Labour made big gains in the local elections in England and Wales today, where they are predicted to finish with a 38 per cent share of the vote, compared to 31 per cent for the Conservatives and 16 per cent for the Lib Dems.

But Labour leader Ed Miliband refused to strike a triumphant note, saying: “We are a party winning back people’s trust, regaining ground, but there’s more work to do.”

We think he’s right to keep today’s comeback in perspective. Here’s why.

The analysis

How useful are local council elections in predicting what will happen at the next general election? It’s a question that has long vexed pundits, pollsters and psephologists.

Every year the country’s leading election experts, Professors Colin Rallings and Michael Thrasher, tot up the local results and calculate the equivalent share of the national vote the parties would have won in a general election.

The results since 1979 have been handily summarised here (page 6) by the House of Commons library.

At first glance, this raw list of results doesn’t tell us a great deal.

It’s no surprise that the main opposition party tends to do better than the incumbent in local elections. That’s happened 20 out of 25 times since 1979.

But we know that success in mid-term council elections doesn’t always translate into a parliamentary majority.

In 1991 Neil Kinnock’s Labour got the most votes locally, but the party was handed a humiliating victory by John Major’s Conservatives at the general election next year.

The opposite happened in 1996, with Labour’s resounding victory at council level echoed by Tony Blair’s landslide the following year.

Since 1979, the party that got the most votes in a local election also got the most votes in the next general election 54 per cent of the time. So outcome alone isn’t much better than flipping a coin when it comes to helping us predict who’s going to win in 2015.

Luckily, cutting-edge statistical analysis may now be able to sharpen up our tools of prediction.

Chris Prosser, a leading researcher at Oxford University, has looked at local election results since 1973 and run a series of regression analyses that allows us to pick the winner of the next general election an impressive 86.21 per cent of the time. Statistics fans can check his methodology here.

We’re grateful to Chris for running today’s results through his model, and his analysis shows that the strong likelihood is that Labour won’t win the biggest share of the vote in 2015.

His best predictions at time of writing are that Labour would win 34.04 per cent of the vote in the next general election, but the Conservatives would still be ahead on 36.59 per cent.

Chris puts the Lib Dems on 23.25 per cent, although that may be a little high as the Lib Dems have never been in power before and so are something of a statistical wild card.

These percentages should be accurate to within 2.8 percentage points on average, so it’s not an out-and-out declaration of Conservative victory, rather a strong probability.

To put it into perspective, Chris says there is a 76.24 per cent chance that the Conservatives will be the biggest party in 2015 and a 15.35 per cent chance Labour will be the biggest party.

But remember that in our first-past-the-post system, getting the biggest share of the vote doesn’t mean that you will get a parliamentary majority.

Labour tend to get more seats with a smaller percentage of the vote. That’s because the Tories have more safe seats where they win with big majorities, while Labour tend to have more marginal seats where a small number of votes is decisive.

So it’s entirely possible that, according to our prediction, Labour could still end up with the most seats even if they don’t get the most votes.

If we feed Chris’s numbers into the website Electoral Calculus, Labour come out top with 296 seats, the Tories are just behind on 272, and the Lib Dems are on 54.

So Labour would be 30 seats short of an overall majority and the coalition could technically continue, although there would undoubtedly be fierce debate about who had the real mandate to govern, and the possibility of a Lib-Lab team-up.

The verdict

Of course this is still a crystal ball, albeit a slightly more polished one, and anything can happen in politics.

But if you’re going to make political forecasts based on these local election results, as a vast army of commentators are doing right now, why not enlist the help of good mathematics?

As things stand, Chris’s prediction is that Ed Miliband is unlikely to win the biggest share of the votes at the next general election, and despite the idiosyncrasies of our electoral system, Labour will fall short of an absolute majority.

By Patrick Worrall