The math proves it: Hillary Clinton is about to clinch the nomination

The Democratic presidential race is about to end.

Barring something truly extraordinary, Hillary Clinton will be declared the presumptive nominee by the media, probably on Tuesday after the results of New Jersey's primary.

It will happen even if she loses every remaining contest, and it will probably happen even before the polls close in California — no doubt igniting the fury of some of Sen. Bernie Sanders' supporters.

Clinton has 2,313 delegates, putting her just 70 short of the 2,383 needed to win the nomination.

She will cover at least half the distance before Tuesday. Puerto Rico holds caucuses worth 60 delegates on Sunday, and the Virgin Islands awarded seven delegates on Saturday. Clinton is favored to win in Puerto Rico, but in order to shut out Sanders in the delegate count, she would need to keep him from reaching 15 percent support. Both campaigns say they don't think that's likely. There are also three superdelegates from the two territories who have yet to announce their support for Clinton or Sanders.

That puts Clinton on target to then go over the top with New Jersey, not long after 7 p.m. Twin Cities time, on Tuesday. The state is worth 142 delegates, and Clinton will be awarded many of them when the polls close.

The 2,310 delegates she has accumulated include superdelegates, but she's not winning solely because of them. In fact, superdelegates are basically Sanders' only hope at this stage: He would need many of them to change their minds.

That's because Clinton has effectively locked up the race for pledged delegates — those awarded based on votes cast in actual contests. She leads Sanders by 54 percent to 46 percent.

Clinton earned this advantage by winning more states, and by bigger margins in bigger states. She has also done better in primaries than in caucuses: Overall, she leads by 14 points in the national popular vote, 56 percent to 42 percent.

If there were only pledged delegates, Clinton would clinch the nomination with 33 percent of the vote in the remaining contests. This is why it's fair to say that she doesn't need to win any remaining states: Democrats award delegates proportionally, so she needs only around one-third of the remaining vote.

Clinton has won at least 33 percent of the vote in every primary except Sanders' home state, Vermont. She's also a big favorite in three of the largest remaining contests: New Jersey, Puerto Rico and the District of Columbia. California is more competitive, but barring a catastrophe for her, she's not likely to lose by 30 points.

The superdelegates can vote for whomever they want at the convention. That's why Clinton will be characterized as the "presumptive" nominee; she wouldn't actually become the nominee until the vote at the convention.

But superdelegates count like any others, and the media includes them in determining whether a candidate has clinched the nomination.

News organizations projected then-Sen. Barack Obama as the presumptive nominee in 2008 on this basis — in fact, he went over the top with the support of 4.5 superdelegates. Donald Trump did the same thing last week, thanks to the support of additional unpledged delegates.

Sanders trails in pledged delegates by about 8 percentage points. Because the Democratic system is proportional, he basically needed to improve by about 8 points in every state.

That Michigan win that got him so much attention on March 8, for instance? He needed to win there by 10 points, not 2. Iowa on Feb. 1? He needed to win by 8, not fight to a draw.

Even that interpretation is generous: It supposes that Sanders could have expanded his margin by 8 points in caucus states and Vermont, where it's probably not realistic to expect that he could have done all that much better. He probably needed to narrow Clinton's margin by more than 8 points in the South, where there was more room for improvement.

If Sanders had made 8-point gains across the board, he would have flipped Iowa, Nevada, Massachusetts, Illinois, Missouri, Connecticut and Kentucky. It would have left Clinton with Southern victories and a handful of narrow victories in states like Pennsylvania, New York, Ohio and Arizona.

Clinton's sweep of the South all but precluded a victory for Sanders. If he couldn't have done better in those 11 states (and remember, that means 8 points better), Sanders would have needed to sweep the rest of the country to win the election.

Sanders was hurt by closed primaries, where he did about 3.5 points worse. But most states aren't closed, so Sanders wasn't hurt that badly overall. And Clinton was hurt more by caucuses, where she did about 10 points worse. If every contest in the country had been an open primary, Clinton's delegate lead would actually have grown.