After another strong showing by former Vice President Joseph R. Biden Jr. in Tuesday’s primary contests, Senator Bernie Sanders of Vermont announced that he was staying in the race for president.

But Mr. Sanders will need to do substantially better in the contests that remain to secure enough delegates to win the Democratic presidential nomination. Here are some possible outcomes for the primaries, and what the candidates will have to do to reach them.

What if: Biden keeps doing as well as he has

If Mr. Biden performs as well as he has in previous contests, he will secure the nomination by late April or early May, according to New York Times estimates of how the candidates might fare in upcoming primaries.

Biden Sanders Est. delegates won Delegates remaining 1,991 delegates to win 0 500 1,000 1,500 Narrow win Clear win

These estimates are based on the support each candidate has received in primaries and caucuses since Super Tuesday. The results make Mr. Biden a favorite in nearly every remaining contest, at least if he maintains the approximately 20-point lead he holds in national polls.

Mr. Biden’s lead could be even greater: Our estimates do not assume who will get support from many of the delegates of candidates no longer in the race, though many are likely to back Mr. Biden after all but one withdrawn candidate with delegates endorsed him.

What would it take: For Biden to lose his delegate majority

Mr. Biden could do about 12 percentage points worse than he has and still win a majority. If he fared any worse, Mr. Biden would fall short of a majority and risk a contested convention.

Biden Sanders Est. delegates won Delegates remaining 1,991 delegates to win 0 500 1,000 1,500 Narrow win Clear win

This means Mr. Biden could lose a bit of the support he has gotten so far and still be on track for the nomination. He could still win a majority of delegates even if he loses big states where he’s currently favored, like New York, Illinois and Arizona.

However, Mr. Sanders has said that Mr. Biden should still be the nominee if he wins the most delegates, even if he falls short of a majority.

What would it take: For Biden to lose his delegate lead

Mr. Sanders would need to perform about 17 percentage points better to receive a plurality of delegates.

Biden Sanders Est. delegates won Delegates remaining 1,991 delegates to win 0 500 1,000 1,500 Narrow win Clear win

Mr. Sanders would need to win a majority of the vote share in all but a handful of the remaining states to secure a delegate plurality.

Mr. Sanders has said that the candidate who receives the most delegates should be the nominee, even if they do not receive a majority, but other candidates disagree.

What would it take: For Sanders to win a majority of delegates

Mr. Sanders would need to do about 21 percentage points better to win a majority.

Biden Sanders Est. delegates won Delegates remaining 1,991 delegates to win 0 500 1,000 1,500 Narrow win Clear win

More than half of all delegates remain up for grabs, and Mr. Sanders has another opportunity to gain support nationwide during the one-on-one debate with Mr. Biden on Sunday. But Mr. Biden’s momentum over the last two weeks will make his decisive lead difficult to overcome. Mr. Sanders would need to perform much better than he has so far to secure a majority of delegates before the convention.