The senator from Vermont is Hillary Clinton’s rival in the contest for the Democratic presidential nomination.

senator from Vermont, hopes to do well enough in Super Tuesday’s contests to stay in the race against Hillary Clinton.

senator from Vermont, hopes to do well enough in Super Tuesday’s contests to stay in the race against Hillary Clinton.

Bernie Sanders packed another campaign rally here Sunday night with the kind of display of enthusiasm that he hopes will power him to a series of victories on Super Tuesday. But for the senator from Vermont, Tuesday also could be the day he begins to feel the bracing realities of the Democratic presidential nominating process.

If Hillary Clinton’s landslide victory in South Carolina on Saturday marked a psychological turning point for her in the Democratic race, Super Tuesday could prove to be the first sign of a mathematical turning point. If she builds on Saturday with a series of victories in Southern primaries, she will emerge with her small lead in pledged delegates increased. And soon, the rules of the nominating process will begin to work decisively in her favor.

The Democratic rules, which allocate delegates on a proportional basis, are designed to keep the pledged delegate count relatively close as the early process unfolds. Some would say they actually help candidates who lose early contests. Once someone gains a lead, it becomes increasingly difficult for a challenger to make up that ground.

Given the number of delegates at stake, Super Tuesday will mark the first serious step in that process. By March 15, at which time half of the delegates will have been awarded, it is highly possible that Clinton’s lead will be big enough to create a nearly insurmountable obstacle for Sanders, barring a major turnaround in their fortunes.

Sanders’s advisers know well the realities of the process. Prepared for Tuesday’s results, they acknowledge that he will need to defeat Clinton in showdown primaries after Tuesday, when the campaign shifts to more friendly ground in industrial and other Northern states. Nonetheless, Tad Devine, senior strategist for Sanders and a veteran of delegate battles, said Sunday, “I’m not intimidated by the numbers.”

How do the rules play to the advantage of the front-runner? For starters, the calendar is working in Clinton’s favor. Only about 4 percent of the approximately 4,000 delegates have been awarded. On Super Tuesday, Clinton and Sanders will be competing in 13 contests (11 states plus American Samoa and Democrats voting from abroad) with 878 delegates at stake — about 20 percent of the total.

Sanders’s best chance for victories Tuesday comes in five states: Colorado, Massachusetts, Minnesota, Oklahoma and Vermont. Those states will distribute fewer than 300 delegates. Clinton has the advantage in six states, all with a higher percentage of nonwhite voters, which account for almost all the remaining delegates at stake: Alabama, Arkansas, Georgia, Tennessee, Texas and Virginia.

“If Clinton repeats [her South Carolina performance] in those big Southern states on Tuesday, she ought to have a nice, substantial lead that will hold her in good stead,” said Elaine Kamarck, a fellow at the Brookings Institution and an expert on the nominating process.

Democrats award all pledged delegates proportionally — unlike Republicans, who beginning on March 15 allow states to distribute delegates on a winner-take-all basis. The Democratic rules mean that no matter how well Clinton does Tuesday, she will be far short of a majority needed to clinch the nomination.

Still, she will enjoy a small lead, and if she wins more states with margins close to that of South Carolina, her lead would be more substantial. On Saturday, she won more than twice as many delegates as Sanders.

History shows that once a candidate gains the lead, it is difficult for the challenger to make up that ground. That happened to Clinton eight years ago against then-Sen. Barack Obama of Illinois. It also happened to then-Sen. Edward M. Kennedy of Massachusetts in his 1980 challenge to then-President Jimmy Carter. That is the potential challenge for Sanders in the weeks ahead, and he would need to rebound with decisive victories in states such as Illinois, Michigan and Pennsylvania, among others, to turn around the race.

Clinton learned this lesson the hard way eight years ago in her losing battle with Obama. He turned what seemed at first to be an almost negligible lead in pledged delegates into the key question in the race. Although it went to the end of the primary season, Clinton could not overtake him. She and her advisers are hoping to apply the same approach to the race against Sanders.

Here is what we know about who is expected to do well when 13 states head to the polls on Tuesday, March 1. (Julio Negron,Sarah Parnass/The Washington Post)

Eight years ago, Obama’s campaign advisers played the rules like virtuosos, while Clinton and her team were caught flat-footed, particularly in the caucus states where Obama rolled up lopsided victories and was rewarded with big delegate hauls.

Here is one example of how the Obama campaign’s mastery of the rules worked against Clinton: Among the states with contests on Super Tuesday 2008 were Idaho and New Jersey. New Jersey’s primary awarded 107 delegates. Clinton won the state 54 percent to 46 percent but emerged with just 11 more delegates than Obama. Idaho’s caucus awarded a mere 18 delegates. Obama won the state with about 80 percent and netted 12 more delegates than Clinton.

By the time the Clinton camp awoke to its problem, it was too late. That history was burned into the minds of Clinton’s current team, led by campaign manager Robby Mook. This year, her advisers vowed not to repeat those mistakes.

“Having seen what happened in 2008, there was an effort this time to make sure she was properly organized and would concede nothing in the caucus states,” said Jeff Berman, a consultant to the former secretary of state’s campaign and one of the key architects of Obama’s delegate strategy in 2008.

There is another twist to the rules that could help Clinton on Tuesday and will aid her throughout. Democrats award many delegates on the basis of past election results in each congressional district. The more Democratic a district is, the more delegates that district has to award in the primaries. Because districts with the strongest Democratic performance also happen to have a high percentage of African Americans or Latinos, Clinton gains an extra advantage.

For example, the majority-African American 7th Congressional District in Alabama will award nine delegates. No other district in the state has more than five. The same holds for the predominantly African American 2nd Congressional District in Mississippi.

South Carolina was a big blow to Sanders, who conceded Sunday on ABC’s “This Week” that “We got decimated.” But before a cheering crowd on the campus of Colorado State University on Sunday night, Sanders did not mention what happened Saturday as he delivered another ringing call for upending the system.

Only in the closing minutes of his hour-long speech did he refer to Tuesday’s contests, saying, “Colorado can play an enormously important role in leading this country forward to a political revolution.”

Through the first four contests, Sanders and the insurgency he leads more than held their own. He narrowly lost two caucus states — Iowa and Nevada — won a blowout victory in New Hampshire, then lost badly in South Carolina.

No one would have predicted six months ago that the insurgent campaign of a senator with little national profile would stand up so well against the force of the Clinton machinery. But now, as Clinton said Saturday in her victory speech, the campaign is going national.

Devine acknowledged that the rules “give an enormous advantage” to a front-runner. But he added that, with Sanders’s loyal following and a healthy campaign bank account, Sanders has the capacity to keep fighting indefinitely, arguing that he is the strongest Democrat for the fall.

“We can win delegates everywhere,” Devine said. “We can stay in [the race], win big showdown battles and wind up with more pledged delegates. Then we can make a very strong case that Bernie Sanders should be the nominee.”

Clinton has another big advantage, although one she probably will be reluctant to emphasize because it highlights her establishment support. She has a substantial edge over Sanders in support from “superdelegates” — the approximately 700 elected officials and party leaders who are convention delegates. Her advisers know that she must prevail in the battle for pledged delegates above all else.

Sanders’s advisers recognize her strength among superdelegates, as well as the obstacles created by long-standing party rules. But they are not prepared to surrender to the numbers. “Everybody wants to write the obituary,” campaign manager Jeff Weaver said. “But we very much are where we expected to be.”