In October 1924, British voters went to the polls. It was an unstable time: over the previous two years, as one inconclusive election followed another, the country had got through three prime ministers. This time, however, the result was decisive: Stanley Baldwin won the biggest Conservative landslide in British history. The story will no doubt provide comfort to Boris Johnson as he seeks to win his own snap election. But a Conservative majority in 2019 is by no means guaranteed; Johnson faces many more obstacles than Baldwin.

Many observers have focused on the Lib Dems’ impact on the Labour vote. That’s a mistake

In the last few weeks, as it’s become clear that a general election is around the corner, the pollsters have gone into overdrive. UK-wide polls should always be approached with some caution. They are often incorrect, even if only slightly; on average, the final week’s polls in 2017 suggested that the Tories would win by six points (they won by 2.5 points). Each time an individual poll is published, there’s a tendency to focus on its headline figures – but you can learn more by looking at the underlying data, as well as the average of the different polls being carried out.

One of the big political stories of the year has been the resurgence of the Liberal Democrats. Since the EU elections, the party has surged in the polls, rising from an average of 9% in April to 18% in September thus far. Many observers have focused on the Lib Dems’ impact on the Labour vote. That’s a mistake: of the Lib Dems’ 19 top target seats (seats where they are behind their opponent by 20 points or less), just two are held by Labour. There are virtually no Labour/Lib Dem marginals left. Some seats that were once Lib Dem strongholds now have huge Labour majorities: in Bristol West, for instance, the Lib Dems’ share of the vote fell from 48% in 2010 to just 7% in 2017.

Instead, the Lib Dems pose a bigger threat to the Tories. Thirteen of their top target seats are currently held by Conservative MPs. This creates a major obstacle to the Tories’ chances of winning a majority. The Tories were only able to get one in 2015 by gaining dozens of seats from their former coalition partners. Four years later, the Lib Dems remain their main opponents in dozens and dozens of constituencies.

Those aren’t the only seats that will be fiercely contested. One under-reported aspect of the 2017 election was that it transformed the electoral landscape for any future election, leaving the outcome even more uncertain. In the 2015 election, just 56 seats out of 650 had a majority of less than five points; since the 2017 election, there are now 96 such seats. As a result, small swings in the popular vote can have a massive impact.

An average of polls thus far in September shows the Conservatives on 33% (-11 points since 2017), Labour on 26% (-15), the Lib Dems on 18% (+10), the Brexit party on 12% (+12), the Greens on 5% (+3) and the SNP on 4% (+1). On a “universal” swing (ie Labour losing 15 points in each seat, the Tories losing 11 points in each seat, etc), the Conservatives would win 315 seats (-2), Labour 228 (-34), the SNP 50 (+15), the Lib Dems 32 (+20), Plaid Cymru four (-), the Brexit party one (+1) and the Green party one (-).

But if the poll average changes by a mere three points, say, giving the Tories 30% to Labour’s 29%, then the Tories would win only 284 seats to Labour’s 260. With so many highly marginal seats, a few percentage points could make all the difference in the world. This goes both ways, of course. Forty Conservative seats have a majority of less than 5%, but so do 30 Labour seats. The Tories may well lose dozens of seats to the Lib Dems and SNP, but pro-leave Labour seats in the north of England and the Midlands can provide them with an alternative pathway to a majority government.

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And as we have seen before, polls can change very rapidly. Between April 2017 and election day itself, Labour’s vote share rose from a poll average of 27% to a final result of 41% (+14). Equally, the Conservatives went from averaging 32% in February 2015 to winning 38% on the day of the 2015 election.

This time, of course, so much hinges on Brexit. The election will almost certainly be held after 31 October. Many things could happen between now and then: Johnson could successfully pass a new Brexit deal, he could ask the EU for an extension, or Corbyn could even be installed as the PM of a caretaker government. All of these outcomes could potentially transform the electoral landscape.

As recently as June, the Conservatives were averaging 21% in polls, with the Brexit party ahead of them on 22%; Boris Johnson’s promise to deliver Brexit changed this. In September thus far, the Tories are on 33%, and the Brexit party is on 12%. If Johnson does not take the UK out of the EU, he will not only find it difficult to win a majority; he will struggle to get enough seats to form any kind of government.

• Ell Smith is the founder of Stats for Lefties, a blog and podcast that examines polls and elections