“Polls Apart!” used to be the cliché newspaper headline whenever two opinion polls about an impending election reported fractionally differing findings. For the 2015 election, they’re rapidly running out of puns. The sense of frustration is palpable. Those polls keep coming, and none gives a clear idea of who will win.

The Independent recently produced a whole story, complete with charts, on “the four utterly contradictory polls” that dominated election coverage at the start of the penultimate week of campaigning before the big day. “This roller-coaster ride in the polls is repeated every day”, it explained, demonstrating “how close and unpredictable this election campaign is”.

This must have caused readers to wonder why, if they’re apparently so useless, polls still attract so much attention. Others are turning to bookmakers’ odds to try to decide the winner. So who are more reliable in this uncertain contest: pollsters or bookies?

Bookies

Bookies reckon £30m was bet on the outcome of the 2010 UK election and £50m was spent predicting whether Scotland would vote for independence in September 2014. They say this election will be the first non-sports event to break £100 million in bets.

William Hill has taken bets online of £200,000 at odds of 2/9 on a hung parliament, and over the counter of £50,000 at 1/8 – or, as it’s sometimes expressed, 8 to 1 on. Clearly some see it as an easy earner, and they could be right.

These big bet odds may be short: £50,000 at 1/8 would win just £1 for every £8 you’ve staked, or £6,250 plus the returned stake – as opposed to, say, the 8/1 you could get on the next government being a coalition involving the Scottish Nationalists. That outcome’s extreme unlikelihood is reflected in the much longer odds, and the extreme unlikelihood of your winning £400,000 plus your returned stake. Very short odds, therefore, are not necessarily unattractive.

Pollsters

The Conservatives recently unleashed their latest secret weapon – famous soapbox campaigner and former prime minister, John Major. He warned of impending doom if the next government turns out to be a partnership between Labour and the SNP, but his campaign appearance inevitably reminded many of the historic 1992 electoral triumph that earned him his status as the UK’s most electorally successful living Conservative.

In that election, the four main final polls, averaged out, put Labour ahead on 39%, the Conservatives on 38%, and projected a hung parliament.

In the event, Labour managed just 35%, while the Conservatives won nearly 43% and a 21-seat Commons majority. It would be 18 years before a hung parliament emerged. A young and still mistrusted polling industry had suffered a humiliating setback.

However, as the 2015 campaign demonstrates on a daily basis, it has recovered, grown, and evolved methodologically almost beyond recognition. That’s fortunate since the proliferation of smaller parties has made both polling and seat prediction considerably harder than in 2010.

As parts of large companies with numerous business clients, political pollsters are necessarily both rigorous and pretty good – provided you judge them reasonably.

They’re not, whatever the media may imply, predictors or forecasters. They take time-specific opinion snapshots – some using online panels, some random digit phone dialling – of what they hope are statistically representative samples of the whole electorate.

They also clearly quantify the probabilistic nature of their work and the margins of error. With standard samples of 1,000 or more respondents, only about 19 times in 20 will any single response be within 3% (plus or minus) of what it would be, had the whole population been surveyed.

For the record, all four of the polls that befuddled the Independent had both parties within 3% of being level-pegged on 33%. So while two put Labour ahead and two gave the Conservatives the edge, they weren’t “utterly contradictory”.

Sampling probability does decree, though, that roughly every 20th finding or poll will be outside that +/- 3% margin of error – and so appear to presage a “shock” result. And human nature decrees that a rogue poll will invariably attract more media attention than all the rest put together – which is almost certainly what happened in the last weeks of the Scottish referendum.

A Scottish test case

Of nearly 40 polls published between June and the September 18 polling day, only two put the Yes vote ahead. But just one was enough to trigger ten days of crazed panic among political and business leaders.

It doesn’t, though, explain why the averaged five final polls put the No vote on 49.2%, with a lead of just 4.2%. The actual result was 55.3% to 44.7% – the No vote ended with a lead of 10.6%. Poor methodology or very late change, either way, the pollsters got it wrong.

Meanwhile, the bookies, who overwhelmingly predicted a No throughout the campaign, hardly wobbled. The odds stood at around 7/2 against Yes, and a pretty short 1/4 on for No. One firm even paid out a six-figure sum on a No bet three days before polling day.

That contrast wasn’t a one-off – in fact it was repeated in this year’s Israeli Knesset elections, as the final polls suggested a Zionist Union victory and defeat for Benjamin Netanyahu’s Likud party, the exact reverse of what actually happened.

Rather, it’s what’s logically to be expected. Pollsters ask about our intentions and attitudes; bookies, as we have seen, focus only on results and outcomes. Above all, though, they back their judgement with their cash.

So study the polls, as of course the bookies do, and even the trickier poll-based seat projections such as those at Election ForecastElectoral CalculusThe Guardian, and New Statesman.

Perhaps, though, don’t take the latest predictions from US statistician Nate Silver as your guide. In a recent interview with the BBC, he was somewhat harangued into predicting a Conservative victory. But, as shown in the table, being spot-on in US elections didn’t stop his being burned in the UK’s last one.

Certainly by comparison with the polls, the bookies are united: increasingly confident the Conservatives will get most seats, but that Miliband is the more likely next PM. Best odds on most seats, therefore, from any of Oddschecker’s 24 bookmakers are 3/10 on the Conservatives and shortening, 3/1 on Labour and lengthening. For next PM, Miliband is available at 4/6, Cameron at 11/8.

If the polls conflict and projections confuse, you may as well follow the money – or at least what the money’s saying.

This article was originally published on The Conversation.