With all eyes on Donald Trump and Hillary Clinton, pundits haven’t had much time to focus on third-party candidates Jill Stein of the Green Party and libertarian Gary Johnson.

Do they even matter?

To their diehard supporters they do.  But unless either candidate manages to secure 15% of the vote in national polling, neither will qualify for the nationally televised debates beginning next month.  And with comparatively little funding and only mild interest from the mainstream media their overall impact on the race is likely to be marginal.

Still, there is some fear among Democrats, especially, that Stein or Johnson or possibly both could siphon off enough votes from Clinton to tilt a close race in a battleground state to Trump.  Remember 2000?  Consumer advocate Ralph Nader’s 3% of the vote was thought by some to have allowed George W. Bush to prevail over Al Gore in Florida – allowing Bush to win the state and the White House.  And many Democrats have considered Nader a “spoiler” ever since.

But there are a number of fallacies associated with the “spoiler” thesis.  First, it’s not clear that third-party voters have “second-order” preferences among the candidates of the two leading parties.  If their preferred upstart candidates weren’t on the ballot, most Stein or Johnson supporters might just join the enormous ranks of registered voters in both parties who don’t even bother to show up on election day.

Second, there are other voters groups in the election whose preferences are just as important if not more important than the presumed influence of third-party voters.  Gore, for example, failed to galvanize the Hispanic vote in Florida, while Bush suffered setbacks with African-Americans.  It’s tempting and easy for mainstream parties to scapegoat third-parties for their own inability to rally their base or to prevent voter disaffection.

Even if we accept the spoiler thesis, current polling suggests that Stein and Johnson’s influence is mixed, at best.  Their presence may favor Trump by 1-4 points nationally, or Clinton, in a few cases by a slighter margin — or they may have no influence either way.   In individual states, their influence seems to run in two different directions.

I analyzed 15 of the last national polls over the past month and found the following results:  In 4 of the 15 polls, the spread between Clinton and Trump was exactly the same whether Stein’s and Johnson’s share was included or not.

In another 5 of the 15 polls, the difference either way was just 1%.  For example, in the just-released McClatchy/Marist poll, Clinton led Trump by 15 points in a head-to-head match-up.  With Stein and Johnson included, she led by 14 points, a marginal difference.

In the remaining 6 polls the margin was larger, and in all but one case favored Trump, but the difference in the spread never exceeded 4 points –well within the polling margin of error.  In other words, there’s really no evidence that Stein and Johnson are influencing the race nationally at all – at least in a statistical sense.

What about the state races?   Consider the two most important battlegrounds:  In Florida, Trump appears to gain by 1.2 points on average when all four candidates are considered. In Ohio, it’s the reverse:  Clinton gains by 1.6 points, on average.

So, even if you believe in spoilers in 2016, the direction of the spoil could well vary.

It’s worth keeping in mind that no third-party candidate in recent times has ever been popular enough to capture a single state.  In 1992, Texas businessman H. Ross Perot wound up with 19% of the vote, and Republicans to this day still believe he cost George H.W. Bush his re-election – in part, because Perot had urged his supporters to back Clinton as a second choice.

In fact, exit polling revealed that Perot voters would have split their allegiances evenly – casting more doubt on the the spoiler thesis.

So, do third-party candidates even matter?  In shaping the debate, perhaps.  And though third parties typically criticize both parties, their anti-establishment message would seem to reinforce the anti-incumbent message of the party out of power, especially in a change election.  Arguably, that’s what happened in 1992, giving Clinton a slight edge after three straight terms of GOP control.

But don’t look to Stein or Johnson to help Trump, at least not across the board.  And not unless the two candidates receive a lot more media attention than they are getting now.