The three national tracking polls that were published on Friday all moved toward President Obama, probably reflecting momentum from the Democratic convention.

In the Gallup national tracking poll, Mr. Obama moved into a three-point lead over Mitt Romney, up from one point on Thursday.

What’s a bit more worrisome for Mr. Romney is that Gallup’s reporting of the head-to-head results in its poll occurs over a lengthy seven-day window, meaning that only a minority of the interviews in the poll were conducted after the major speeches at the Democratic convention.

In fact, most of the interviews in the poll were conducted just after the Republican convention in Tampa, Fla., a period in which Mr. Romney should have been enjoying a convention bounce of his own.

Gallup’s approval ratings, however, are published over a three-day window, meaning that they will be quicker to respond to shifts in opinion. Mr. Obama’s approval ratings shot up to 52 percent in the version of poll published on Friday, while his disapproval ratings declined to 43 percent. The FiveThirtyEight forecast model does not use approval ratings directly, but this is a sign that there could be more good news for Mr. Obama in the head-to-head portion of the poll in the days ahead.

Mr. Obama still trails Mr. Romney in the Rasmussen Reports national tracking poll, but he narrowed his deficit to one point from three on Thursday. Rasmussen publishes its results using a three-day window, quicker than the Gallup, though almost none of their interviews yet reflect reactions to Mr. Obama’s speech on Thursday night.

Finally, Mr. Obama moved into a two-point lead in the online tracking poll conducted by Ipsos, which had given Mr. Romney a one-point lead on Thursday. About half of the interviews in the Ipsos poll were conducted after Michelle Obama’s speech on Tuesday — although only about one-quarter will reflect reaction to former President Bill Clinton’s Wednesday night speech, and almost none to the speech given to Mr. Obama.

It’s certainly important to be cautious when interpreting one-day changes in the polls. But so far, this data is tracking toward a decent-size convention bounce for Mr. Obama. It’s quite unlikely, in fact, that the movement in the polls reflects statistical noise alone.

I looked for previous instances in our database in which both the Gallup and Rasmussen tracking polls each moved toward Mr. Obama by at least two points on the same day, and found only six other occasions on which they did so, out of about 140 days on which they were both published simultaneously. The Ipsos poll has started to be published only recently, but the fact that it moved toward Mr. Obama also further strengthens the case.

Instead, that Mr. Obama has gained two or three points in polls conducted essentially halfway through his convention suggests that his gains could eventually be larger, perhaps on the order of five points, once the surveys fully reflect post-convention data. Typically, the bounce grows over the course of the convention, peaking in interviews conducted just a day or two after it.

The caveat is that — and yes, this reflects my personal, subjective view — I thought the speeches delivered by Mrs. Obama and Mr. Clinton were stronger than the one given by Mr. Obama himself, and that Democrats’ momentum seemed to peak on Wednesday night rather than on Thursday. Then, Mr. Obama got a mediocre jobs report on Friday.

The better question, then, is not whether the movement in the polls toward Mr. Obama is “real,” but rather how much more of it (if any) he will get, and how long it persists.

Mr. Obama has made considerable gains in the FiveThirtyEight forecast over the past week or two, based initially on the fact that Mr. Romney’s bounce in the polls after his convention was subpar, and now because the numbers have begun to shift back toward Mr. Obama.

However, Mr. Obama will need to continue making gains in the polls over the next several days to retain the improvement he has seen in the forecast. Each day that interviews predating the Democratic conventions are replaced by fresher ones in these polls, the model’s standards will become a little higher for him.

More specifically, Mr. Obama will need to show leads of around four or five points in national polls conducted next week to maintain the advantage the model is now showing for him.

But there is the risk of getting too lost in the technical details, when the calculus is actually fairly simple. Mr. Romney entered the conventions in a narrow deficit to Mr. Obama. The fact that he only pulled into a rough tie in the polls after the Republican convention was a bearish sign for him. If Mr. Obama emerges from the conventions in a stronger position than he entered them with, Mr. Romney’s position will have become a bit difficult.

I don’t want to encourage anybody to root for poor economic news, but it ought have been a relief to Mr. Romney’s campaign that the job growth numbers for August were so tepid. Republicans could use a buzzkill after a convention period that does not appear to have gone terribly well for them.