On July 1st Sir Ed Davey, the leader of the Liberal Democrats, performed another publicity-seeking stunt in a campaign full of them—bungee jumping. Dangling by his ankles, Sir Ed shouted: “Do something you’ve never done before: vote Liberal Democrat!” It is far from the likeliest outcome but the Liberal Democrats could be about to do something they have never done in the post-war era: become the official opposition.

The Liberal Democrats are on track for at least their best result since 2010; the central estimate of The Economist’s prediction model has them winning 48 seats on July 4th. But the party could easily pull off a greater shock: there is a small but significant chance that Sir Ed’s party overtakes the Conservative Party in terms of seats. Our model gives the Liberal Democrats a 13.4% chance of becoming the official opposition. Betting markets give the party a one-in-five chance. For a once-in-a-century-type event, these are remarkably short odds.