After starting small, the presidential campaign has exploded into a nationwide contest that on Tuesday could all but decide the Democratic and Republican nominating fights.

Thirteen states from Alaska to Massachusetts will hold caucuses and primaries that day, awarding roughly half the delegates needed to secure the two major party nominations.

The balloting marks a fundamental shift away from the close-quarters campaigning in states like Iowa and New Hampshire and the drive for momentum that came with victory — or, for the second- and third-place finishers, exceeding expectations.

From here out, the race is about cold, hard mathematics and piling up convention delegates.

Democrat Hillary Clinton and Republican Donald Trump, who start out ahead after winning three of the four opening contests, seem likely to expand their lead in the delegate count on the day known as Super Tuesday. The question is whether their margins prove insurmountable.

"If Clinton stretches out to a 100-delegate lead, it will be tough … to catch up," said Josh Putnam, a political scientist at the University of Georgia who has studied the nominating process. "On the Republican side, there is a little more leeway. But a lot of chips have to fall in line for anyone to be able to overcome Trump at this point."

Clinton and Sanders are not that far apart in the number of pledged delegates. But Clinton enjoys a massive advantage among "super delegates," party leaders and other elected officials, who are free to support whomever they choose at the party convention in July.

To catch up, Sanders will have to perform much better than he has in every state so far save New Hampshire, which he won handily.

That could be difficult. Seven of the states voting Tuesday are in the South, where black voters make up a significant part of the Democratic electorate; African-Americans have been among Clinton's most loyal constituents.

Sanders will also be hampered by the way Democrats award their delegates. Even a candidate who loses a state can win a share of its delegates.

That system undercut Clinton when she ran for president in 2008. She carried several big states against then-Sen. Barack Obama but was unable to overcome the delegate lead he built early on.

"Under the proportional system it's very hard for someone to close even a small gap," Putnam said.

The rules on the Republican side are different: some delegates are awarded on a winner-take-all basis. But the climb will be no less steep for rivals trying to push past the front-running Trump.

The candidate with perhaps the most at stake on Tuesday is Sen. Ted Cruz, the winner of the Iowa caucuses. He is favored to carry his home state, though he may have to share some of its 155 delegates.

Cruz has focused his campaign on winning the support of evangelical Christians and the most ideologically conservative voters, and Super Tuesday, with its Southern flavor, was supposed to be his breakout moment.

Surprisingly, though, it is the irreligious Trump who has done best among evangelical voters in carrying New Hampshire, South Carolina and Nevada, and he is leading in most polls ahead of Tuesday. A poor showing could effectively end Cruz's campaign.

Two of Trump's other rivals, Florida Sen. Marco Rubio and Ohio Gov. John Kasich, finished second in New Hampshire and South Carolina, respectively. They have every incentive to hang on until their home states vote March 15 in big winner-take-all primaries.

mark.barabak@latimes.com

Twitter: @markzbarabak