By KATIE GLUECK

Fresh off a string of resounding primary victories, Joseph R. Biden Jr. is now well ahead of Senator Bernie Sanders in the race for the Democratic presidential nomination — and curiosity about Mr. Biden’s preferences on a running mate is intensifying.

Mr. Biden fueled even greater interest in that subject on Sunday, when for the first time he pledged to pick a female running mate should he win the Democratic nomination.

But Mr. Biden, himself a former vice president, has also made clear that he has a detailed set of criteria, requirements that go well beyond biographical or geographical considerations.

And while Mr. Biden is certainly not yet the nominee — he faces Mr. Sanders in primaries in Arizona, Florida, Illinois and Ohio on Tuesday — he has engaged on the subject in depth throughout the campaign, having fielded questions about a running mate from voters and journalists alike for months.

Here is a guide to how Mr. Biden discusses what is poised to become one of the most closely watched matters of the campaign to come: the veepstakes.

The most important factor: A running mate with whom he is “simpatico.”

While Mr. Biden often says it is “presumptuous” to discuss a running mate, he has something of a routine down when asked about it.

He will discuss the strong working relationship he had with President Barack Obama, and say that he is looking for a running mate with whom he is similarly “simpatico” on key issues — and for someone who could be entrusted with presidential authority.

“I’m going to pick someone who is simpatico with me philosophically,” he said in August. “Agrees with me. Now if you’re not, that’s O.K., I have great respect. But you’ve got to be able to turn and say to your vice president, ‘This is your responsibility.’ Because the job is too big anymore for any one man or woman.”

And in an interview on “The Last Word” with Lawrence O’Donnell on MSNBC last Monday, he added more texture: “Someone who is simpatico with where I want to take the country. We can disagree on tactic but not on strategy. And so, that’s the first test. And there are a number of women and African Americans as well who would meet that criteria for me.”

The former vice president cares about experience in a running mate.

Mr. Biden often suggests on the campaign trail that the presidency is no place for on-the-job training — and he has signaled that he greatly values experience in a running mate, too.

In the past, some nominees have tapped vice-presidential candidates who were untested on the national stage as part of an effort to shore up a political vulnerability. During the 2008 presidential campaign, Senator John McCain, for instance, picked Sarah Palin, then the governor of Alaska, in an effort to appeal to conservatives — but she often stumbled in the spotlight, creating problems for his team.

Mr. Biden seems leery of that approach, though he has indicated that he would find a range of backgrounds to be useful, from presidential primary debate-stage experience to resumes forged at both the state and national level.

Age is also a factor, the 77-year-old Mr. Biden has said.

“One, that they are younger than I am,” he said in Hudson, N.H., last month, “And No. 2, that they are ready on Day 1 to be president of the United States of America.”

“There has to be some correlation between their views and mine,” he added at that stop. He said that someone who “insisted that we do ‘Medicare for All’” would present “a real problem.” Senator Elizabeth Warren championed Medicare for all last summer and fall, but then pivoted and proposed waiting as long as three years to seek passage of the legislation.

The coronavirus could become a new factor — here’s how.

At his best, his allies say, Mr. Biden is a steady, seasoned hand ready to lead in a tumultuous time. It is a message he and his supporters have increasingly stressed as the country grapples with the coronavirus outbreak — and Mr. Biden appears unlikely to undermine that point with a vice-presidential choice that could be perceived as risky or gimmicky.

His running-mate pick would be seen through the lens of a public health crisis, arguing against selecting someone who is untested in the face of potential catastrophe. Given Mr. Biden’s emphasis on electing a president who does not require on-the-job training, he seems inclined to apply that standard to a running-mate as well.

Here are some of the possible candidates he has mentioned.

Mr. Biden has mentioned by name, or alluded to, a long list of potential running mates that includes many of his former rivals.

During an interview with NBC News last week, he proactively mentioned Senator Amy Klobuchar.

A day after Senator Kamala Harris dropped out, Mr. Biden said: “She can be the president one day herself. She can be the vice president. She can go on to be a Supreme Court justice.” He has expressed openness to Ms. Warren, though more recently he emphasized her value in the Senate.

And in November, he alluded to several women outside of Washington, without explicitly naming them: Sally Q. Yates, the acting attorney general who was fired by President Trump early in his term; Stacey Abrams, the former Georgia House minority leader and 2018 nominee for governor; and Senators Jeanne Shaheen and Maggie Hassan of New Hampshire.

Other names generating chatter include Gov. Gretchen Whitmer of Michigan, Senator Catherine Cortez Masto of Nevada and Representative Val Demings of Florida.

Representative James E. Clyburn, the South Carolina Democrat who played an influential role in reviving Mr. Biden’s once-flagging campaign, said in an interview with Axios on HBO that he preferred that Mr. Biden select an African-American woman for the ticket.

“I promise you,” Mr. Biden said during the MSNBC interview, “My administration, from vice president on, is going to look like the country.” (The New York Times)

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