In the wake of the first presidential debate, a chorus of top Biden allies and campaign officials has advanced a simple message: The race has not fundamentally changed.

In a sense, they’re right.

Far from upending the contest, the latest New York Times/Siena College poll on Wednesday finds that the debate reinforced the central dynamic of the election: the political decline of President Biden, who no longer possesses the advantages that allowed him to defeat Donald J. Trump four years ago.

Overall, the poll finds Mr. Trump leading Mr. Biden by six percentage points among likely voters and nine points among registered voters nationwide. In each case, it’s a three-point shift toward Mr. Trump since the last Times/Siena survey, taken immediately before the debate.

Historically, a three-point shift after the first debate isn’t unusual. In fact, it’s the norm. Over the last seven presidential elections, the person generally considered the winner of the first presidential debate has gained an average of three points in post-debate polls. Sometimes, the shift lasts; other times, it fades. But either way, debates don’t usually fundamentally change a race.

In terms of the polling, this debate is not an exception — at least not yet. The debate may ultimately prove to be the breaking point for Democratic politicians considering whether to stand by Mr. Biden, but the poll doesn’t show that the debate completely upended public opinion about the candidates. Instead, the debate exacerbated Mr. Biden’s political liabilities, which had already imperiled his re-election chances.

Four years ago, it was the absence of any major political liabilities that allowed Mr. Biden to prevail over Mr. Trump. He won the Democratic nomination and ultimately the presidency because he was a well-liked, relatively moderate, broadly acceptable candidate who could unite the politically diverse voters who disliked Mr. Trump. At the time, polls showed that a majority of voters had a favorable view of Mr. Biden. It was just enough for him to narrowly prevail in the Electoral College — by less than one percentage point across deciding battleground states.