Supporters of UKIP and the Green Party left their pre-election conferences confident they are on track to cause a political earthquake on 7 May and decide the course of the next government. They are half right.

The advance of the two parties, from opposite ends of the political spectrum, changes the dynamic in about a fifth of the 650 seats in the Parliament by threatening to siphon off votes from the two main parties, the Conservatives and Labour. But as the ballots are counted, the surge is unlikely to translate into more than a handful of seats, leaving them on the sidelines when it comes to in any coalition negotiations.

“There’s an expectations management problem,” said Matthew Goodwin, co-author of Revolt on the Right, a study of the rise of UKIP. “Activists are measuring the curtains for Downing Street, but UKIP will do well to win six seats.”

The vote promises to be the tightest since the 1970s, with any number of scenarios dictating who forms the next government. The electoral system is based on competing for individual seats, meaning vote share nationwide counts for nothing if candidates can’t win a majority.

Since 2010, when it won 3.1 percent of the vote and no seats, UKIP has ridden a tide of anger toward the main parties over the economy, immigration and relations with the European Union. It now polls in third place, with about 13 percent.

With the Greens, they account for more than 20 percent of the vote. The Greens won just one seat in 2010 and, despite competing in more than 500 in May, are unlikely to win any more. The Scottish National Party, by contrast, might take less than 4 percent of the U.K. national vote yet come away with as many as 50 seats, based on recent polling.

All three have rejected being part of a formal coalition, and instead have talked about selling their support in parliament on a vote-by-vote basis. At his party’s election launch on 12 February, UKIP leader Nigel Farage spoke of “campaigning” for policies rather than promising to deliver them, a marked contrast from some others in his party.

“I think what we can achieve 20 or 30 seats, and hold the balance of power,” Sue Ransome, 63, from Boston, a market town in Lincolnshire where many immigrants from eastern Europe have settled, said at the UKIP conference. “That’s how we’ll make a difference.”

Nigel Jones, the party’s candidate for Eastbourne, was a little less optimistic. “I’m pretty certain that we will get 10 to 12 seats,” he said. “We can be one of the brokers of power.”

There were similar voices at the Green’s gathering in Liverpool. Caroline Lucas, the party’s only MP, predicted an alliance with the Scottish and Welsh nationalists to drive an anti-austerity and anti-nuclear agenda.

“We can support Labour when they do the right thing, but block them when they try to ape the Tories,” Lucas said in her conference speech. “After this coming election we can do far more whether we have one Green MP or 10, we can be part of a progressive force for good.”

Should UKIP end up winning six seats, its influence is likely to matter only in very tight votes. Farage has ruled out supporting a Labour government, and he won’t have much to offer to Conservative leader David Cameron.

Two of those UKIP members would be likely to be former Tories Douglas Carswell and Mark Reckless, who both defected last year. Cameron might point out to Farage that even when they were in the Conservatives, voting records show they couldn’t be relied on to support the party’s policies.

That doesn’t mean that UKIP and the Greens aren’t important. They can upset results in tight seats by taking votes that other parties were counting on.

Goodwin, the author, estimates UKIP threatens the Conservatives in about 70 seats and Labour in 60. And if UKIP comes second in a large number of Labour seats, the party may reconsider its position on an EU referendum.

“The number of seats they can win is quite minor, the number of seats that they could complicate is quite large,” Andrew Russell, professor of politics at Manchester University, said. “You’ve then got the chance to influence the agenda of the other parties as well.”

At the Green conference, while some activists were realistic about their party’s prospects, others still said they believe power is in their grasp.

“Everyone’s going to be in for a surprise, we’re really going to put the other parties to shame this time,” said John Devine, 65, the Green candidate in Amber Valley in the Midlands. “There are so many people out there who are starting to look seriously at our policies.”