“We have path toward victory,” Sanders tells cheering supporters in Madison, WI, touting big victories in AK, ID, UT. — Sahil Kapur (@sahilkapur) March 26, 2016

One thing Sanders understands well is the need for a horserace. Without that, he and his principal issue, economic inequality, won’t get covered.

It is possible to put a probability on the outcome that Sanders has outlined above: less than 5%. It’s also possible to calculate how long he can keep saying there’s a path: until June 7th.

For estimating the outcome of the Democratic nomination race, thanks to the relatively transparent rules, it is not necessary to game out individual states. Indeed, excessive focus on detail can confuse matters.

To keep the calculation simple, let’s just focus on pledged delegates, which are driven entirely by voting. In other words, what is the probability that Sanders gets half of all pledged delegates? This is useful, since if such an event did happen, then superdelegates might potentially follow suit to give him an overall majority.

Sanders has won 44% of pledged delegates so far. How would he get to 50%-of-delegates-plus-1?

First, let’s work out a simple equation. If fraction F of delegates have been assigned so far, and Sanders has fraction S of those, then in order for him to get a majority by the end, the following condition has to be satisfied:

final fraction of pledged delegates = S*F + X*(1-F) > 0.5,

where X is what fraction of the remaining delegates he will win in the remaining races.

What X would have to be to get a majority: Rearranging the equation above, we get

X > (0.5 – S*F)/(1-F).

According to The Green Papers, F=0.56 as of today. At this moment Sanders has 1038 out of 2304 pledged delegates, so S=1038/2304=0.45. With those numbers, the above equation works out to X > 0.563. In other words, Sanders needs to earn 56% of the remaining pledged delegates.

Luckily, it is an easy problem to figure out what fraction of the vote Sanders needs. The Democratic Party’s rules assign delegates proportionally to the popular vote. (In this respect, the Democrats’ rules are more truly democratic than either the Electoral College or the Republican Party, which are both dominated by winner-take-all contests. Indeed, if the Democratic Party’s delegates were assigned on a winner-take-all basis, tonight’s delegate count would be Clinton 2020, Sanders 734, a 2.7-to-1 margin.) So Sanders needs to win the popular vote 56%-44% in the remaining elections, i.e. he needs Sanders +12%.

Now let’s look at national opinion surveys. In the last 8 polls (spanning March 17-23), Clinton led by a median of 9.5 +/- 2.1%. Overall, Democratic polls have been pretty accurate. Therefore, assume that the upcoming 22 primaries and caucuses will have an average margin that is similar to national opinion.*

For national opinion to come into line with what Sanders needs, there would have to be a change from Clinton +9.5% to Sanders +12%. That’s a 22-point swing. To put that into perspective, that is about how much the Clinton-Sanders margin has moved over the last seven months, since the start of August. Going forward, opinion would have to start moving about three times faster. And for this to happen, Sanders would have to start to cut into Clinton’s support, which has stayed in the 50-55% range this whole season. Basically, her support would have to drop to 40%. That simply isn’t going to happen.



The probability of a massive polling error (movement of at least four sigma) is basically zero. However, the real question is whether some unanticipated externality can impose a massive swing across all states at once. I estimate that the probability of such a drastic swing in the remaining 10 weeks of the primary season is quite low – well below 5%. Therefore the probability that Hillary Clinton will have a majority of delegates at the convention is greater than 95%.

How long can Sanders keep up his optimism? Although Sanders’s optimistic outcome is highly unlikely, he will probably still keep saying it until there are so few delegates left that it becomes impossible, even if he wins every single one.

That won’t happen until the very end. On the last day of voting on June 7th, nearly 17% of all delegates will be determined, in California, Montana, New Jersey, New Mexico, North Dakota, and South Dakota. As long as Sanders stays above 39.1% of pledged delegates, he can still say, technically speaking, that a last-minute win in June can put him over the top. Considering that he entered this race to get a message out, that’s probably what he will do.

*Relatively recent polls are available in WI, NY, MD, PA, WV, CA, and NJ, which account for 69% of the remaining delegates. Clinton leads in six out of seven of these states. Using these numbers, and national surveys to fill in the rest of a delegate-weighted total, she currently appears to be headed for getting 54% to 60% of the remaining pledged delegates, similar to the 56% that she has won so far.

Update: as I describe in a later post, the aggregated poll average for all states to date has been off by only 3.0 percentage points. Therefore polls, taken as a whole, are a very good guide of where the race is today.

