Decision-making in betting markets

feature Decision-making in betting markets The placing of a bet is a classic example of decision-making under uncertainty. A betting market is also an example of a simple financial market, but one which possesses the advantage that each bet is characterised by a well-defined end point at which it possesses a definite value, i.e. the amount won or lost. Leighton Vaughan Williams explains the implications for our understanding of economic decision-making of the observed tendency for the expected returns on bets to differ markedly at different odds levels. The favourite–longshot bias In recent years there has developed a rapidly growing economics literature which has focused on the nature and behaviour of betting markets. This literature has been published in some of the foremost international academic journals, and has increasingly influenced mainstream economic enquiry. The most significant focus of the published literature to date has been the issue of information efficiency, i.e. the way in which and the degree to which a market incorporates available relevant information. In the strictest sense, a market is informationally efficient if it incorporates all available information. No consumer or investor operating in such a market could, therefore, know more than the market. In the particular context of a betting market, this means in one sense that no bettor could make a profit except by chance. Numerous studies have sought to investigate whether betting markets are indeed informationally efficient, and if so to identify the extent to which this is so. If betting markets are efficient, one might expect that the average return to a bet at any given odds level will be the same as that at any other odds level. By odds level we mean the net amount gained by a winning bet to a given stake. For example, odds of 5 to 1 against would imply that a £1 bet on a horse would, if successful, return a net amount of £5, i.e. £5 and the £1 returned to the bettor. A losing bet would lose the stake. In fact, there is significant published evidence to suggest that the expected return differs markedly at different odds levels. This phenomenon has come to be known as the “favourite–longshot bias”, and can be traced to a seminal piece of work published in 1949 by Richard M. Griffith, a psychologist based at the Veterans Administration Hospital, Lexington, Kentucky1. In his paper, Griffith produced evidence, derived from the US racetrack, that, the shorter the odds about a horse, the better on average the value. In other words, those who systematically bet on the favourite (the horse with the shortest odds) would over the long term win more, or at least lose less, than those backing any other horse or horses in the field. This was a startling discovery because it suggested that it was possible to earn above-average returns by following a simple system which required no knowledge of anything other than the available odds. This was significant not only for horse race bettors but also for economists interested in the operation of markets, and in particular financial markets. After all, if markets were efficient, in the sense of incorporating all available information, how could betting markets leave open this loophole? The answer has fascinated economists ever since, and some interesting explanations have been teased out. Attitudes to risk The most obvious explanation is that those who bet at the racetrack simply like risk, and so don’t want to back favourites. Favourites are, after all, the least risky option of all the choices available to the bettor because they win, on september2004 “There is significant evidence that the expected return differs markedly at different odds levels” 109 Charles Trevelyan average, more often than any other available option. Those who like the thrill of the chase would therefore, according to this explanation, steer away from these relatively safe bets, and tend to favour alternatives (“longshots”) which pay out less often but which pay out more when they do come in. This is the “lottery effect”, the observed tendency of people to flock to the opportunity of winning a large sum of money in one go even though the probability of doing so is small. The problem with this interpretation of the evidence of a “favourite–longshot bias” is that it conflicts with the tenets of all conventional economic theory. Such theory dictates that people are, in general, risk averse, which means that they need to be compensated for taking on extra risk. For example, an investor would require a higher expected return for venturing £1000 into an exploratory oil venture in South America than for investing the same £1000 in a savings account at the local high street bank. One explanation for the different attitude to risk exhibited by bettors and investors is that money spent in a betting context is treated differently from money spent in an investment context. This is the idea that people employ “mental accounts” into which they file different sorts of expenditure. 110 september2004 Such an explanation is convenient, of course, because it allows us to explain away any observed anomalies as simply a special case. On this basis, however, it is possible to construct as many special cases as there are anomalies; a solution which is anathema to most scientists, and no less so to traditional mainstream economists. “If you know nothing else about football, your best bet is to back the shorter-priced team” An integrated approach For this reason, economists have more recently addressed the issue of the “favourite–longshot” bias within a more broad-based framework. Such approaches seek to explain the bias as a natural consequence of established economic principles, avoiding the need to consider the betting market and/or bettors as in any way special or different. One such approach is to regard the bookmaker as somebody facing the problem of setting odds in the face of a number of individuals, of uncertain identity, who may know more than they do. These individuals are usually called “insiders”. In such an environment, the bookmakers may seek to contract those odds which expose them to the greatest potential liabilities, i.e. longer odds. This does not, however, explain the existence of a bias (albeit of less extent) in so-called “share-of-the-pool” (parimutuel) markets, where winning bettors share the pool of all bets. After all, there is no bookmaker in such markets to take fright at the informed insiders. Another explanation is that bettors may overlook some fraction of their losses, but not their winnings. If so, it can be shown that bettors will tend to bet too much, relative to the objective chance of success, and will do so increasingly as the odds lengthen. In my own work, I have sought to distinguish between these competing explanations by examining whether the bias against longshots is particularly strong where insiders have the greatest potential to operate2. The evidence indicates that this is indeed the case, which suggests that the shortening of odds at the longer end of the spectrum in response to the threat of insider activity is at least a partial explanation of the established favourite–longshot bias. It does not, of course, explain the bias in US betting markets, which operate on a parimutuel basis. Perhaps surprisingly, the well-established phenomenon of a favourite–longshot bias, apparent in most studies of the US, UK, Ireland, Australia, New Zealand and elsewhere, is absent in studies of racing in Hong Kong and Japan3,4. Perhaps the difference can be explained by the motivation of bettors at Asian racetracks. At those tracks, where the pools and rewards are particularly large, it may be that bettors are operating more like investors than punters. Favourites appear also to offer no special advantage in the US baseball betting market5. Unlike racetrack markets in the US, which are parimutuel only, the American baseball market is conducted at fixed odds, i.e. the odds are given at the time that the bet is struck. One explanation for this has been couched in terms of the type of bettor (relatively sophisticated) inhabiting the baseball betting scene, in an environment characterised by relatively low costs. A recently published analysis of English Premier League football, however, confirms the existence of the traditional favourite–longshot bias for football, i.e. the odds available with fixed-odds bookmakers about the favourite of two teams is better value on average than the odds available about the underdog6. In other words, if you know nothing else about football, your best bet is to back the shorter-priced team. Among correct score odds, incidentally, the best value, according to the study, seems to lie in backing very strong favourites to win by 1–0, 2–0, 2–1 or 3–2. Spread betting—less biased? Even so, this bias seems to be limited to fixedodds betting, at least on the basis of my own research into football “spread” betting markets. Just to clarify, in spread betting, bettors are not offered odds but are instead invited to buy or sell notional assets associated with an event (for example, goals in a football match or the price of gold), based on a “spread” set by market-makers (bookmakers). If the market-maker, for example, expects a team to score 3 goals, a typical spread may be set between 2.9 and 3.2. Bettors who expect the number of goals to exceed the top end of the spread (3.2) are invited to buy at this level. Similarly, bettors who expect the number of goals to fall short of the bottom end of the spread (2.9) are invited to sell at this level. The spread may move upwards or downwards before or during the course of the game until the value of the asset is known with certainty (at the end of the game). At this point a bettor who bought (sold) the asset will win or lose the difference between the ex-post value of the asset and the bid price, multiplied by their original stake. The bettor may “close” the trade at any time. Spread betting markets have historically been characterised by a low level of transaction costs, at least relative to traditional betting markets, partly because of their relatively favourable tax treatment. They have therefore offered an attractive option both to small traders, motivated primarily by wealth considerations, and to larger traders using financial spread betting markets as part of a more general risk management strategy. In particular, spread trading is often used to hedge against, for example, a potential short-term fall in the market. The low transaction costs also make it possible for potential arbitrageurs to profit from relatively small mispricings in the market. The absence of a favourite–longshot bias in these markets may, therefore, be explained by the relatively low transaction costs, or perhaps because these markets are inhabited (like the baseball markets examined earlier) by relatively sophisticated bettors. In truth, we still do not know for sure why some markets are apparently more efficient in processing information than others, or why biases which exist in some betting markets are absent from others. september2004 111 Charles Trevelyan The Quarb strategy This is the bad news. The good news, at least for those of a more practical turn of mind where betting markets are concerned, is the evidence I have found that those who seek to exploit price differentials offered by different market-makers (what I have termed a “Quarb” strategy7) have historically been able to earn significant profits in spread betting markets, at least in the market available about the number of disciplinary cards issued in Premiership football matches in the UK, i.e. the “bookings” market8. In this market, 10 points are awarded for a yellow card and 25 for a red card. The logic behind the Quarb strategy goes like this. In the absence of other information, the mid-point of all spreads provides us with an obvious point estimate of the expected value of the asset. On this basis, we can expect positive returns as long as this value is greater (less) than the price at which we buy (sell). Take the case of the bookings market, for example, in a game between Arsenal and Manchester United. Suppose three of the market-makers offer a spread of 46–50 bookings points, while the fourth market-maker offers a spread of 50–54 bookings points. Now, the mean mid-point of 112 september2004 all spreads in the market is (48+48+48+52)/4, i.e. 49, which is below the spread offered by the “maverick” market-maker, of 50–54. The strategy would be to sell bookings with this outlying market-maker at 50. If the outlying spread was 40–48, with a mean of 49, on the other hand, the strategy would be to buy bookings at 48. If no market-maker offered a spread everywhere outside the mean of the mid-points of all the spreads, this would imply no trade. As I stated above, there is supporting evidence of significant profits to be made, at least historically, from following this trading strategy. Does the opportunity still exist? Why not try it and see! After all, it’s only money. References 1. Griffith, R. M. (1949) Odds adjustment by American horse-race bettors. American Journal of Psychology, 62, 290–294. 2. Vaughan Williams, L. and Paton, D. (1997) Why is there a favourite-longshot bias in British racetrack betting markets? Economic Journal, 107, 150–158. 3. Busche, K. (1994) Efficient market results in an Asian setting. In Efficiency of Racetrack Betting Markets (eds D. B. Hausch, S. Y. Lo and W. T. Zeimba), pp. 615–616. London: Academic Press. 4. Busche, K. and Hall, C. (1988) An excep- tion to the risk preference anomaly. Journal of Business, 61, 337–346. 5. Woodland, L. and Woodland, B. (1994) Market efficiency and the favourite-longshot bias: the baseball betting market. Journal of Finance, 49, 269–279. 6. Cain, M., Law, D. and Peel, D. (2000) The favourite-longshot bias and market efficiency in UK football betting. Scottish Journal of Political Economy, 47, 25–36. 7. Vaughan Williams, L. (2000) Markets and information efficiency: evidence from the UK. In Global Business and Economics Review—Anthology 2000, pp. 24–29. 8. Paton, D. and Vaughan Williams, L. (2004) Forecasting outcomes in spread betting markets: can bettors use ‘Quarbs’ to beat the book? Journal of Forecasting, to be published. Further reading Paton, D. and Vaughan Williams, L. (1998) Do betting costs explain betting biases? Applied Economics Letters, May, 333–335. Leighton Vaughan Williams is Professor of Economics and Finance, Director of the Betting Research Unit, and Head of Economics Research at the Nottingham Trent University. He has written and published extensively in the area of betting research, and acts widely in a consultative capacity on betting and gaming issues.