For months, Vice President Biden has run third in polls of Democratic voters, behind Hillary Clinton and Bernie Sanders. Even as Sanders came out of nowhere to scoop up a quarter of the Democratic base, Biden was in the mix, eventually surging to a position only slightly behind Sanders. It was a three-way race.

But that picture was deceptive. Biden's surge corresponded to Clinton's fall. The people that were moving to Biden were people that had been with Clinton. After the first Democratic debate, as Clinton regained strength, Biden's support dropped.

In electoral politics, there's a fairly self-explanatory concept called "splitting the vote." The idea is that two candidates will appeal to the same base of voters, and that the base will then split, with some part of the group backing Candidate A and the other backing Candidate B. For Candidate C, this is a good thing: If your two opponents split a large group of voters, it gives you a chance to win the election even if your base is smaller.

As we've noted repeatedly in the past, Biden split Clinton's base of support. In Fox News polling from earlier this year, the similarity in composition of the two candidates' supporters was obvious.

Since June, CNN has asked Democrats whom they backed both with and without Biden. The beneficiary of Biden not being in the race has consistently been Hillary Clinton.

In the Post's new poll with ABC News, released on Tuesday, the same thing happens. With Biden in the race, Clinton is up 31. Without him, she's up 39.

Sanders will see some benefit from Biden not throwing his hat in, to be sure. But most of the benefit is likely to go to Clinton. And for Sanders, whose momentum in the polls appears to have stalled, that's the opposite of what he needs to see. Sanders has only a few months left to peel enough support away from Clinton to win enough primaries to get the nomination. Biden handing Clinton a bunch of support moves him in the opposite direction from that goal.

It was always an uphill fight for the senator from Vermont, thanks in part to Clinton's strength with non-white voters. But with Biden in the race, Sanders could hope that the vice president might peel enough support away from Clinton to allow Sanders to win the plurality of votes. Now, it's all up to Sanders.

It's possible. But as of Biden's announcement, it's far less likely.