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The most unusual general election races in Texas are the competitive ones, and in those, third-party candidates can have an outsize influence.

But in a bizarre turn of fate, the most reliable source of third-party candidates — the Libertarian Party of Texas — didn't field contestants in most of the state’s few remaining swing districts.

It’s always hard to tell which party that might help, but the folklore in Texas — i.e., what many politicians and consultants will tell you — is that votes for Libertarian candidates come disproportionately out of the Republican column.

Since 2002, at least a dozen congressional and legislative seats in the state have flipped from one party to another after races that included third-party candidates.

Those races were in competitive districts where the field included either Libertarian or Green Party candidates (or both) along with Republicans and Democrats. The victors won by fewer than four percentage points.

After the political maps were redrawn in 2001, the Green Party played its only significant role in a recent Texas legislative election. Democrat Patrick Rose of Dripping Springs won the 45th House district by 335 votes out of 38,170 cast. The Green Party candidate in that race, John Schmidt, had 1,239 votes — more than enough to swing the race. The loser that year was incumbent Republican Rick Green.

John Wilford, chairman of the Libertarian Party of Texas, points to three examples of past elections he believes were swung by Libertarian candidates.

In 2010, Republican Blake Farenthold beat the incumbent U.S. Rep. Solomon Ortiz, D-Corpus Christi, by 775 votes. The Libertarian candidate, Ed Mishou, garnered 5,372 votes.

In that same year’s race in HD-47, Republican Paul Workman defeated Democratic state Rep. Valinda Bolton in a district that covers parts of western Travis County. Libertarian Kris Bailey got 4.13 percent.

And in the 2004 race in HD-50 in Northeast Travis County in which Democrat Mark Strama got 569 more votes than Republican state Rep. Jack Stick, the Libertarian in that one, Greg Knowles, had 2,390 votes — more than enough to cover that margin.

Conventional wisdom notwithstanding, Wilford contends Libertarians pull from both Democrats and Republicans. He says that makes it hard to tell who might have won without them in the races.

This year, the chances have narrowed because nearly all of the Libertarian candidates in state legislative races signed up for districts where either the Democrat or the Republican candidate is a prohibitive favorite.

The party’s candidates also figured in back-to-back state legislative races where Corpus Christi-area incumbents were defeated. In 2006, Democrat Juan Garcia beat Republican state Rep. Gene Seaman by 767 votes. Libertarian Lenard Nelson received 2,038 votes. The GOP snatched it back in 2008, when Todd Hunter, a former Democrat running as a Republican, beat Garcia by 1,850 votes. Nelson, running again, received 1,705 votes.

This year, the chances have narrowed because nearly all of the Libertarian candidates in state legislative races signed up for districts where either the Democrat or the Republican candidate is a prohibitive favorite.

An exception is Ruben Corvalan, a San Antonio engineering consultant running as a Libertarian in the 23rd Congressional District, a piece of geography that neither of the major parties seems able to control for more than two years at a time. He’ll face U.S. Rep. Will Hurd, R-San Antonio, and Democrat Pete Gallego of Alpine, who lost the seat to Hurd in 2014.

Other than that, the Libertarians are absent in nearly a dozen races that — on paper — seem to be competitive in the Texas House.

They could still have some influence in other contests. The party has two former Republican governors — Gary Johnson of New Mexico and William Weld of Massachusetts — running for president and vice president in a year when the apparent Republican and Democratic nominees are remarkably unpopular.

Texas libertarians are running a full slate of statewide candidates, too, for the Texas Railroad Commission and for three spots each on the Texas Supreme Court and the Texas Court of Criminal Appeals. The party also has contestants for three State Board of Education seats.

Results in those races have been more lopsided than legislative races in recent elections — although big numbers from someone other than a Democrat or Republican could still dramatically change a statewide race.

In the 1992 race for president, Dallas businessman Ross Perot ran as an independent and won 22 percent of the vote in Texas. Democrat Bill Clinton got 37.1 percent, more than 6 percentage points less than Democrat Michael Dukakis received four years earlier. The incumbent president from Texas, George H.W. Bush, escaped with 40.6 percent, a drop from the 56 percent he received in his 1988 race against Michael Dukakis. One big difference is that no third-party candidate had a significant following in that earlier election.

In this year’s competitive statehouse races, it looks like that’s one problem GOP candidates won’t have to deal with.

Catherine Wendlandt provided research assistance for this story.