Regression-based tests for market efficiency can suggest bets which offer abnormal returns but the relevant strategies can be successful only if the biases investors observe from the pattern of odds and results in one period prove stable across time. Accordingly, in this section, we test whether a regression model estimated from one season’s data is capable of being used in the following season to select a set of bets that will earn superior returns. The bets we examine are those which would have been made whenever the probability of a win as estimated from the previous season’s model is more than one-fifth greater than that implied by the bookmaker odds. Table 2displays the results. The number of bets recommended by the model in any one season may be interpreted as reflecting the degree of inefficiency embodied in the regression results for the previous year. The success of those bets will then depend on whether or not any biases continue to characterise odds setting behaviour in the current year. Both aggregate and disaggregated results for 1997-98 revealed the presence of several specific biases in the pattern of odds. The model accordingly generates a large number of bets
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passing the 1.2 filter ratio for season 1998-9. The biases in 1998-9 proved sufficiently congruent with those for 1997-8 for the betting strategy to be successful. At the aggregate and for PL/D1 and D2/D3 separately, returns were sharply higher than the –10.5% implied by the level of overround Indeed, in D2 and D3 the level of return calculated at posted odds was sufficiently high (22.14%) to cover the extra commission (17.7%) charged for the privilege of betting on a single match via the device of a half-time/full-time double. The strategy would therefore have been profitable but for tax. In any case, the levels of return in 1998-9 available from assuming the continuation of biases noted for 1997-8 may fairly be described as ‘abnormal’ and the market therefore ‘inefficient’.
However, we find in the regression results for particular seasons, a distinct trend towards efficiency since 1999. In PL/D1, very few bets (22) are recommended in 1999-2000 and the impressive profit cannot be regarded as significant because it depended on a very small number of long-odds wins. In D2/D3, the pattern of odds the previous season generated 197 recommended bets in 1999-2000; 162 of these were on away teams and only 35 on home teams. Here, it was still possible to make a bare positive profit (without accounting for tax and restrictions on singles bets). Some evidence of an inefficient market remained therefore in the lower divisions. The rather poor result from applying the ‘all divisions’ model probably reflects that the previous season, 1998-9, had seen a gap opening between the upper and lower tiers in terms of the degree of efficiency exhibited in the odds: this is evident from the regression results (Tables 1B and 1C) and therefore the application of an aggregated model was by 1999-2000
The most telling illustration of the extent to which the market was moving towards efficiency is that application of 1999-2000 regression results to betting in 2000-1 yielded not one recommended bet whether one used an aggregate model or two disaggregated models. By 1999- 2000, no specific biases (other than DIFFATTEND) appeared to be present in the odds and so ‘value’ bets were hard to obtain in 2000-1 if relying on a regression model for guidance. As noted above however, gains still accrued to those following a simpler strategy based on only one indicator, DIFFATTEND. Overall, the betting simulations point to inefficiency in the market being close to eliminated over our four year study period.
Interpretation and Conclusions
The literature on efficiency in wagering markets has overwhelmingly been motivated from the perspective of finance and financial economics. That has led others to expect patterns of odds to
display efficiency in the sense that all bets should be equally good (or, more strictly, bad) bets.
The perspective ignores that, with sufficient transactions costs to deter professional arbitrage, the
wagering market in sports may be more usefully represented as a consumer good market where
potential consumers have preferences on what bets they make that go beyond expected financial
return. In that framework, it is easier to understand biases in the odds as reflecting price discrimination across groups of potential bettors. Price is here identified not (as is traditional)
with the bookmaker over-round for the event but rather as the expected bettor loss on each
possible unit bet (home, draw, away).The profit maximising price may differ in respect of each
result because of customer preferences and this will manifest itself in biases in the odds.
Bookmakers have strong incentives to be (or to hire) sophisticated odds setters. This is particularly so in a market such as that on British soccer where they have eschewed the right to vary the odds during the betting period. In fact, they do display a high level of expertise. Goddard and Asimakopoulos (2001) acknowledged that there is very little difference in forecasting performance between bookmaker odds and their own very rich and detailed statistical model drawing on past team performance and many years of soccer information data. If odds setters are so skilled as to be able to match very advanced statistical forecasting models, it is reasonable to assume that biases in the odds in the dimensions studied in this paper are, if present, there by design rather than accident and that they should be viewed as a means to maximizing profit. Specific biases should be viewed not as aberrations but as examples of price discriminating strategy. Any reverse favourite-longshot bias could be interpreted merely as odds setters taking due account of bettor risk aversion.11 The similarly familiar home-away bias could
be interpreted as a response to perceived elasticity of demand amongst bettors who attend a game
and consider betting to show support for their local team (they often indeed place the bet in the
stadium itself). And our DIFFATTEND bias is readily interpretable along the same lines of demand being driven by the utility of a bet including non-financial elements (the fun is greater if betting on one’s ‘own’ team) and odds setting recognising that. Biasing the odds as a strategy may, however, be constrained by the potential presence in the market of arbitrageurs. In the absence of transactions costs, risk-neutral professional betters would be able to punish bookmakers whose odds were biased and render efficiency an essential feature of a sustainable market.
Here and in other papers, biases have been identified which (at least until 1999) created some favourable betting opportunities. But the gains here and in other earlier analyses have mostly been modest in the sense of showing a positive sign only if one assumed singles betting and no tax. Restrictions on singles and the presence of a tax have, however, been institutional features of the British market and the implied extra transactions costs have facilitated biased odds as possibly sustainable and equilibrium features of soccer betting. For illustration, we have argued that where a particular team attracts a large following, those who support it in the betting market may be offered a better price (less unfair odds) than usual. We found one betting strategy based on this idea was capable of yielding in excess of a 9% profit, a figure not untypical of the range of wagering gains cited by those who have sought to identify strategies for profitable trading. On the face of it, it appears unlikely that a bookmaker would be so eager to attract bets from fans of heavily supported teams that he would award them an expected profit of 9%. But, given the bar on singles, he would not in fact be doing so.
The fan bettor would have two choices. The first would be to bet on the one game, employing the device of a series of half-time/full-time doubles; but the shading of the odds on this type of complex bet would be sufficient to convert the expected return from + 9 to – 9%, a respectable profit for the bookmaker. Alternatively, the bettor could combine the bet on the match in which he had a special interest with bets on two or more other games. The fan bettor is likely to be less well informed regarding matches not involving his own team, so the bookmaker might expect to earn a ‘normal’ commission on the other legs of the combination bet to again realize an expected profit for himself (and loss for the bettor). Vis a vis this group of customers, 30 the favourable odds offered on their own team’s results is unlikely to expose the bookmaker to loss.
But what of the risk-neutral professional bettor who could destroy the ability of the bookmaker to offer ‘biased’ odds? This potential arbitrageur could acquire sufficient expertise to identify three ‘favourable’ bets and combine them in a treble : the variance of returns would be high but the expected gain still positive. That is true but the level of tax expected in the past is equivalent to extra bookmaker commission and, in the case of the 9% prospective gain hypothesised here, the tax would be just sufficient to deter the arbitrageur from entering the market.
It has, then, been customary for bookmakers to price discriminate in terms of different bets offering different degrees of value; but the restrictions on singles betting made any prospective gains unrealisable by the leisure bettors while tax deterred the professional arbitrageurs from entering the market. “Inefficient” odds were, in these circumstances, sustainable and indeed to be expected. The degree of price discrimination was of course constrained by the extent of the cushion offered by the tax on gaming (and this constraint may or may not have been binding).
The rapid growth of internet betting made it feasible and desirable for British bookmakers to move offshore by 1999 to cater to a wider, international market where the interest in betting on English soccer (particularly the Premier League) is very high but where competition from bookmakers in other countries was now intense. British 31 bookmakers would have been poorly positioned to exploit the growing international market for their product if tax had had to be levied, as it would have been if they had remained based at home. Since British households could also use offshore branches of familiar bookmakers the abolition of betting duty became inevitable and this occurred in 2001. The reduction in transactions costs inherent in the removal of tax (essentially optional since the establishment of offshore operations in 1999) severely limits the ability of bookmakers henceforth to offer biased odds. The importance of transactions costs is, of course, central to whether a market will display efficiency. If there were no transactions costs in the form of bookmaker over-round or tax, then any bias in the odds would be non-sustainable because it
would create an opportunity for positive gain which arbitrageurs would be expected to eliminate.
The removal of tax (and greater flexibility in taking singles bets at least on Premier League games) has greatly reduced the extent to which transactions costs impede the arbitrage process in soccer betting. It is unsurprising therefore that, while our study confirms ‘traditional’ biases in the betting market up to 1999, there is a rapid move to ‘efficiency’ by 2001.
It is perhaps anomalous that the ‘DIFFATTEND’ bias was still present in D2/D3 at the end of our period and evidently still capable of generating opportunities for positive returns. Thus far, betting on lower divisions has still been primarily a domestic market. Information is much less readily available on lower-tiers of English soccer, so transactions costs are effectively still high for potential arbitrageurs. Bookmakers have, evidently, still felt able to ‘bias’ the dds for the presence in (or dominance of ) the market by fan-bettors. Equally, bookmakers still rigorously protect themselves by restrictions against singles betting for these less high-profile games (where inside information and match fixing are larger risks). But we would not necessarily expect this lower-tier market to escape the attention of arbitrage indefinitely if taxfree gains are prospectively to be made. Globalisation, by forcing the dismantling of betting tax, appears to have triggered a strong move to market efficiency in this particular wagering market. In other jurisdictions, offshore betting is likewise a threat to any ‘inefficiency’ protected up to now by tax or indeed by legal or regulatory restrictions. With a globalised gaming environment, we might in future expect fewer articles which can point to biases and ‘favorable trading strategies’ in wagering markets.
1 A large and convenient collection of such articles is provided by Hausch et al (1994). In the season studied in this paper, 1997/8, the English FA Premiership comprised 20 clubs while Divisions 1 to 3 of the Football League comprised 24 teams each. Each team meets a division rival twice, once home and once away. Movement between divisions is achieved by promotion and relegation. 3 Although the bulk of fixtures are played on Saturday, the number of Saturday games will occasionally be educed because either the date is earmarked for knockout cup competition or because of international fixtures. A few games each week are moved to different days in order to be televised and betting is still possible in these cases. 4 Pools entries were (and are) made by mail or through a door-to-door collector. 5 An exception is a televised match. Perhaps the exemption is linked to the high-profile nature of the contest chosen for television coverage. Inside information or match fixing are unlikely to present a serious problem if the teams are well-known and the betting volume high This involves staking £0.222 on the first bet, £0.182 on the second and £0.043 on the third. 7 The over-round on bets is typically 11.7, i.e. one would spend £111.70 to bet on all three outcomes at a level to earn £100 in pay back from the bookmaker. With a fully balanced book , the bookmaker would return £11.70 of each £111.70 staked to earn a commissionof 10.5%. 8 A similar model is used by Lee (1997) in examining the final ranking of teams in the 1995/6 English FA Premiership season. 9 Home advantage in soccer is very important (Clarke and Norman (1995) and Courneya and Cannon (1992)) to such an extent that, in the UK professional game, approximately twice as many wins are recorded by home teams compared with away teams. 10 Actual bookmaker return would vary from 10.5% if the book was not fully balanced, i.e. if liabilities to bettors differed accordingly to which outcome occurred. 11 Positive favourite-longshot bias, noted in home racing markets, is sometimes (tautologically) attributed to risk-loving bettor utility functions. This is not necessarily in contradiction with the analysis here. Team sports are organised so that games seldom have a genuine outsider in the horse racing sense. Unit bets on team sports are therefore very unlikely, relative to the horse racing case, to generate opportunities to lift the bettor to a different range of his utility of wealth function.
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Dixon, M., and Pope, P., (1996), “ Inefficiency and bias in the UK association football betting market”, University of Lancaster, mimeo. Dobson, S., and Goddard, J., (2001), The economics of football, Cambridge: Cambridge University Press. Global Betting and Gaming Consultants, (2001), 1st annual review of the Global betting and gaming market, 2001, West Bromwich : Global Betting and Gaming Consultants. Goddard, J., and Asimakopoulos, I., (2001), “Forecasting football results and the efficiency of fixed-odds betting”, University of Wales Swansea, Department of Economics, mimeo. Golec, J., and Tamarkin, M., (1991), “The degree of inefficiency in the football betting market” Journal of Financial Economics, 30:311-323. Hausch, D., Lo, V., and Ziemba, W., (1994), Efficiency of racetrack betting markets, San Diego: Academic Press.
Jackson, D., (1994), “Index betting on sports”, The Statistican, 43:309-315. Kuypers, T., (2000), “Information efficiency : an empirical study of a fixed odds betting market”, Applied Economics, 32:1353-1363. Lee, A., (1997), “Modelling scores in the Premier League: is Manchester United really the best?”, Chance, 10:15-19 Maher, M., (1982), “Modelling association football scores”, Statistica Neerlandica, 36:109-118. Mintel Intelligence Report, (2001), Online Betting, London: Mintel International Group Ltd. Pope, P., and Peel, D., (1989), “Information, prices and efficiency in a fixed-odds betting market”, Economica, 56:322-341. Sauer, R., (1998), “The economics of wagering markets”, Journal of Economic Literature, 36:2021-2064. Sharpe, G., (1997), Gambling on goals: a century of football betting, Edinburgh: Mainstream Publishing Company. Shin, H., (1993), “Measuring the incidence of insider trading in a market for state-contingent claims”, Economic Journal, 103: 1141-1153. Snedecor, G., and Cochran, W., (1967), Statistical Methods, 6th. Edition, Ames, Iowa: The Iowa
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Regression results – Premier League and Division One [ ] number of cases where coefficient estimate is significantly different from one Table 2 Results of wagering on all available ‘to win’ bets where Probability of success implied by model Calculations assume posted odds (no restriction against single bets) and ignore tax. 1 A large and convenient collection of such articles is provided by Hausch et al (1994). In the season studied in this paper, 1997/8, the English FA Premiership comprised 20 clubs while Divisions 1 to 3 of the Football League comprised 24 teams each. Each team meets a division rival twice, once home and once away. Movement between divisions is achieved by promotion and relegation.
3 Although the bulk of fixtures are played on Saturday, the number of Saturday games will casionally be reduced because either the date is earmarked for knockout cup C ompetition or because of international fixtures. A few games each week are moved to different days in order to be televised and betting is still possible in these cases. 4 Pools entries were (and are) made by mail or through a door-to-door collector. An exception is a televised match Perhaps the exemption is linked to the high-profile nature of the contest chosen for television coverage. Inside information or match fixing are unlikely to present a serious problem if the teams are well-known and the betting
This involves staking £0.222 on the first bet, £0.182 on the second and £0.043 on the third. 7 The over-round on bets is typically 11.7, i.e. one would spend £111.70 to bet on all three outcomes at a level to earn £100 in pay back from the bookmaker. With a fully balanced book , the bookmaker would return £11.70 of each £111.70 staked to earn a commission of 10.5%. 8 A similar model is used by Lee (1997) in examining the final ranking of teams in the 1995/6 English FA Premiership season.
9 Home advantage in soccer is very important (Clarke and Norman (1995) and Courneya and Cannon (1992)) to such an extent that, in the UK professional game, approximately twice as many wins are ecorded by home teams compared with away teams. 10 Actual bookmaker return would vary from 10.5% if the book was not fully balanced, i.e. if liabilities to bettors differed accordingly to which outcome occurred. Positive favourite-longshot bias, noted in home racing markets, is sometimes
(tautologically) attributed to risk-loving bettor utility functions. This is not necessarily in contradiction with the analysis here. Team sports are organised so that games seldom have a genuine outsider in the horse racing sense. Unit bets on team sports are therefore very unlikely, relative to the horse racing case, to generate opportunities to lift the bettor to a different range of his utility of wealth function.