On January 7, Ross Douthat of The New York Times wrote a column entitled “How Donald Trump Loses.” In it, Douthat argues that however strong Donald Trump’s support seems now, his chances of being the Republican nominee remain vanishingly small. This argument has been made countless times, with multiple pundits predicting an eventual drop in Trump’s polls. More interestingly, though, Douthat claims that even if Trump maintains his current level of support — around 30 percent in the early states — throughout the primaries, he still has no path to the nomination. According to Douthat, “for Trump to lose, he doesn’t actually have to collapse; he just has to fail to expand his support.”

This second claim seemed controversial to me. After all, 22 of the Republican nominating contests can be loosely described as winner-take-all, combining for 1,418 bound delegates. To win the nomination on the first ballot at the Republican National Convention, a candidate needs only 1,236 delegates. Trump will almost certainly win a significant number of delegates in the 36 states and territories that award delegates proportionally; it seems, then, that he might only need to win a few winner-take-all states in order to reach the magic number. With the Republican contest as fractured as it is, it appears possible that Trump could win enough states with 30 percent of the vote to clinch the nomination.

I decided to test Douthat’s claim by creating a model to simulate the Republican primaries (R Code Included at Bottom of Article). This model is built on several assumptions:

Cruz’s eventual support can be approximated by aggregating the polling numbers of the most conservative candidates (Cruz, Carson, Fiorina, Huckabee, Santorum, and Paul). The emergent establishment candidate’s support can be approximately by combining the polling numbers of Jeb Bush, John Kasich, Marco Rubio, and Chris Christie. The 22 states and territories loosely titled as “winner-take-all” will in fact each award all of their bound delegates to a single candidate. This is a flawed assumption, because most of these states actually award only a fixed number of delegates to the statewide winner, allocating the remainder to the winners of each congressional district in the state. However, this sort of assumption is needed to create the simple model I am looking for. Moreover, though a statewide winner might not win every congressional district in a single state, they might offset those losses by picking off a few congressional districts in other “winner-take-all” states. Thus, the “winner-take-all” assumption is probably more accurate than it might initially seem. The 36 states and territories that award their delegates proportionally will do so invariably. This is also an imperfect assumption; some of these states do not award any delegates to candidates who do not receive some minimum percentage of the statewide vote (such as 10 percent). However, for simplicity’s sake, we will assume that the candidates still in the race always meet this threshold, and are thus always allocated their proportionate share of delegates.

In addition to this first model, I also prepared a model for a campaign in which two establishment candidates remain in the race throughout the primaries. This second scenario might occur if, for example, Chris Christie were to win the New Hampshire primary. Since Christie is still somewhat politically damaged, it is entirely possible that an additional establishment candidate (such as Rubio) could still see a path to the nomination. In this second model, I assume that the two establishment candidates split the moderate or pragmatic Republican vote evenly.

I used 12 recent early-state polls listed on the website RealClearPolitics to gauge current support for Trump, Cruz (plus the other far-right candidates), and the establishment candidates. I considered early-state polls rather than national polls when determining each candidate’s status, because they are generally considered a more accurate description of how voters truly feel about the candidates. Individuals in Iowa, New Hampshire, and South Carolina are paying closer attention to the candidates than people are nationally, and their opinions are currently better informed. The 12 polls I included were five of the most recent polls from both Iowa and New Hampshire, in addition to two of the most recent polls from South Carolina. I averaged the results of these 12 polls for each candidate, and took their standard deviation. Using this data, I created normal distributions for each candidate’s average support. Random draws from these distributions would determine a candidate’s final vote share in each state.

Using these two models, I simulated the number of delegates each candidate would win if they entered the Republican primaries 10,000 times and maintained their current level of support throughout. Histograms describing delegate distribution appear below.

As the above histograms show, Trump has almost no chance of winning the Republican nomination if he only maintains his current level of support. In fact, in only one of 20,000 simulated elections did Trump achieve the requisite 1,236 delegates outright, and that was with two establishment candidates splitting the moderate vote. The most delegates he managed to win in the first model (one establishment candidate) was a mere 1,018.

Moreover, in both of the models, the establishment candidate failed to ever garner enough delegates to win the nomination outright. In the first model, the high-water mark for the establishment candidate was 1,207 delegates, while in the second, that number was 410. By contrast, Ted Cruz won the nomination outright 105 times (1.05 percent of simulations) in the first model, and 1,196 times (11.96 percent of simulations) in the second model. This indicates that Cruz is most likely to win the nomination without a brokered convention.

In the vast majority of cases, however, the models suggest that no candidate will win enough bound delegates to claim the nomination before the convention. According to the prevailing wisdom of the day, this would seem to favor the emergent establishment candidate. After all, the individuals who run the RNC are, quite literally, the Republican establishment, and if they get to decide the matter, they would most likely selected a candidate similarly oriented. Furthermore, establishment candidates are generally perceived to be more electable by top Republican decision-makers, which could be the deciding factor in selecting a nominee at a brokered convention. Both factors would benefit the leading establishment candidate in the event that no one wins the Republican nomination outright.

Donald Trump, on the other hand, would most certainly be at a disadvantage during a brokered convention. Republican Party operatives believe that Trump poses a serious, if not existential threat to the party. They fear that with Trump atop the ticket, the Republicans would lose not only the Presidency, but most down-ballot races. The U.S Senate would likely return to Democratic control, and even the House of Representatives might be up for grabs. With these potential consequences, it is hard to imagine a convention fight leading to Trump’s nomination. Thus, it appears Ross Douthat was right. Trump has basically no chance of winning the Republican nomination outright if his support merely stabilizes, and the odds of his winning a brokered convention are astronomically low. If the status quo holds, Trump will not be on the ballot as a Republican in November.

***