Odds Efficiency & the Favourite–Longshot Bias

It’s been tradition amongst less sophisticated punters to believe that backing favourites is a mug’s game and the real value can be found with the longshots. Part of this probably stems from the fact that many people see more benefit, or utility as an economist would say, aiming for bigger rewards, and part probably from the belief that everyone else is backing favourites so there can’t possibly be any value there. Yes, it’s true to say that more people back favourites, and with more money; that’s what you would expect. If that wasn’t the case, then the favourites wouldn’t remain favourites for very long. But the key question is whether there are more (or fewer) punters backing favourites with more (or less) money that would be predicted from the “true” probabilities of possible outcomes.

Of course we can’t know what the “true” probabilities of sporting outcomes are, but we can retrospectively compare actual betting odds to theoretical betting returns, thereby allowing us to see whether those betting odds were accurate or inaccurate, or as an economist would say: efficient or inefficient. Let’s take a look at this for the 1X2 football betting market. The table below shows the returns from theoretical level stakes betting at average market prices for European domestic football league matches played from the 2005/06 to 2011/12 seasons.

It’s immediately obviously that the losses backing favourites are significantly smaller compared to the losses backing longshots. It would appear, then, that the bookmaker builds most of his overround advantage into the longer prices, contrary to the intuition of the majority of punters. Why; firstly because the bookmaker faces a greater (percentage) liability if he makes a mistake on a longshot; and secondly because punters in the main place too much money on those longshots.

Suppose the bookmaker has estimated the fair chances of Phil Taylor beating Michael Van Gerwen at 75%. Consequently, fair odds would be 1.33 and 4.00 for Mr Taylor and Mr Van Gerwen respectively.  What if the bookmaker has got it wrong? Suppose the true probability of Taylor winning is 74% and that for Van Gerwen 26%. Anyone backing Taylor now faces a disadvantage of 1.33% (given by 1 – 0.74/0.75), whilst anyone backing Van Gerwen has gained an edge of 4.00% (given by 0.26/0.25). Of course, the turnover the bookmaker sees for Taylor will still be much greater than that for Van Gerwen, but in percentage terms he is facing 3 times the potential liability he would have faced had the mistake been on Taylor and the “true” win probabilities had been 76% and 24% instead.

Making mistakes on longshots increases the bookmaker’s percentage liability far more than it does for favourites. That’s why a bookmaker will look to shorten his longshot prices relative to what the “true” outcome probabilities would predict they should be. When the bookmaker’s overround is factored in, we find that there is generally less of a percentage disadvantage faced by the punter backing favourites, as is witnessed for 1X2 football match betting. In absolute terms of profit and loss, a larger percentage mistake on propositions that take less money is not necessary a problem in itself. The danger comes when someone has some insider information that the bookmaker isn’t party to. That’s why bookmakers will care about percentage liability. And of course, insider information on a longshot can do far more damage than on a favourite. In the extreme, the biggest mistake the bookmaker can make with Taylor’s win expectancy is 25%. For Van Gerwen it is 75%.

The behaviour of punters also forces bookmakers to shorten their prices on longshots. Whether they are simply risk-seeking or merely misjudging the win expectancies of lower probability betting propositions, the reality is that as a population punters bet too much money than a retrospective analysis of the betting odds and outcomes suggests they should be. As with any betting market, the more action the bookmaker sees, the more he has to shorten his price. This pricing bias, where favourites tend to be under bet and longshots over bet is commonly referred to as the favourite–longshot bias. Economists describe it as an example of market inefficiency, because the opinions of the players (the punters), as described by the money they wager, do not accurately reflect the “true” probabilities of the outcomes they are betting on.

This type of odds inefficiency exists pretty much for any sport: football, tennis, basketball, darts, snooker and so on. Probably the only sport where it is not present is Major League baseball, and this is essentially because there isn’t really much of an odds spread for the majority of matches, with no overwhelming favourite and as many as 75% of teams showing a win expectancy within the narrow range of 0.40 to 0.60 (or odds of 2.50 and 1.67). In conclusion, where we find a market with a hot favourite the likelihood is that without any additional information to assess whether a bookmaker has made a mistake, you will be facing a bigger disadvantage betting the longshot.

Of course, this is not to say you can win more by backing favourites. On the contrary: the shorter the odds, the smaller the potential profit. If we only backed propositions with odds of 1.05, for example, the maximum profit over turnover we could make is 5%. Naturally, where odds are longer, there is more potential scope for gaining an advantage over the bookmaker who has made a mistake, as we saw for Taylor v Van Gerwen example. But it is precisely this greater profit potential that bookmakers guard against, by shortening the odds for longshots and limiting their liabilities if they get things wrong.

Naturally, when we look to place a bet we’ll try to take the best available odds. One might reasonably expect that if best prices generally reflect “true” probabilities, the bias would disappear altogether. The table below compares the same sample of European domestic football league matches, but this time to best prices.

It’s apparent that even at best prices, a residual but much weaker bias still exists. So even for bookmakers who offer the most efficient betting markets – and it is these bookmakers that contribute almost all of the best prices for the lower probabilities propositions – they still need to protect themselves against the behaviour of the unsophisticated punter. In fact, probably the only market that is more or less fully efficient is the one you will find at a betting exchange. Betfair doesn’t need to ever worry about balancing action to secure a profit no matter what the result; they just lets the punters fight things out amongst themselves, according to how much they are willing to risk against each other, skimming a commission from profitable plays. (We’ll learn more about how an exchange like Betfair works in the next lesson.) No matter how efficiently a bookmaker tries to manage his odds, the very nature of wanting to offer a market with availability for all possible outcomes makes him vulnerable to the different (and something unsophisticated) utility preferences of his customers.