The Republican nomination race, as we have noted, has become less a battle between Mitt Romney and Rick Santorum and more one between Mr. Romney and the math: how certain is Mr. Romney to reach the 1,144 delegates required to clinch the nomination before the convention in Tampa, Fla., and when will he do it?
These are questions that can benefit from a detail-oriented approach — going state by state through the remaining contests and coming up with reasonable estimates of how many delegates Mr. Romney is likely to win in each one. Doing that suggests that Mr. Romney has a decent shot of coming up with the requisite number of delegates on June 5, when California, New Jersey and three other states vote — or if not then, on June 26, when Mr. Romney will almost certainly win all of Utah’s 40 delegates.
However, it is also helpful to think about the situation more holistically — particularly given that the delegate math may begin to affect the behavior of candidates and voters. For instance, if Mr. Romney is 39 delegates away from 1,144 before Utah votes, there would not be any real justification for Mr. Santorum to continue his campaign, because those 40 Utah delegates can safely be assumed to be in Mr. Romney’s column. (Mr. Romney won 89 percent of the vote in Utah in 2008.)
Long before California or Utah votes, meanwhile, Mr. Romney could reach other key thresholds that could change the context of the race — even if Mr. Romney is still technically short of a majority.
For instance, if Mr. Romney has clinched the plurality of delegates, that could have some bearing on the contest. It might suggest that even if the convention were contested, Mr. Romney would have the advantage on the floor. That, in turn, could dissuade voters who wanted to block Mr. Romney from following through with what would probably be a losing effort.
The threshold for Mr. Romney to hit a plurality of delegates is not a constant number — it changes based on how the delegates are distributed among the remaining candidates. However, it will always be lower than the majority threshold — right now, it would require 1,050 delegates, rather than 1,144. Moreover, the mathematics of this number are such that it can only get lower over time.
A third important threshold is when Mr. Romney would secure enough delegates to prevent any other candidate from getting a majority, even if he is not guaranteed one himself. If Mr. Romney achieves this mark, that means that no candidate except Mr. Romney could win the nomination before the convention. The academic literature suggests that once a candidate hits this threshold, it can sometimes signal the effective end of the race and serve as a victory condition.
This Romney-or-brokered-convention threshold, like the plurality threshold, changes. But it is lower still — right now, just 956 delegates, meaning that Mr. Romney is already more than halfway there.
We have developed an interactive feature that monitors these key boundaries — what I call Mr. Romney’s “magic numbers” — based on the current Associated Press delegate count. You can find that feature here.
In addition to telling you how many delegates Mr. Romney needs to reach these magic numbers, the application also evaluates them on a percentage basis. Right now, for instance, Mr. Romney would need 46 percent of the remaining delegates to clinch a majority, 38 percent to clinch a plurality, and just 31 percent to prevent any other candidate from reaching a majority.
So far, Mr. Romney has won 56 percent of the delegates awarded, so he is on pace to meet each of these thresholds. But the application allows you to stress-test his math by entering your own prediction for how many of the remaining delegates he might receive.
Suppose, for instance, that you think the “Etch A Sketch” comment made by one of Mr. Romney’s advisers could harm him. You predict that Mr. Romney, instead of winning 56 percent of the remaining delegates, will take just 49 percent.
That would still be enough for Mr. Romney to win the majority since he needs only 46 percent the rest of the way. But it would make his situation much more tenuous — with a slip-up in a key state like California, he could fall just short of it.
So the feature also asks you to enter a margin of error (or 95 percent confidence interval) for your prediction, and calculates the probability that Mr. Romney will meet each threshold based upon it.
For instance, if your best guess is that Mr. Romney will win 49 percent of the remaining delegates but your margin of error is plus or minus 10 percent, that would imply he has a 74 percent chance of reaching a majority before the convention — meaning that a contested convention is still a realistic possibility. (A technical note: this calculation assumes that the error in your forecast follows a bell curve, or normal distribution, which is an oversimplification in practice.)
It is hard to know what the “right” number for this margin of error calculation should be. But the feature is designed to let you experiment with it. If you think the race is likely to be volatile, you might set it fairly high. If you think the race has settled down into a more predictable pattern, you might tune it down. (By default, it is set to a fairly high number, plus or minus 15 percent.)
In general, I found that making these calculations tended to speak to the robustness of Mr. Romney’s lead. Under the model’s default settings — that he will win 56 percent of the remaining delegates, plus or minus 15 percent — Mr. Romney has a 91 percent chance of clinching a majority and a 99 percent chance of clinching a plurality. And it is already almost impossible for any candidate other than Mr. Romney to win a majority of delegates before Tampa — something that his opponents have started to acknowledge.
Still, if you have a different idea about the race — or if Mr. Romney’s advantage begins to narrow as the results from other states roll in — you can use this tool to see how much stress he could endure before a contested convention becomes more probable.