Earlier this morning an alert reader directed us to an article in the Daily Express which seemed to make an eye-catchingly remarkable claim. It turned out to be one actually made by Ruth Davidson on Saturday (which had already been reported in the Express that day), when she appeared on Iain Dale’s radio show on LBC.

A 27% swing? From the SNP to the Tories? Putting the Tories AHEAD in the polls? That would be such a stupendously Earth-shattering development in Scottish politics that you’d think the media would have made more of it than a couple of mentions in an embarrassing low-circulation comic like the Express.

So we thought we’d better check.

It took a bit of hunting, but we found the show eventually.

And sure enough, she said it:

“We’re seeing in Scotland now a big shift in the polls. I think the last poll for the Times just yesterday showed a 27% swing between the election of 2015 and now, between the SNP and the Conservatives.”

In the 2015 election the SNP got 50% of the vote to the Tories’ 14.9%. The definition of “swing” in political terms is a clear-cut one: it means the sum of the differences in each party’s vote shares at the two points of comparison, divided by two. By way of example, here’s the Glasgow North East result at that election and in 2010.

You can see that the SNP vote share increased by 44 points (14.1 to 58.1), while the Labour share decreased by 34.6 points (68.3 to 33.7). So we add those two numbers together to get 78.6 (which is the margin change), then halve it to get to the figure of 39.3% that’s the actual swing from Labour to the SNP.

For the 2015 general election result to undergo a 27% swing would mean the SNP lead of 35.1 points in 2015 having to become a Tory lead of 18.9 points today. (Because for the swing to be 27 the margin change has to be 27×2, which is 54.)

But despite the bewilderingly insane headline in the Express, that quite plainly hasn’t happened. So we had a look in Friday’s Times, and what it actually reported was a poll that put the Tories on 28% and the SNP on 41%. That’s an SNP lead of 13 points, which is a 22-point margin change, and therefore a swing of just 11% rather than the 27% claimed by Davidson.

We can find no combination of figures anywhere in the poll findings which produce the number 27 in any context at all. (The SNP are down by nine points, which you could also express as 18% of their 2015 vote share. The Tory vote, meanwhile, is up by 13 points, which is an 87% improvement. The points margin is down by 63%. We banged all those numbers together pretty hard but couldn’t get them to form a 27.)

There are no detectable routes by which Davidson could have arrived at that figure, so far as we can tell. She hasn’t mistaken/mis-spoken a margin shift for a swing. She’s simply exaggerated the reality by a rather impressive 145% for the sheer heck of it, confident that nobody would challenge her.

We’d have done it sooner, but we try not to read the Express if we can help it.