On Friday we took a second look at why we think Ed Miliband is likely to be the UK’s next prime minister.
Our pieces haven’t been justifications of Miliband’s reign as Labour leader. In the past four and a half years Labour has lost the whole of Scotland; won over very few 2010 Tories; and shed voters to Ukip and the Greens. But the maths is still clearly in Miliband’s favour.
Even though Labour may not win more seats than the Tories in 11 days, and may win only a handful more than they did under Gordon Brown in 2010, almost every close race will have to go against Miliband for Cameron to stay in Number Ten after May 7.
That was our conclusion. And that analysis hinged on a graph that we will be focusing on more than any other over the next 11 days. The graph, shown below, is a way of making sense of the seats that will decide this election: the Tory-Labour marginals.
This graph shows how likely various seats are to vote Labour.
It shows how likely various seats are to vote Labour. It focuses on the 80 or so seats that the Tories won most narrowly in 2010 (i.e. they won Warwickshire North by 0.1 percentage points and Basildon South by 12.9 points). And it compares the predicted margin of a Labour victory in each of these seats according to May2015, with the probability of a Labour victory according to Election Forecast (an academic forecast reproduced by Newsnight and Nate Silver).
You’ll see that there are four thick red lines in this graph (click on it for a bigger, zoomable version). If a seat is in the upper right quadrant, it means that both we and Election Forecast think it will vote Labour. If it is in the bottom left quadrant, we both think it will stay Tory. If it is in the upper left quadrant Election Forecast think it will turn Labour but we don’t. And if it is in the bottom right quadrant we think it will turn Labour and EF don’t.
When we say “we think”, we mean “the polls suggest”. Our predictions are purely based on the polls. If Ashcroft has polled a seat – and he has polled 69 of the 82 listed here – we take his results and then adjust them every day as national polls change. So if Ashcroft hasn’t polled a seat since last summer, that poll will now be slightly more favourable to the Tories, because the Tories have since caught up with Labour in national polls.
These are the seats that the BBC’s Jeremy Vine will throw up onto a big virtual board on election night. And we think that if Ed Miliband wins 34 of them, he and the other ‘anti-Tory’ parties in the House will have enough seats to “lock Cameron out” of power. (Why 34? Please see our previous piece.) 
So the question we are asking ourselves every day is: Will Miliband win 34 of these seats? When we released this graph on Friday, 33 seats were in the upper right quadrant; if he wins all of these he would need to win only one of the many truly marginal seats, coloured green in our graphic.
In other words, David Cameron would need to win every single marginal seat – every green (and every light blue) seat – to stay in power. If the odds in these green seats are 50:50, that would be like winning 10-15 coin tosses in a row.
But, as Election Forecast have noted, and this engaging post by Thomas Oleron Evans stresses, these seats are unlikely to be wholly independent of one another, as this coin toss analogy assumes. They are likely to be right or wrong en masse, because of a structural polling error. In Oleron Evans’ words:
“The marginal seat contest [is] less like a series of separate coin tosses, with Cameron needing an unlikely sequence of heads, and more like a single coin toss, albeit with a coin that may be slightly biased in Labour’s favour.”
We wouldn’t accept the odds are only slightly biased in Labour’s favour. This seems to assume the error will be in the Tories’ favour, when Ashcroft’s polls could be systematically wrong in Labour’s favour.
So our previous post was slightly more strongly worded than that, but the odds of a Tory victory are undoubtedly greater than 10 consecutive coin tosses – that happens 1 in every 1,000 times. (It was a flippant analogy.)
This debate – over the relationship between seats and errors, or over ‘co-linearity’ – continues one that began last week. But has anything now changed? Are fewer seats now in the upper right quadrant? Have some green seats – the truly close marginals on which we and Election Forecast disagree – become light blue seats that now ‘lean Tory’?
We created our graphic slightly before we released it. Since then, three new polls have put the Tories ahead by 3-4 points. And on Friday, Election Forecast predicted a 19-seat win for the Tories on Newsnight, a bigger margin than they had been predicting earlier in the week.
On Friday, 33 seats were in the upper right quadrant. Has anything changed?
Yet very little has changed. The polls are still tied as a group – other, less noticed polls have put Labour ahead of or equal with the Tories. And EF have now reverted to a 12-seat Tory win. 
We have re-created our graphic, having added these new polls and uploaded EF’s latest probabilities, and 33 seats are still in the upper right quadrant. If Labour win all of these, David Cameron will still have to win every close marginal seat.
Here’s the version of the graph we released on Friday.
The Tories want all the seats to head towards the bottom left corner (or actually be in the bottom left). Labour want them to all head towards the top right. We would be less confident in an ‘anti-Tory’ victory if the red and green seats started to move towards the bottom left en masse.
The Tories want all the seats to head towards the bottom left.
Seats move towards the bottom if Election Forecast think a seat is less likely to vote Labour. Seats move leftwards if our purely polling-based predictions start to swing towards the Tories.
Has either happened? Here is the graph with Election Forecast’s new probabilities added, but our poll-based predictions unchanged. If the Tories were doing better, the seats would move towards the bottom.
That hasn’t happened. In fact, Labour’s position has technically strengthened – each seat is now, on average, 0.3 percentage points more likely to vote Labour. (In reality, nothing has really changed.)
But have the seats moved towards the left? If we now also update May2015’s poll-based predictions, this is what the graph looks like.
It is hard to see any differences. The seats have in fact moved very slightly leftwards. In other words, new polls have been slightly more favourable to the Tories, and so our model now shows slightly smaller Labour victories. But Election Forecast’s model has moved in the opposite way, albeit almost imperceptibly, so there is no discernible effect.
How can our polls and EF’s probabilities move in different directions? Because Election Forecast’s model is based on more than just polls. They discount the polls; they take them and revert them back to the 2010 election, because election day polls have typically only been around 80 per cent accurate in the past.
The pro-Tory polls of late were already part of Election Forecast’s prediction.
This helps the Tories; they polled 7 points higher than Labour in 2010. So the slightly more pro-Tory polls of late were already part of Election Forecast’s prediction.
The only significant changes since Friday are Bristol North West, which is now rated as a safe Tory win (it already leant towards them) after Ashcroft showed Charlotte Leslie well ahead on Saturday morning, and High Peak and Colne Valley, two marginals which now lean Tory after Ashcroft put Cameron’s party ahead by two in each seat.
If the Tories really were now ahead by two in every marginal, that would be concerning for Miliband. But a poll that puts the Tories ahead 2 really puts them ahead by 5 or down by 1 (and 19 times out of 20 a poll is less accurate than that).
33 seats are still in the upper right quadrant, and 24 of those are still in our arbitrarily-defined upmost upper right quadrant (marked by the light red lines), which groups together the seats that seem particularly likely to vote Labour.
What is the data really telling us? This is a simple game of probability. And the odds are in Miliband’s favour. If Miliband can win all of the red and light red seats in the graph above, he only needs to win only one more of Amber Valley, Brighton Kemptown or Norwich North (or the other close marginals not shown in this image)
Cameron can win – and we’ll be taking a closer look at his two paths to victory later this week – but the maths is against him.
 On Friday we said Miliband needed to win 35 of these seats. We have now reduced that to 34 as Ashcroft has shown Labour are far ahead in Lib Dem-held Bristol West, a seat we charitably suggested the Lib Dems could hold on Friday.
Labour are also favoured to win Lib Dem-held Leeds North West by Election Forecast (Ashcroft hasn’t polled it), not to mention Sheffield Hallam, which is essentially a 50:50 race. But we pessimistically assume they will win neither. If Labour win both they will only need 32 of these Tory seats.
 They just swung back to a 19-seat Tory win this morning, but this hasn’t had a significant effect on our analysis. Maybe they’ll be back to 12 after Populus don’t put the Tories ahead this morning (Populus haven’t put the Tories ahead all year).