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Market Inefficiency and the Favourite–Longshot Bias

Bookmakers, not surprisingly, are in the business of restricting value; they do this by shortening the betting odds they offer relative to what they believe the fair odds to be. Of course, bookmakers are prone to making mistakes, which is what allows a successful punter or tipster to find value in the first place, but as a generalisation, their betting odds will always be shorter than the "fair" odds. What is not clear, initially, is just how they manipulate the odds, and how they construct their advantage across the range of betting prices that they make available. Let's take a look.

Suppose Roger Federer has a fair price of 1.25 to beat Andy Murray in a Wimbledon final, that is to say an 80% win expectancy. Murray, consequently, would have fair odds of 5, or a 20% chance of winning. If the bookmaker's overround is 110%, where will he build in the additional 10%? Intuitively one might expect that to ensure he builds the same advantage on both players, he will load this proportionally, in other words, 8% on to Federer and 2% on to Murray. Put mathematically, 80% multiplied by 1.1 is 88% and 20% multiplied by 1.1 is 22%, making a total win probability of 110%. Thus the betting odds will become 1/0.88 and 1/0.22, or 1.136 and 4.545 for Federer and Murray respectively. The profit expectancy will be the same for both players and inversely proportional to the magnitude of the overround.

Such a market, where the price of each competitor provides the best forecast of its (true) probability of winning, and where the profit expectancy for each is the same and is equal to the negative take of the market operator, is described by economists as being efficient. Whether a real betting market conforms to this normative theory, however, depends on both the risk preferences of the bookmaker and the flow of money coming from the punters, although it is not at all straightforward separating these two influences. The two major odds comparisons Betbrain and Oddsportal assume this market efficiency when calculating their value bets. Unfortunately, it appears neither the bookmaker nor the punter readily conform to normative theories of economic efficiency and most of the value bets shown are worthless.

Whilst market efficiency implies an equality of expected return for differout betting outcomes, some punters express different utility preferences to bets of equal profit expectancy if the bets have different win probabilities or variances. Put more simply, a risk-loving bettor sees more point to a 4/1 shot than a 1/4 shot even though over the long term he won't win any more or less on either if both have the same level of value. He sees more benefit or utility in a short term reward of £4 for a £1 stake than making 25 pence even though he is 4 times more likely to win the latter. Consequently, the bookmaker will see more money bet on the 4/1 shot than is justified by its objective chances of winning. Meanwhile, the bookmaker, ever mindful of guarding against insider information will seek to shortern prices on the biggest longshots to protect his liabilities. Market inefficiency of this kind is more commonly known as the favourite-longshot bias. In such biasd markets the longshot is over-bet whilst the favourite is under-bet. Consequently, the price for the longshot will shorten whilst that for the favourite will lengthen. This favourite–longshot bias is simply the result of too much money being bet on longshots, and too little on favourites, relative to their true chances of winning.

Next time: Evidence of the favourite-longshot bias a football betting market.