It has since become very clear that the decline in approval was real. It is also clear that Biden’s position in his bid for reelection is shaky. But Biden’s approach to that concern — expressed loudly and vehemently by members of his own party in recent weeks — is to once again dismiss the polls as inaccurate or to cherry-pick the numbers he wants.

Those in the Democratic Party hoping to replace Biden with someone better positioned to win are obstructed, in part, by this obstinance from Biden. But they are obstructed, too, because while Biden’s position is historically weak, polling doesn’t (and perhaps can’t) show someone else doing demonstrably better.

At his news conference on Thursday, Biden repeatedly dismissed questions about dropping out of the race or about his ability to win.

“How accurate does anybody think the polls are these days?” Biden said at one point. He noted that some polls showed him winning, some losing, some tied. (In the past few days, in fact, polls from NPR, PBS NewsHour and Marist University showed Biden with a statistically insignificant lead over Trump; The Washington Post’s poll with ABC News and Ipsos showed him tied.) The polling data, Biden said, was “premature because the campaign really hasn’t even started.”

At another point, he tried to suggest that his position wasn’t as bad as it seems.

“There are at least five presidents running or incumbent presidents,” he said, “who had lower numbers than I have now later in the campaign. So there’s a long way to go in this campaign.”

This is not a good way to illustrate his point. If he’s talking about support in presidential polling, it is true that other incumbent presidents have seen lower support later in the campaign, according to 538’s average of polls. Those presidents were Gerald Ford in 1976 and Jimmy Carter in 1980. They are not role models for electoral success.

Several presidential candidates have seen lower support in mid-July than Biden does now. But most went on to lose. The exceptions were Bill Clinton in 1992 and Donald Trump in 2016, both running against unpopular opponents with strong third-party candidates in the mix. As Biden is now.

If Biden was talking about his approval numbers, here, too, history isn’t kind. The only presidents with lower approval in July of an election year either lost reelection or saw their parties lose the White House in November.

Beyond the specifics, analogies to past contests are fraught. For one thing, there simply haven’t been many presidential elections, especially in an era with modern polling and certainly none like this year’s, pitting a former president against the current one. So we look at the polls.

Near the end of the news conference, Biden was asked whether he would step aside for a candidate better able to win in November.

“No,” he replied, “unless they” — meaning his advisers — “came back and said, there’s no way you can win. Me.” He shifted to a conspiratorial whisper. “No one’s saying that. No poll says that.”

That is true. No poll says he can’t win and no poll says that some other candidate definitely will win. As we noted on Thursday, this is in part because the race will likely come down to a handful of swing states that will be determined by slim margins. And polls aren’t effective at sussing out those sorts of small differences.

The NPR-PBS NewsHour-Marist poll mentioned above included another battery of questions pitting Trump against various Democrats. As has been the case with other similar polls recently (including ours and one from CNN), Biden doesn’t do much differently against Trump than other candidates.

Those included in Marist’s poll were Vice President Harris, California Gov. Gavin Newsom and Michigan Gov. Gretchen Whitmer. In each case, the Democrat ran even with or slightly ahead of Trump. Interestingly, in every non-Biden matchup, some of those who said they planned to support Biden in a Biden-Trump matchup defected to Trump when he was running against another Democrat. But some of Trump’s support flipped to the Democrat. The effect, then, was that swapping candidates was a wash.

Where the non-Biden candidates had an edge was among the sizable segment of respondents who viewed both Biden and Trump unfavorably. Asked whom they preferred in a Biden-Trump matchup, those double-haters (as the vernacular has it) preferred Trump by four points. But they preferred Harris by five points and the less well-known Newsom and Whitmer by nine points and 14 points, respectively.

Yet, overall, Newsom and Whitmer still ran about as well against Trump as Biden. Perhaps, as Biden suggested, their position would shift over the course of a campaign as voters learned more about them. Or perhaps it wouldn’t. Maybe they, too, would end up battling for fewer than 100,000 votes in the Upper Midwest the way Hillary Clinton and Biden did.

That’s why Biden is immobile. He is convinced that he has overcome doubts in the past, particularly in the 2020 Democratic primary. He believes that other incumbents have been in difficult shape before rebounding. He knows that polling continues to give him a shot, however distant. And he is advantaged by the fact that polling can’t replicate all of the effects of a campaign — neither the potential of a surge in popularity for a governor prosecuting an effective case against Trump nor the result of an incumbent taking a tumble at an October campaign rally.