Mitt Romney took a narrow lead after the first presidential debate in 2012, but there is considerable evidence that his gains were exaggerated. For that period, the Democrats became less likely than Republicans to respond to surveys — what pollsters call differential nonresponse.

After the first presidential debate in 2000, George W. Bush surged in the polls — going from an 11-point deficit among likely voters to an eight-point lead in the Gallup tracker. But half of the swing was because of changes in who was assessed to be a “likely voter.” A postelection study found that those swings in likely-vote intention had no predictive value; it was just noise.

So there’s good reason to be cautious about Mrs. Clinton’s rise in the polls. But that doesn’t mean it should be dismissed out of hand. After the first presidential debate in 2004, John Kerry truly did rally to make it a close race.

Usually, a good way to test the durability of a swing in the polls is to ask whether it brings the race closer or farther from the so-called fundamentals, like the president’s approval ratings.

A shift that brings the polls in line with the fundamentals might be a little likelier to last than one that cuts the other way. Mr. Kerry’s recovery, for instance, brought the tighter race implied by Mr. Bush’s approval ratings. Barack Obama’s gains in 2008 gave him the considerable advantage implied by the economy and Mr. Bush’s low approval ratings. The opposite could be said of Mr. Bush’s and Mr. Romney’s surges in 2000 and 2012.

This year, it’s a lot harder to tell. That’s in part because there is no incumbent president on the ballot, which always makes it a little harder to tell where the natural resting point of a race sits. But it’s also because Mr. Trump is such an extraordinary candidate that many analysts believe the fundamentals will be less significant than usual.

In lieu of the traditional fundamentals, here’s something to consider instead: Over the longer term, Mrs. Clinton has led Mr. Trump by around five percentage points nationally.

The debate has bumped her poll standing back closer to her longer-term average, and it seems plausible it could stay in that range. The debate has also reinforced doubts about whether Mr. Trump is prepared for the presidency. No matter how you interpret polls, Mrs. Clinton is in a decent position with less than 40 days to go.