What happens to candidates who don’t clear the 15 percent threshold?

Candidates who fail to clear that bar in a particular state or district cannot win delegates there — and are locked out of the most critical part of the nominating contest.

Some could find their paths to the nomination all but blocked, as the cold reality of delegate math overtakes the bluster and spin used to paper over poor showings in early states. As these lower-tier candidates fall further behind in the hunt for delegates, donations could dry up and volunteers may quit.

The 15 percent rule, which was adopted in 1988, was designed to weed out candidates who don’t have a viable path to the nomination, Ms. Kamarck said.

“You have to shrink this somehow, right? And that’s what this was designed to do: Take out the smaller candidates,” she said.

What if just a few candidates clear the 15 percent bar?

The more candidates who fail to clear the threshold, the better it is for those who do. That’s because the votes of the failed candidates are effectively discarded when the delegate count is calculated. The math can significantly bump up the haul for the leading candidates.

For example, if only one candidate were to clear the bar in a given state or congressional district, even if he or she earned just 16 percent of the vote, that candidate would take home all the delegates in that area. If two or more clear the bar, they split the delegates proportionally, with the votes of the failed candidates excluded.

This could play out in powerful ways on Tuesday, when more than 1,300 delegates will be awarded — about a third of the total at stake in the entire nominating contest.