These 9 Slides Show the Surprisingly Low Impact of Libertarian Candidates

Almost no one seriously thinks that Sean Haugh will be the next senator from North Carolina. But political observers in both major parties are worried that the pizza deliveryman and Libertarian candidate could siphon enough votes to sway the election, likely to be one of the closest in the country on Tuesday. And stakes couldn’t be higher: any one election could determine control of the Senate in 2015.

But which party has more to fear from Haugh? Kentucky Senator Rand Paul campaigned for Republican nominee Thom Tillis in early October, a move seen as an attempt to shore up Libertarian-leaning Republican voters. More recently, the American Future Fund, a conservative outside spending group, bet $225,000 that Haugh could flip the election in the Republicans’ with an ad campaign focused on his unembarrassed enthusiasm for marijuana, aimed to draw away younger supporters of Democratic incumbent Kay Hagan.

Though Haugh is currently polling at around 5 percent—more than the margin between Tillis and Hagan—he is very unlikely to spoil anything other than the hopes of a few misled pot smokers. While the threat of spoiler candidates makes for breathless headlines and titillating front-page reads, the real odds of this happening are extremely slim.

For starters, it is very rare for a Congressional contest to be decided by a margin small enough for a third-party candidate to make a difference. Of the 1,873 elections that TIME examined—every House and Senate race going back to 2006, not including special elections and runoffs—only 70 were won with less than 50 percent of the vote. A Libertarian candidate ran in 46 of them.

The threat of a spoiler candidate is further exaggerated by the common assumption that third-party voters would otherwise turn up at the polls at all.

“That’s the old style to think about voting,” says Stanford professor Jon Krosnick, a social psychologist and polling expert. “We’ve now come to recognize that the candidates influence turnout. The presence of the third-party candidate can lure people to vote who otherwise wouldn’t have voted at all.”

It’s impossible to know with any precision how people would have behaved without the presence of a third-party candidate. Even asking them in polls is unreliable, given that pollsters typically report unrealistically high turnout figures when they ask people if they voted.

The picture is confounded yet further by the fact that a distaste for the major parties is often the motivation that draw a person to a third-party candidate in the first place.

That’s a view shared by Emily Salvette, who drew 10,630 votes as a Libertarian in the 2012 race for Michigan’s 1st District. “I do honestly think that a lot of people wouldn’t have voted,” she says. “They’re not engaged anymore because they don’t like the choice.” The Republican in that contest, Congressman Dan Benishek, edged out his Democratic challenger by 1,881 votes.

Depending whose base you think Salvette drew from, you might call her either a spoiler or nearly one. But Salvette says she saw support from voters with a variety of viewpoints, including people who supported her views on everything from medical marijuana to gun rights.

This is where the spoiler math falls apart: 1,881 votes doesn’t seem like a large share of Salvette’s 10,630. But to tip the election to the Democrat, every single one of the people who voted for Salvette would have had to show up had Salvette not been in the race—very unlikely—and they would have had to break for the Democrat by a sizable margin of 59-41. The fewer voters that show up, the larger that margin needs to be.

Of course, it is typically the Republican candidate who feels more threatened by a Libertarian in the race.

“Republicans think that the Libertarian vote comes out of their column,” says University of Virginia political scientist Larry Sabato. In fact, there’s evidence from exit polls in the 2013 Virginia governor’s race that Libertarian Robert Sarvis, who garnered 145,762 votes in a race decided by about 55,000, drew more support from winner Terry McAuliffe, the Democrat, than from Republican Ken Cuccinelli. The majority of Sarvis’ supporters said they otherwise would not have voted.

It’s certainly possible to find more compelling cases for spoilers. In 2012, Democrat Jim Matheson beat challenger Mia Love in Utah’s 4th District by 768 votes, while Libertarian Jim Vein received 6,439 votes—and earned some unkind attention from Republicans before the votes were fully counted. Even so, half of Vein’s voters would have needed to show up without him in the race, those supporters would have had to vote for Love over Matheson by at least a 61-39 margin to make a difference.

Even the most famous supposed spoiler in modern history–the 2000 presidential election in Florida–is less clear-cut than most of us recall. One statistical analysis of polls and ballot returns suggests that Nader’s supporters would only have broken for Gore over Bush by a 60-40 margin, if they broke for either candidate. That many of Nader’s supporters would otherwise have turned out and supported either major-party candidate is far from established.

When an election is that close, blaming a third-party candidate is the electoral equivalent of blaming Bill Buckner for spoiling the 1986 World Series for the Boston Red Sox: It is merely the most visible excuse for a loss that could have been reversed if one of a thousand factors had gone just a little better.