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:

Most Seats Bookies Prices

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):

Odds in each constituency

 

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?

3 thoughts on “Are the bookies internally consistent?

  1. You mentioned arbitrage. I believe it’s (essentially) possible, but instead of using bets on the biggest party one uses the banded Tory totals, which are similarly relatively optimistic for the Tories as compared to the conclusion from individual constituencies.

    Essentially the strategy would consist of:

    (1) Place bets on all individual Tory candidates (with varying stakes but equal potential payouts), to give a gain that increases linearly with the number of Tory seats, ranging from a loss if they do badly to a gain if they do well.

    (2) Supplement this with a number of smallish, well-chosen bets on some of the lower bands of the total number of Tory seats.

    Playing with current odds, I can get a graph of gain versus Tory seats that is positive *almost* everywhere, and the few worst-case places where it is slightly negative (which are if they just scrape the bottom end of each of these bands) the loss is relatively very small. The total amount bet on these bands works out a lot less than the total amount bet on individual candidates. With 50:1 offered on the Tories getting 200 seats or fewer, it is cheap to safeguard against what would otherwise be a big loss in this event, and then some bets on the next few bands are needed to deal with some other losses for moderately low Tory totals.

    I am not advising anyone to put this into practice, but the principle is there. There are no doubt also practical variants where one backs Tories in a number of selected marginals rather than laboriously all their 600+ candidates, but opening up an element of risk if the party does well overall but not in the selected marginals.

  2. Pingback: Have the bookies adjusted for Ashcroft? | Reading General Election Blog

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