Forecasting the election – does anyone have any idea?

We’re into the final week before the election, and forecasts abound still. From May2015’s website, most put the Tories ahead, but not by enough to form a majority. May2015 calculate an average of six forecasts and find the Tories 12 seats up on Labour:

A range of bookmakers have been pricing up individual constituencies for some time now, providing an alternative source of information on constituencies to the hugely illuminating Ashcroft polls.

But what do such individual betting markets imply for the national picture? These bookmakers do naturally have overall outcome markets, but to what extent are their individual constituency markets consistent with the overall national picture?

I decided to take the bookmakers seriously with the pricing at constituency level. Each set of odds implies probabilities surrounding outcomes in that seat. However, calculating probabilities for 650 seats to get probabilities of outcomes is a fearsome task. Instead I’ve simulated outcomes: based on the implied probabilities of outcomes in seats, I’ve generated 100 election outcomes for each bookmaker’s set of odds for constituencies (taking any constituency that bookmaker doesn’t have a market for as a certain hold for the incumbent party). The resulting set of outcomes can be thought of as the election occurring according to bookmaker X – what outcome is most likely, what outcome less likely?

What’s the result of this? Considerable disagreement between bookmakers!

This plot shows what the 18 bookmakers (or betting exchanges, including Betfair) imply for the seat totals of Labour and the Conservatives. Betfair’s exchange is the most conservative, only implying LAB 230 and CON 233, while Betway’s prices suggest that CON will get 300 seats to LAB’s 267. Bet Victor, Stan James, 888sport, Betway, Unibet, and 32Red are the bookmakers whose prices imply CON will win 30-50 more seats than Labour; all remaining bookmakers have the two parties roughly neck and neck.

An interesting aside from this is that as we generate distributions of outcomes according to each bookmaker, we can ask more interesting questions such as: how likely is it that Labour wins most seats? How likely is it the Conservatives get enough for a majority outright? For Betfair’s exchange, there’s a 37% chance Labour wins most seats, a 4% chance they win the same number, and a 59% chance that CON wins most seats. Betfair sees no possibility of either party winning a majority. Conversely, Betway’s prices entertain no possibility of Labour being the biggest party.

Have the bookies adjusted for Ashcroft?

Last Wednesday social media was ablaze with Lord Ashcroft’s latest set of Scottish polls, which suggest that Labour are still on course for a Scottish wipeout on May 7. Has this affected what the bookies have to say?

As before, we look at mean implied probabilities for bookmakers, and this time consider the markets for banded ranges of seats for Labour. The impact of worse than previously anticipated polling in Scotland ought to be reflected in a lower seat expectation than previously. Betfair, Bet365, SkyBet, Ladbrokes and William Hill report markets on bands of seats a party wins at the election, and the bands are

• less than 200 seats
• 201-225 seats
• 225 seats and under
• 226-250 seats
• 251-275 seats
• 276-300 seats
• 301-325 seats
• 326-350 seats
• 326 seats or over
• 351-375 seats
• 351 seats or over
• 376-400 seats
• 401 or more seats

Clearly the options towards the bottom of that range are hugely unlikely (bookies rate anything above 375 seats as less than 5% likely to happen), but it’s the upper half of the range when the action has been:

The black vertical line is March 4, when the Ashcroft Polls were released. Hence prices have moved since the announcement, but with the range 276-300 falling in likelihood only from 35% to 34% and 301-325 from 23% to 21%, the impact doesn’t appear to have been dramatic. Lower seat totals like 251-275 increased from 28% to 32%. Less likely events saw bigger moves, with 326-350 seats falling from 12.5% to 7% today.

Overall, the numbers would appear to suggest that the Ashcroft polls are reinforcing the current trends, at least in terms of bookmaker prices; an update to the plot of bookmaker implied probabilities for most seats from two weeks ago emphasises this:

Are the bookies internally consistent?

Seventy one days until the election, arguably the most unpredictable in a generation, and perhaps we might hope that the bookmakers, renowned for putting their money where their mouths are, might be on the pulse.

A co-author of mine, Leighton Vaughan Williams, of the Betting Research and Political Forecasting unit at Nottingham Trent University, says that at least £40m will be staked on the forthcoming election, hence the bookmakers must surely have their prices right?

Making the news recently has been the story epitomised by the plot below:

This plot is of the price 20 bookmakers have been posting since 2010 of the bet for most seats at GE2015. It’s the reciprocal of those decimal odds, which gives the implied probability, and the thick blue and red lines are the Conservatives and Labour respectively, while the different shades of thinner lines are individual bookmakers. The pattern seems clear, that the Tories have shot into the lead recently, and quite some lead.

But bookmakers, and in particular Betfair’s fixed odds wing, have been offering bets in all constituencies around the country (William Hill, Paddy Power and Bet365 also offer north of 100 constituency markets). What can we learn from these?

The following plot, hard to decipher, shows the implied probabilities (vertical axis) for parties across all constituencies (horizontal axis):

What should be clear, hopefully, is that there’s plenty of variation! There’s still 73 days, after all. Digging a little deeper though, if we took the following rule of thumb: a party whose betting price implies a likelihood of victory of above 60% wins that seat, then we get the following outcome on May 7:

Labour 278

Conservative 247

Lib Dem 26

SNP 35

Ukip 4

Green 0

Plaid Cymru 2

In other words the hung parliament we all expect, but Labour with the most seats…?

Clearly this discrepancy (Tories favourites to win most seats, but constituency seats implying Labour to win most) is not one offering a particularly easy arbitrage opportunity, but it does point to the complexity of the forthcoming election – how will the individual fights in constituencies influence the overall outcome?