst stretch of press this August — feuding publicly with a Gold Star family; suggesting his Democratic rival should be shot — he fell behind Hillary Clinton by as many as 7 points in the polls.

If this new tape has a similar effect, Clinton could obviously expect an easy victory. But that kind of Trumpian meltdown would also give Democrats a chance to reclaim a prize that has long looked far out of reach — the House of Representatives.

The House has long looked like impossible to flip because gerrymandering has given Republicans a fortress of extraordinarily safe seats. (In 2012, for instance, Democratic House candidates won 1.7 million more votes than their Republican foes — and still ended up with 33 fewer members of the House.) Democrats need to win 30 Republican-held seats to flip the House, and are widely expected to nab closer to 15.

But one political analyst I interviewed earlier this campaign thinks an epic Trump collapse might be enough to overcome that built-in advantage. Geoffrey Skelley, of the University of Virginia’s Center for Politics, argues that a Clinton victory of 6 points or more might be enough to put the House back in play.

Right now, the polling averages suggest Clinton is running around 5 points ahead of Trump. If she can use this Trump implosion to further increase her national lead, at least according to Skelley’s projections, she may give down-ballot Democratic allies a real chance at reclaiming Congress. And that would have huge consequences for the next two years of American government.

Skelley’s math is rooted in a simple fact: If the Democratic presidential nominee wins a House district, the Democratic congressional candidate also probably wins that House seat.

This is not an ironclad rule, but it’s a pretty good indicator — in 2012, only 6 percent of districts that voted for Barack Obama voted a Republican into the House.

This is the key to understanding why Skelley thinks a 6-point Clinton win could put the House in play. That kind of national victory would likely mean 50 House districts currently controlled by Republicans would vote for Clinton — therefore suggesting they have a good shot of also going blue at the House level.

Of course, a Clinton win in these 50 districts wouldn’t guarantee House Democrats will pick up all of those seats. (Many are held by powerful or longstanding Republican incumbents who are well-funded and enjoy good reputations at home.) But it does mean that Democrats could lose 40 percent of the House races in districts won by Clinton and still take back control of the House.

“A 6-point lead would help create the conditions for Clinton to pull the Democrats over the finish line to take the House,” Skelley says. “It doesn’t mean they would, of course, but it begins looking really possible.”

How does Skelley figure that a 6-point Clinton win would have Democrats winning 50 GOP-controlled House districts?

His model begins by assuming that the distribution of the national popular vote margin to the congressional districts will be exactly the same in 2016 as it was in 2012.

This may be best illustrated by an example: In 2012, Obama won the popular vote total by 4 percentage points. In Skelley’s model, a 4-point Clinton win would mean she’d also win and lose every congressional district by the exact same amount Obama did.

(Of course, this is bound to be wrong in some places — the distribution of Clinton’s vote share certainly won’t be an exact replica of Obama’s. But since there’s no way of knowing exactly how the popular vote will vary by House district from 2012, it’s a useful gauge of what might happen.)

This is why a 4-point Clinton win probably wouldn’t flip the House. Obama’s 4-point win over Romney gave him victories in just 28 congressional seats currently controlled by Republicans. That wouldn’t be enough — remember, Democrats need a full 30 to take back the House.

But what happens if Clinton expands on Obama’s national vote margin? Since Skelley’s model assumes the national vote share will be evenly distributed, every additional point in the national vote total translates into an additional point for each congressional district. House seats where Democrats tied or lost in 2012 become places where they win at the presidential level in 2016.

If Clinton wins by 5 points, according to Skelley, she’d be projected to win in 39 House seats now run by Republicans. That would theoretically put the House in play but would give Democrats very little margin for error.

But if she wins by a full 6 points, then 50 seats slide over to the Democratic column — at least at the presidential level, and maybe for the House as well.

There’s an elephant-size question hanging over all the analyses of whether a Trump implosion could give Democrats the House: What happens to “ticket splitting?”

Ticket splitting refers to the voters who back different parties for Congress and the presidency in the same trip to the polls. In 2012, only a record-low 8 percent of voters did so.

If that number goes up in 2016 amid a Clinton landslide, it could give congressional Republicans a buffer from a Trump catastrophe. (Current polling suggests Republican congressional candidates are much more popular than Trump, but it’s unclear how many of the party’s typical voters will actually show up on Election Day.)

This is why the X-factor of Libertarian candidate Gary Johnson makes these kinds of projections much more difficult. Clinton’s lead over Trump in most polls puts her about 6 points ahead, but that’s in part because of how weak Trump is — she’s normally polling around the 45 percent mark, and he’s closer to 41 percent.

If Johnson gets in the neighborhood of 5 percent of the national vote, do his supporters vote for congressional Democrats? Or will they vote Republican down ballot — and make Clinton’s big national lead less crucial?

This is why Skelley thinks Clinton herself probably needs to win more than 50 percent of the vote to pull Democrats over the finish line. If, for instance, she’s just beating Trump by 48 to 42, then congressional Democrats might need Gary Johnson voters to go blue down ballot, which seems unlikely.

“If she’s only winning barely over 50 percent of the vote, I think it’s difficult to say with confidence that she’ll pull a lot of Democrats with her,” Skelley said. “I think she needs to really win the popular vote by more than that.”

It’s a colossal understatement to say that the stakes are pretty darn high when it comes to control of the House.

If Democrats also go on to win the Senate, winning the House would open the doors for a raft of legislative priorities over climate change, immigration, and a range of other long-held blue sky policy goals for the party. So far, most chatter around a Clinton presidency involves big plans like infrastructure reform and new Supreme Court appointments. Sweeping Congress and the presidency would transform those ambitions into a wholly different kind.

But there’s another, and perhaps equally important, reason this fight is so crucial: It may be Democrats’ last shot at the House for a very, very long time.

New York magazine’s Ed Kilgore explains:

If Democrats do fall short of what they need to regain control of the House even as Hillary Clinton becomes president, prospects for further gains in the near term will probably not be good.

The party controlling the White House almost always loses House seats in midterms (1998 and 2002 were the rare exceptions), and 2018 would be a third-term midterm for Democrats, making the odds of an anti–White House trend even stronger.

Beyond that, Democrats have a well-known midterm turnout problem associated with their heavy reliance on parts of the electorate — notably young people and minorities — that rarely turn out proportionately in nonpresidential elections. As for 2020, it’s worth noting that Democrats gained only eight House seats when President Obama was reelected in 2012.

Many Democrats have certainly come to despise Trump over the course of a long, bitter campaign. But if he can blunder his way into giving them control of the House of Representatives far earlier than anyone thought possible, maybe they can come to forgive him.