More often than not, the presidential nomination of a major party goes to the candidate who has the best story to tell.

By storytelling, I don’t mean the ability to deliver a stump speech or enthrall a crowd with anecdotes. I’m talking about biography and accomplishment, message and issues, and whether they come together in a compelling and credible way.

To be sure, a candidate’s story isn’t all that matters in the outcome of the primaries. The ability to raise money has a lot to do with it, too. But the big money tends to flow to the best story, the one that seems most likely to embody and exploit the political moment.

With that in mind, I spent the last few days in New York at the annual gathering of the Democratic Leadership Council, the organization that helped create the Clinton presidency. There, I listened to five of the party’s leading potential challengers to President Bush take their turns in the spotlight.

And I came away with some impressions about their stories, early impressions in the sense that no one has any idea what the 2004 landscape will look like, not early at all considering that these people have to make go/no-go decisions by the end of the year.

To my ears, the most distinctive story came from John Kerry, the senator from Massachusetts. To get elected, he said, a Democrat must have an agenda that goes beyond the domestic issues with which the party is traditionally most comfortable.

Citing his background as a decorated Vietnam combat veteran, he talked in depth about America’s role in the world, discussing his differences with the administration on carrying out the war on terrorism, his support for more foreign aid as a tool in that war, and his fears about American unilateralism.

Perhaps the least compelling was that voiced by Tom Daschle, the Senate’s majority leader. The South Dakotan seemed hard pressed to get beyond his legislative role, depicting himself mainly as the fellow who stops the Republicans in Washington from doing some bad things and forces them to do a few good ones.

Sen. John Edwards came across as the working-class boy from small-town North Carolina who says he fought for the little guy as a trial lawyer, taking on big business and insurance companies, and would bring that same sensibility to the White House.

Dick Gephardt, the House minority leader, is the working-class boy from St. Louis who talks a lot about fairness and champions such causes as expanded health insurance, universal pensions, and prescription drugs for seniors.

Then there’s Sen. Joseph Lieberman of Connecticut, the centrist whose religious background allows him to quote Scripture, talk about values and frame policy questions, including those related to corporate misbehavior, in terms of “what is right, as well as legal.”

There was one fellow conspicuously absent at this cattle show, who turned down the chance to come. That would be Al Gore. His story is much the best-known and, at the moment, still the most powerful.

As he stressed during a speech on Capitol Hill last week, he was vice president during a time when the economy grew, the stock market rose, unemployment fell, crime was down, and the budget was in surplus. And two years ago, he was the candidate who promised to stand up for ordinary folks against the corporate special interests and, in the end, got 540,000 more votes than George W. Bush.

Some might also say that he was part of an administration that let both corporate greed and the al-Qaida network get out of hand and part of a ticket that somehow managed not to win an election while holding the trump cards of peace and prosperity.

Which story most resonates with Democrats, if and when Gore tries again, will go a long way to determining his fate. But listening to the others this week made it clear to me that the game right now is all about the former vice president.

And it will be until he opts not to run, or somebody beats him.