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Lord Ashcroft, the billionaire Tory peer turned pollster, has released his third batch of Scottish constituency polls.

They are more stunning than the “sensational” first round of results he published two and a half months ago. They show that Jim Murphy, the leader of Scottish Labour, and Douglas Alexander, Labour’s shadow Foreign secretary, are both likely to lose their seats, and suggest Labour will lose almost all of their seats north of the border.

They also show that, despite an ‘incumbency effect’, Lib Dem MPs like Charles Kennedy and Jo Swinson also have little hope of keeping their seats, and that the Lib Dems will lose almost all of their 11 Scottish seats.

Our long-held view, that the SNP will have won at least 50 of Scotland’s 59 seats in three weeks time, has been strengthened by these numbers. There is nowhere where the SNP are not competitive, and there are few places where Ashcroft has not shown them in front.

After Ashcroft’s first batch of Scottish polls were leaked at midnight on February 4, we extrapolated them to suggest the SNP would win 56 seats, as per the graphic below. Since then May2015 has predicted 54-56 wins. (We will predict 55 wins after today’s results have been added, with three seats changing hands.)

Other forecasts have gradually inched up towards 50 seats. Elections Etc – a model run by the Oxford academic Steve Fisher, who is part of the exit poll room on election night – now predicts 51 seats, having initially predicted a total in the high 30s after Ashcroft’s first batch of polls.

Election Forecast, another model run by academics which is used by Newsnight and Nate Silver’s FiveThirtyEight, made a similar prediction in February, but now still only forecast 42 seats.

It’s not that Election Forecast think the SNP will fade in the polls. Like the hundreds of academics who were recently surveyed, they see little reason to expect the SNP to fall below 45 per cent in the polls.

As John Curtice put it yesterday, 45 per cent of Scotland voted SNP in the Scottish Parliament, 45 per cent of them voted for independence and at least 45 per cent are planning to vote for them in May. ‘The 45’ cannot be swayed in 20 days.

‘The 45’ voting SNP cannot be swayed in 20 days.

But Election Forecast are happily conservative on the SNP, and they will be until election day. They have shown how, since 1979, Great Britain-wide polls have been only 78 per cent accurate even on election day. So they will always take at least a fifth off the SNP’s vote in their predictions. We don’t do this because we think the SNP surge is an ‘out-of-sample’ event. Their rise is structural and unique. We shouldn’t use GB-wide precedent to dilute it.

Ladbrokes, the bookies, now agree. They have just jumped from predicting 42-43 SNP wins to 50-51 after these polls.

Here’s how today’s polls contrast with what May2015 was predicting earlier today.

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But the Lib Dems are also cautious about Ashcroft’s results. They published an internal poll earlier today showing Jo Swinson ahead by 2 in East Dunbartonshire (Ashcroft put her behind by 11). The Lib Dems designed the poll’s methodology (which was done by Survation), and it had a margin of error closer to 5 per cent than 3 per cent, but we shouldn’t dismiss it.

Some pundits don’t like the Lib Dems’ methodology, but there is not only one agreed way to ask voting intention questions. More importantly, the Lib Dems actually refer to the local candidate in their polls by name, whereas Ashcroft only alludes to them. The party think that makes a difference.

@patrickwintour different methodology – Ashcroft says LDs over-play incumbency; party says he underplays it. We’ll find out soon… — Stephen Tall (@stephentall) April 17, 2015

But Ashcroft’s polls fit the picture implied by national polls, which have shown the SNP polling above 45 per cent time and again since October (and if anything that’s rising). Pollsters are running internal tests to try and see if they’re overstating the SNP share, but none can see any evidence they are.

And what are the Lib Dems saying, that the people of Ross Skye “don’t know Charles Kennedy is their MP unless reminded by a pollster?” (As one senior pollster put it.)

Labour are still hopeful of fairing better in seats like Edinburgh North and South, and East Lothian, not to mention Glenrothes and Rutherglen, which have huge majorities and Ashcroft hasn’t yet polled.

Ashcroft has now polled 27 of Scotland’s seats (46 per cent), and we can be fairly certain what’s going to happen in another 22-27 (the SNP are going to win). Every indication suggests the SNP are set for more than 50 seats.