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How Daunting Is Santorum’s Delegate Math?

Since Super Tuesday, I’ve been reading a lot of coverage that ignores the challenges that the delegate count poses to Rick Santorum. Here’s one quick test to see if you have a good sense for this stuff. Is Illinois a must-win state for Mr. Santorum?

The answer is basically yes.

No one state is technically a must-win, and for that matter, winning the statewide vote in Illinois has no direct bearing on the delegate count (all of its delegates are awarded by Congressional district).

But Mr. Santorum will have to win in most places like Illinois to have a decent chance at preventing Mr. Romney from securing the nomination. And he’ll have to win in states much more challenging than Illinois — possibly as challenging as California — to overtake Mr. Romney in the delegate count and have the stronger case that he should be the nominee.

Although some awareness of the delegate math is almost assuredly better than none, you really need a detail-oriented approach to come to proper conclusions about this kind of question. For instance, you need to know that Texas’s delegate allocation is quite proportional, while New Jersey’s is strictly winner-take-all based on the statewide vote, while California is mostly winner-take-all by Congressional district. And most states have some kind of twist in their rules — proportional states can become winner-take-all if candidates meet (or their opponents fail to achieve) certain vote thresholds.

What follows is an attempt to project the delegate total in the remaining states. First, we’ll look at a “baseline case”, which assumes that the status quo is mostly preserved — except that Newt Gingrich drops out of the race after Alabama and Mississippi vote. Then we’ll look at a couple of cases that are more favorable to Mr. Santorum.

The first step in projecting the delegate totals is to come to a prediction of the popular vote in each state. Of course, this is challenging, so I’m looking at a couple of different things to make my guesses.

First, I’ve done some regression analysis that spits out a projection based on how previous states have voted, looking at characteristics like the fund-raising achieved by each candidate in the state, how conservative the Republicans are there, and so forth. The reason I’m not relying solely on these numbers is because this is a classic case where data dredging and overfitting can corrupt predictions. Still, it’s a useful reference point.

Second, I’m looking at any polls that have been conducted in the state — although it’s important to consider when the poll was conducted. If it was taken at a time when Mr. Santorum was doing especially well in national surveys, for instance, then some of his performance will reflect the national trend rather than anything intrinsic to the state.

Third, I’m looking at the geography — how have neighboring states voted, especially if they have similar demographics?

But there is some subjectivity involved — and some consideration of special circumstances. Rick Santorum is going to do a little better than the demographics might suggest in Pennsylvania, since it’s his home state. Ron Paul might get some bonus points in Kentucky, since his son was elected to the Senate from there. Mr. Romney might do well in territorial causes, since very few people participate in them and they tend to reflect the preferences of Republican party leaders — who mostly favor Mr. Romney this year.

Many states also allocate some of their delegates by Congressional district, so this represents another challenge. I’m certainly not going district-by-district through every state. But I do have some sense for whether the districts in a state are relatively homogeneous (as in, say, Arkansas) or relatively heterogeneous (as in California). In the former case, narrower margins in the statewide vote should translate into more Congressional district wins, since the districts will behave more alike one another. In the latter, some districts might be insurmountable for a candidate even if he is doing well statewide.

After predicting the popular vote, I apply the rules in each state to allocate the delegates. In cases where some or all delegates are chosen at caucuses or conventions, I assume that the delegates won there are proportional to the statewide popular vote, although that certainly won’t always be the case.

Here’s what I came up with for the baseline case:

I don’t think any of the calls I am making in individual states are especially controversial, but a couple are worth mentioning. I see Wisconsin as a pretty good Santorum state; Mr. Romney has tended to poll very badly there, he’s raised very little money there and he had a poor performance in neighboring Minnesota. And I think Mr. Santorum is the favorite in his home state of Pennsylvania.

I found Montana and New Mexico to be tough states to call — they sit at the frontier of places where Mr. Santorum has performed well and those where Mr. Romney has. I gave a slight edge to Mr. Romney in both states in the baseline case, although this does not matter so much since they both allocate their delegates in a relatively proportional way.

Over all, the baseline case implies that Mr. Romney will beat Mr. Santorum by about 5 points in the popular vote from this point forward. That figure jibes pretty nicely with the analysis I posted on Thursday about what might happen if Mr. Gingrich were to drop out of the race, as this situation assumes.

However, this small advantage in votes would translate into a relatively clear advantage for Mr. Romney in delegates. He would secure another 741 delegates in the remaining contests, versus 505 for Mr. Santorum. When combined with the delegates he already has — 421, according to the Associated Press count — that would put him over the threshold of 1,144 delegates required to clinch the race after the Utah primary on June 26.

In practice, Mr. Romney’s victory would probably come sooner. There are a lot of undeclared super delegates — plus some other unbound delegates who are chosen by state party officials — who are likely to align themselves with him if he maintains something like his current trajectory. So the 225 delegates he is projected to win on June 5 — mostly in California and New Jersey — would probably seal it for him.

Or it could be sooner still if all of Mr. Romney’s viable opponents were to drop out. One opportunity might be after April 3 if Mr. Romney had wins in both Maryland and Wisconsin. Or it could be after April 24, when Mr. Romney should win a large number of delegates in a set of Northeast
ern states — although he may well lose Pennsylvania. If the status quo persists, the writing on the wall should become clearer and clearer to Mr. Romney’s opponents. And there is the chance that Mr. Romney will beat these projections, putting pressure on his opponents — winning Alabama or Mississippi on Tuesday, for instance, could help Mr. Romney to put an end to the race quickly.

Suppose, however, that Mr. Santorum beats his numbers instead. Specifically, suppose that he gets 5 percent more of the vote in each state than under the baseline case, and that Mr. Romney gets 5 percent less.

This would flip four states to Mr. Santorum: Illinois, Delaware (more important than you might think since it’s strictly winner-take-all), Montana and New Mexico. But how would it affect the delegate math?

Under this possibility, Mr. Santorum would run slightly ahead of Mr. Romney in delegates for the remainder of the race, winning 643 to Mr. Romney’s 610.

But this would not be enough to give Mr. Santorum the overall lead given Mr. Romney’s advantage so far. In fact, he would not be particularly close to it. Mr. Santorum would have 824 delegates after Utah, and Mr. Romney would have 1,031.

That would, however, still leave Mr. Romney short of a majority — he’d be 113 delegates shy of the magic number of 1,144.

Does that mean we would be headed to a brokered convention? In my view, probably not quite. There would still be enough superdelegates and other unpledged delegates to put Mr. Romney over the top; he would need the support of about two-thirds of them.

My guess is that he would probably get it, mostly because there was no better alternative. Mr. Romney would need a lot of help in this case. But he would not need as much help as Mr. Santorum. Even if Mr. Santorum won all the unpledged delegates, plus all of Mr. Gingrich’s delegates, that would leave him at 1,127, still just shy of a majority. So a Santorum nomination would require a brokered convention, while one for Mr. Romney would not. That is a pretty powerful reason for the unpledged delegates to align behind Mr. Romney.

Nor would Mr. Santorum have all that strong an argument that the party should act against the delegate plurality. Mr. Romney would have won more popular votes, although barely, and he would have won quite a few more delegates. He would actually have lost the majority of states, but he would have won a number of key ones — this is why his victories in Michigan, Ohio and Florida were so important. It would be ugly, but he would probably win the nomination, and probably before the convention.

In fact, I’d guess that this represents roughly the outer limit of how much support Mr. Romney could lose before getting into serious trouble.

The flip-side is that even if Mr. Santorum starts to win marginal states like Illinois and New Mexico, he still probably won’t have either the delegates or the strongest argument for the nomination.

This is why I call Illinois a “must-win” for Mr. Santorum. Winning that state would be about the minimum he’d need to do to put Mr. Romney’s nomination into some real doubt.

However, if Mr. Romney takes any further losses than that, the dam would start to break. Suppose that we give Mr. Santorum another 5 points worth of support in each state, taken from Mr. Romney’s column:

Now we begin to see some truly shocking losses for Mr. Romney, most notably California, which he’d lose by a single point. He’d also lose Maryland, Oregon and Hawaii, although the latter to Mr. Paul rather than Mr. Santorum.

Nor would Mr. Romney maintain his advantage in the delegate count. Mr. Santorum would have 974 delegates to Mr. Romney’s 865 after Utah voted. Mr. Santorum would also have a material advantage in the overall popular vote.

And yet, even under this case — even if Mr. Santorum won Illinois, Maryland, Montana, New Mexico and Oregon, and won California or essentially battled Mr. Romney to a draw there — he’d still be quite a bit shy of the delegate majority. He’d need to win literally every available unpledged delegate, which would give him 1,144 exactly, and odds are that at least some of these delegates would have committed to one of Mr. Santorum’s opponents well ahead of the convention.

This does not mean that Mr. Santorum would fail to become the nominee — he’d certainly have a much stronger case for it than Mr. Romney in this situation — but it probably would require a brokered convention.

Of course, a brokered convention would also introduce the possibility of a new candidate, like Jeb Bush or Paul Ryan, being given the nomination. If Mr. Santorum had really done this well — winning California, for instance, along with the clear majority of states that voted from this point onward — I would assume that he would have a considerably stronger argument than any of them. The sweet spot for a dark-horse nominee, instead, might lie somewhere between the second and third possibilities, where Mr. Romney and Mr. Santorum had roughly an equal number of delegates and both were shy of a majority.

But let’s take a step back. To contemplate Mr. Santorum winning the nomination, you probably have to contemplate him winning a state like California. He might not literally have to win it; losing it by a couple of points would still imply grave problems for Mr. Romney. But he’d probably have to come close.

Just how likely is that? Some of the polls in California have shown a reasonably tight race. But they were conducted a time when Mr. Santorum was running much stronger nationally than he is now, and this neglects the effect of the actual campaign. California is a state where Mr. Romney’s advertising advantages would pay dividends, as well as his campaign’s skill in microtargeting voters, especially since most of the state’s delegates are allocated by Congressional district.

Of course, if Mr. Romney were being given a run for his money in California, that would mean that something had gone seriously wrong with his campaign. He would be an underdog to be the nominee under these circumstances, although whether Mr. Santorum or a dark-horse candidate was the more likely alternative is another question.

This, however, is not meant to cast Mr. Santorum’s path to the nomination in favorable light. He is no longer at the point where he can win the nomination just by winning the marginal states, or even the “l
ean Romney” states like Illinois. Instead, he’ll have to profoundly alter the dynamics of the race and cause embarrassing losses for Mr. Romney that would cause voters to consider him damaged goods.

It is hard to know exactly how likely that is — other than that the probability is certainty low. Whether it’s a 10 percent chance or a 1 percent chance, I don’t quite know.

And it will certainly not be enough for Mr. Santorum to merely hold serve. If he wins Mississippi and Alabama and Missouri and Kansas this month, but Mr. Romney wins Illinois, that will be fairly consistent with how the states have behaved thus far. It will just so happen that a number of Mr. Romney’s poorer states will have come in a row, as Barack Obama had rough stretches against Hillary Rodham Clinton in 2008 when states like West Virginia and Kentucky voted. One should not confuse the deviations caused by the order in which states vote for momentum.

Instead, Mr. Santorum’s path to the nomination probably involves generating some real momentum by sweeping just about everything in March — other than perhaps Puerto Rico, Hawaii, and the territorial caucuses. If he won Illinois on March 20, for instance, and then followed it up with an April 3 result in which he won Wisconsin clearly and if Maryland was close, that’s about the point in which Mr. Romney would be in extreme danger. It’s not impossible, but Mr. Santorum has a very high bar to clear.

Nate Silver founded and was the editor in chief of FiveThirtyEight.