Democrats woke up on Monday to a spate of bad polls for Hillary Clinton, which brought Donald Trump to perhaps his closest position yet in the Electoral College. They had reason to go to bed feeling a lot better. Clinton bested Trump in the first presidential debate according to a variety of metrics, and the odds are that she’ll gain in head-to-head polls over Trump in the coming days.

Start with a CNN poll of debate-watchers, which showed that 62 percent of voters thought Clinton won the debate compared to 27 percent for Trump — a 35-point margin. That’s the third-widest margin ever in a CNN or Gallup post-debate poll, which date back to 1984. The only more lopsided outcomes were the 1992 town hall debate between Bill Clinton, George H.W. Bush and Ross Perot — widely seen as a maestro performance by Clinton — and the first debate between Barack Obama and Mitt Romney in 2012, when the CNN poll showed a 42-point win for Romney and the horse-race polls moved in his favor in the following days.

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Post-debate surveys like CNN’s aren’t always popular with poll mavens, in part because the universe of debate-watchers may not match the electorate overall. The voters in CNN’s poll were Democratic-leaning by a net of 15 percentage points, for instance, a considerably wider advantage than Democrats are likely to enjoy on Election Day.

But the CNN survey also historically correlates fairly well with movement in the post-election polls. Below, you’ll find a comparison between the perceived winner of the CNN/Gallup poll in debates since 1984, and how much the horse-race polls changed afterward. In 2012, for instance, Romney gained a net of 4.4 percentage points on Obama, although he eventually lost most of those gains. Bill Clinton, meanwhile, saw the polls swing by 4.1 points in his favor after the town hall debate of 1992.

The data is certainly noisy, but an emphatic win on the order of what Clinton or Romney achieved — and perhaps what Hillary Clinton achieved on Monday night — might be expected to produce a swing of 2 to 4 percentage points in horse-race polls. Even a 2-point gain would do wonders for Clinton, who would go from a fairly uncomfortable position in the Electoral College to a fairly comfortable one, and who would emerge with a 3-to-4-point lead in the popular vote.

Of course, there’s not necessarily any guarantee she’d hold on to those gains — Romney didn’t in 2012. But let’s not get too far ahead of ourselves, and consider various aggravating and mitigating factors for Clinton in terms of her potential for an immediate post-debate bounce.

On the mitigating side, as I mentioned, CNN’s poll had a Democratic-leaning sample. (On the other hand, if Democrats were more interested in watching the debate, that isn’t necessarily a bad thing for Clinton since she’s had trouble engaging her base.) Also, a separate post-debate poll from Public Policy Polling found Clinton winning by a narrower margin, 52-40. And historically, it’s the challenging party’s candidate, and not the incumbent’s, who gains after the first debate.

But there are several other reasons to think Clinton could get a bounce, and perhaps a relatively meaningful one. In addition to the polls, a variety of post-debate indicators implied a Clinton win, including focus groups, betting markets, and the post-debate coverage on television networks. The TV coverage matters because the pundits’ reaction doesn’t always match that of voters in instant polls, and it’s sometimes the TV spin that wins out. Voters narrowly scored the first presidential debate of 2000 as a win for Al Gore, for instance, but after intense media focus on Gore’s demeanor, it was George W. Bush who eventually gained ground in polls.

This time, pundits and pollsters seem to agree on the Clinton win. It’s certainly possible that by the time you’re reading this — I’m writing at 3 a.m. — some storyline that cuts against Clinton (and which didn’t seem like a big deal on Monday night) will have emerged. But the correlation between the instant-reaction polls and the eventual effect on horse-race polls has actually grown stronger in recent election cycles, perhaps because the conventional wisdom formulates itself more quickly.

The effect of major campaign events has also tended to be magnified in 2016 because of the much larger number of undecided and third-party voters than we had in recent previous elections. Clinton got a large bounce of about 8 percentage points following her convention, for instance. There’s also an argument that Clinton is poised to rebound because the race was out of equilibrium — she’s led by about 5 points on average over the course of the campaign, as compared with just 1 or 2 points now — although it’s not clear how predictive that tendency is.

What if Clinton doesn’t improve in the polls — or they even move toward Trump? Then that ought to be scary for Democrats, obviously. While Trump’s lack of preparation could also potentially cause him problems in the second and third debates, he showed off some of his worst qualities on Monday night, appearing to be the weaker leader than Clinton and less presidential than her, according to the CNN poll. If undecided and marginal voters were willing to shrug off Trump’s performance, then perhaps they really are in the mood for the sort of change that Trump represents, his faults be damned.

But in general, Clinton has gained after the set pieces of the campaign, which reward her knack for planning and preparation, including her first primary debate against Bernie Sanders, her (anticlimactically) clinching the Democratic nomination on June 6 and 7, and the Democratic convention. Clinton doesn’t seem to have as much of an edge on her opponents in the daily free-for-all of the campaign. So if Trump and his advisors don’t like the post-debate storylines, they may try to create a distraction or two — something they’re uniquely skilled at doing.

As a warning, you should give the debate five to seven days to be fully reflected in FiveThirtyEight’s forecasts. It will take a couple of days before reliable, post-debate polls are released, and then another couple of days before the model recognizes them to be part of a trend instead of potential outliers. Also, check the dates carefully on polls released over the next few days to make sure they were conducted after the debate. Although pollsters released dozens and dozens of polls over the weekend in anticipation of the debate, there are probably a few pre-debate stragglers that will slip through.

Our Elections Podcast team recapped the debate Monday night. Listen here, or watch video of the taping below.