About two and a half hours after polls closed in Pennsylvania’s 18th Congressional District special election last month, it was clear that the race was close but that Democrat Conor Lamb was going to defeat Republican Rick Saccone. At about that time, Lamb’s Libertarian opponent, Drew Miller, tweeted, “We’re only a few hours away from me being the most hated man in America #PA18.”

Miller was referring to the fact that his vote margin was greater than the difference between the top two candidates. It is true that had all of Miller’s voters instead cast ballots for Saccone, the Republican would have eked out a victory. But does this mean Miller was a “spoiler,” ruining Saccone’s chance to continue the GOP’s hold on the district? The answer is no, not without making some pretty herculean assumptions about Miller voters.

In order for Miller to actually have been a spoiler, he would have had to earn support from a certain (and very rare) type of voter. They’d had to have 1) wanted to vote differently had they known the race was close, 2) sincerely liked the Republican better than the Democrat, and 3) been willing to turn out to vote even if they weren’t voting for Miller.

But it was comparatively just a handful of votes — 627 at last count — between Lamb and Saccone. Sure, the assumptions are tough to meet, but they would certainly apply to at least some Miller voters. Might it be enough? It turns out, almost certainly no. In fact, there is very little room for error.

While we cannot run a counterfactual election without Drew Miller, we can calculate the scenarios that would need to happen in order for Rick Saccone to win Pennsylvania’s 18th. We take the actual vote total for each candidate and then suppose Miller is no longer on the ballot. His 1,379 voters have two choices: stay home or select another candidate. If they choose to select another candidate, they have two choices: Saccone or Lamb.

Therefore, we can take any possible level of Miller voter turnout and any possible Saccone vote share among those Miller voters who turn out and generate, for a given combination of turnout and voting proportion, a new vote total for each of the two remaining candidates. In other words, if half of Miller’s supporters turn out and 75 percent of them vote for Saccone, we can add 0.5 x 0.75 x 1,379 = 517 votes to Saccone’s total (and 172 to Lamb’s total, not enough to eke out a Saccone victory).

In order for Miller to actually have been a spoiler, he would have had to earn support from a certain (and very rare) type of voter. They’d had to have 1) wanted to vote differently had they known the race was close, 2) sincerely liked the Republican better than the Democrat, and 3) been willing to turn out to vote even if they weren’t voting for Miller.

To help visualize the possible outcomes of the election, the plot below displays the ranges of turnout for Miller voters and proportion voting for Saccone. The area in blue represents combinations in which Lamb would still win, while the area in red represents combinations where the race would go to Saccone instead. The solid black curve marks minimum turnout-voting proportion combinations that would lead to a Saccone victory.

Because Connor Lamb already has a lead of 627 votes and there are only 1,379 Miller votes, most combinations of libertarian turnout and libertarian votes for Saccone still lead to a Lamb victory. In fact, it would be impossible for Saccone to win if fewer than 46 percent of Miller voters turned out, and at this level of turnout, Saccone would have to have received 100 percent of those votes to win.

In the event that every single one of Miller’s voters still turned out, Saccone would have had to receive 73 percent of these votes to win the election. You can select your own value of either turnout or voting proportion that you think is realistic and see what value of the other variable would be required. For instance, if you think that 80 percent of Miller voters would still turn out, then you would see that Saccone would have to get around 79 percent of those votes to win the election. This might allow us to better understand how our assumptions map to actual electoral outcomes.

In other words, one would have to believe that all three assumptions are true for nearly all of Miller’s voters. And Miller’s voters are an unusual bunch, given that most voters do not bother to turn out in most elections. These voters braved western Pennsylvania snow squalls to get to their polling places. They did so to cast one vote in the sole race on the special election ballot. They likely knew the race was close. And still, they cast that vote for a candidate who had no hope of winning. The idea that nearly all of them would just as soon vote for Saccone seems unlikely.

Kevin Greene is a graduate student in the department of political science at the University of Pittsburgh. Kristin Kanthak is an associate professor of political science at the University of Pittsburgh and co-editor of State Politics and Policy Quarterly.