You cannot talk about Douglas Carswell for long in Westminster without hearing about his “personal vote”, the supposed popularity with which he is uniquely blessed and without which, whichever party he was currently a member of would certainly have lost.

That issue is front and centre now that Carswell has defected, this time quitting Ukip to sit as an independent. That leaves May with the question of whether to let him back into the Conservatives again.

There are lots of political reasons why that probably isn’t a great idea – it would annoy Conservative MPs who have stayed loyal, for one thing – but what if there is an electoral reason? What if Carswell’s personal vote is so large that he has to be accommodated?

Well, I’ve been looking at the numbers, and the long and the short of it is that talk of Carswell’s personal vote is mostly talk.

The idea that Carswell has a personal vote seems to rest on two, incredibly shaky foundations. The first is that he is uniquely popular in Clacton. I’ve visited Clacton, albeit some time ago, and it’s clear that, for all he doesn’t live in the seat, Carswell works it fairly hard and is respected for doing so. There were far more people who saw him as someone who put a shift in than when I did the same exercise for Zac Goldsmith.

But being respected for working hard and being a decent bloke isn’t the same as a personal vote. I found about the same level of gratitude towards Carswell on the doors as I did for Jeremy Corbyn in Islington North. Corbyn actually lives in his seat, unlike Carswell, and is widely agreed to be an exemplary constituency MP. But despite that, and despite being chair of the Stop the War coalition, he suffered the exact same Labour-to-Liberal-Democrat swing against him in 2005 as every other Labour MP in a seat of those demographics did. Being appreciated by the voters isn’t the same as the voters being beholden to you. (Just ask Winston Churchill.)

That’s the anecdotal stuff. It is true that Carswell increased his share of the vote and had a swing towards him in 2010 after his first term as an MP. There are a couple of things to note here: the first is that when Carswell ran for the seat of Clacton (then called Harwich), the Conservatives were led by Michael Howard, when he ran for re-election, they were led by David Cameron. Cameron had quite a big effect on the Conservatives’ electoral performance. They gained more parliamentary seats in 2010 than they did at any other election since 1931. There is a politician with the initials “DC” with something to brag about, but it ain’t Douglas Carswell.

It is true to say that Carswell slightly overran the national swing and the nationwide increase in the Tory vote from 2005 to 2010. But that was true of all but one of the 26 Conservatives who won seats from Labour in 2005 and contested the same seat in 2010. Psephologists call this the “sophomore swing”, and most politicians seeking re-election for the first time benefit from it, slightly overperforming colleagues who have served for longer.

Carswell’s performance was boosted by favourable boundary changes in which he lost Labour-leaning wards and gained Conservative-tinted ones, but he still finished middle of the pack, with the seventh-best swing. The biggest second-term swing was that secured by Peter Bone, who won his seat of Wellingborough by 687 votes in 2005 but had a majority of 11,787 in 2010, though like Carswell he benefited from favourable boundary changes. The best performers in materially unchanged seats: Justine Greening, Stephen Hammond, Philip Hollobone, and Philip Davies.)

Carswell also underperformed most of the 2005 Conservative intake on his first go-around, so his slightly larger than average 2010 performance may just have been reversion to the mean.

As for his heroics under Ukip colours, his seat had the most Ukip-friendly demographics of any constituency in the country, and he still managed a less impressive increase in his share of the vote than Mark Reckless, his fellow defector, pulled off in the Rochester and Strood by-election. In the following general election, he also suffered a bigger fall-off than Reckless did. (The Ukip vote in Clacton fell by 15 points, and by 12 in Rochester and Strood.)

So if you’re a frugal marker, you can make a persuasive case that Carswell has no personal vote at all, though I personally would shy away from that. It feels more likely to me that he has a small personal vote of about 0.5 to 1.5 per cent of the vote – which is more impressive than it sounds. Around 67,000 people vote in Clacton, so that’s still potentially a thousand people who would vote for Carswell regardless of his party. That’s not bad as it goes.

But that highlights the slight pointlessness of the debate about “personal votes” – even a really impressive personal vote of say, four per cent would only be about 2700 votes in Clacton. That’s not something you can win a parliamentary seat with or anything like it.

All of the evidence suggests that he has kept his seat thanks to the popularity of the party leaders he has consistently undermined and worked against, be they Michael Howard, David Cameron or Nigel Farage, not from his own appeal. If he retains it now he has left Ukip, it will be because it was in the gift of Theresa May.