Just when you’d almost forgotten they existed, the Liberal Democrats have come crashing back. In last night’s local elections, Vince Cable’s party – against all expectations – managed not only to win back Richmond and hold onto Sutton, Eastleigh and Cheltenham, but also make gains in leave voting Sunderland and Hull. A Thrasher projection has suggested that if last night had been a general election, the Liberal Democrats would have won 14 new seats in the Commons.

And about time too. After the party’s disastrous performance in 2015, there was a general belief among optimistic activists that with a new leader, they would rise – phoenix like – from the ashes of Nick Clegg’s coaltion. It didn’t happen. In fact, if anything, the party slipped even further out of public consciousness.

In a YouGov poll at the beginning of this year, 35% percent of participants said that they “didn’t know” when asked to choose a Prime Minister between Jeremy Corbyn or Theresa May – a more popular answer than either of the two leaders. This generous third of the population should have been low hanging fruit for the Lib Dems, but for one reason or another, they resisted Vince Cable’s advances.

So, why the sudden reversal of fortune? Here are a few thoughts.

1. Liberal Democrats take local elections seriously – and almost always do disproportionately well in them.

Lib Dem MPs are more likely than any others to come up through the local councillor route, and it was liberal democrats who popularised the tradition of candidates having some sort of connection to the area they are trying to represent. While the main parties get preoccupied discussing ivory tower politics, Liberal Democrats traditionally concentrate on electing hardworking local representatives – who fight tooth and nail for their area.

2. The party has quietened down (a bit) on Brexit.

For the past 18 months, the Westminster Liberal Democrats (and Nick Clegg) have put all their might into fighting against Brexit in a very specific way which never had – and never will have – mass appeal. Unlike the vast majority of remain voters, who voted to stay in practical reasons and are now resigned to Brexit and bored by it, Clegg et al voted to remain because they feel a deep and visceral affiliation with the European project and the EU.

Despite what Twitter (a platform dedicated to artificially curating an identity) would have us believe, most ordinary people don’t think too much about their cultural identity – and those who do are statistically far more likely to gravitate towards their nation state. Even among those who want the referendum result to be overturned, the Liberal Democrats impassioned speeches about Patriotic Europeanism fall flat.

It was the Tories who used the slogan “bins not Brexit” for these local elections, but the Liberal Democrats were clearly listening. In Leave voting Sunderland, councillors avoided mentioning the referendum result, concentrating instead on domestic and local policies.

With Brexit now very definitely happening, the party – at last – seems to have worked out that to stay relevant, it must talk about something else.

3. They are picking up Liberal Conservative votes

When Theresa May took over from David Cameron, it was clear that the Conservative Party was moving in a less liberal direction. On social policy, May is tough on drug control, staunchly supports immigration targets, and believes in measures like the sugar tax to improve national health. Economically, she has only a passing interest in the free market – and sways towards protectionism.

In her original cabinet, there were four liberal Conservative ministers to balance these instincts: Justine Greening, Damian Green, Amber Rudd, and Michael Gove.

Now, only one of them remains.

Liberal Conservatives who supported David Cameron are politically homeless – and it’s no wonder they’re moving towards the Liberal Democrats.

After a gruelling three years, Vince Cable has every right to look smug today. A year ago, there were predictions his party might collapse entirely before the next election. Now, there’s a chance he could be a kingmaker.