The Favourite-Longshot Bias in English Football

Transcription

1 The Favourite-Longshot Bias in English Football Abstract The favourite-longshot bias is an empirical phenomenon found in sports betting markets where favourites are systemically underbet relative to underdogs given their likelihood of winning. This study looks at the fixed-odds match results market for the English Premier League for the last five completed seasons, and finds evidence that a favourite-longshot bias is in operation when bookmakers set odds. As a consequence, weak form efficiency is violated, but it is unclear whether profits can be extracted through a technical betting rule.

2 2 I Introduction Gambling on sporting events is hardly a new phenomenon, but the advent of the internet and global television audiences has spawned a multi-billion dollar and growing industry. Including illegal markets, estimates put the sports match-betting industry anywhere between $700bn and $1tn ( 435bn to 625bn) a year 1, up to 70% of which is attributed to soccer. Even at the conservative end of these ranges, the sums wagered on football matches dwarfs the revenues generated by the leagues, the richest of which, the English Premier League, brought in around $3.5bn ( 2bn) in While the legal market for Premier League betting may be considerably smaller, it is undoubtedly large and liquid enough to use as a testing ground for market efficiency and rational expectations. Thaler and Ziemba[13] note that betting markets are in many ways more suited to testing these concepts than stock or asset markets, as each bet has a clearly defined point at which the value is realised, and the environment, featuring quick repeated feedback, is conducive to rapid learning. Despite these qualities, several inefficiencies have been observed in sports betting markets. One of the most prominent is the favourite-longshot bias, an empirical phenomenon where returns to bets placed on longshots are systematically lower than returns from bets on favourites. Ottaviani and Sorensen[7] note that this implies the market probabilities of longshots (obtained from market prices) overpredict on average their empirical probabilities (computed from observed outcomes), an observation first attributed to Griffith[5]. Several explanations have been posited for the existence of such a bias. Weitzman[14] and Rosett[9] suggest that risk-loving gamblers will pay a premium to bet on highly improbable events, despite knowing the true odds. A more sophisticated model of insiders and outsiders, primarily developed by Shin[10, 11, 12] aims to explain the persistence in the bias when odds are set by bookmakers as opposed to in a parimutuel setting. The Shin model describes bookmakers, facing a percentage of insiders with knowledge of the outcome, setting odds in order to raise enough revenue from outsiders to pay insiders their winnings. Alternative behavioural explanations focus on the public simply misinterpreting the relative probabilities implied by a given set of odds. This clearly has implications for assessing weak form efficiency in betting markets, as the bias implies it may be possible to formulate a trading strategy with positive expected returns. The purpose of this paper is primarily to establish whether the favourite-longshot bias exists in modern English football, and secondly to investigate if the bias can be used to formulate a positive expected return trading strategy for the public. The paper focuses simply on the fixed-odds market for match results. Odds are fixed a number of days in advance, and remain available until the event takes place. Bookmakers offer odds against the simple outcomes of a home win, away win, or draw. It is important to note that, while not discussed in depth in this paper, bookmakers also offer odds against a vast array of other outcomes in a given match (for example: the final score; first goal scorer; number of yellow cards) and across a wide range of sports. As such, the results detailed here can be interpreted from a portfolio value maximising standpoint for the bookmaker and serious bettors. The fixed-odds match result market is not self-contained, but part of a diverse range of similar but differentiated 1 2

3 3 products. The fixed-odds model has an inherent source of potential inefficiency. Between the time of the odds being set and the event taking place, the relevant information set may well change, for example a key player for one team may suffer an injury. This change cannot influence the set odds, but could be exploited by the public. As a result, bookmakers may look to hedge against this risk in a variety of ways, including exploiting a well-known bias like the favourite-longshot. The paper is structured as follows. Section II describes the existing literature around the bias and football betting markets. In section III, the data and methodology is described. Section IV examines the bias and potential profit opportunities and Section V concludes. II Literature Review The majority of early studies focused on the socially determined odds found in a parimutuel betting market setting, in which the bookies played the role of market makers. In such markets, winning bets divide the money wagered on losing bets, less transaction costs[13]. Such markets are especially common in horse racing, which was also the overwhelmingly dominant arena for sports gambling up to the late 1980s. The existence of a favourite-longshot bias in American horse-race betting was initially noted by Richard Griffith[5] in 1949, and subsequent research confirmed the finding of systemic underbetting of favourites relative to longshots. Hausch and Ziemba(1981, 1984)[6] [15] expanded the literature considerably with consideration of systemic trading rules to exploit the bias for profit. Using their system, the authors achieved a rate of return of around 11%. Additionally, they estimated that, at a minimum, several hundred bettors would need to be using the optimal strategy predicted by their system in order to satisfy the weak form efficient market condition of non-positive expected returns once considering transaction costs. This points to a strong and consistent bias that was further documented by Thaler and Ziemba[13] in a seminal paper. The authors found across several racetracks that expected returns from parimutuel markets was slightly positive for favourites and rapidly decreasingly negative as market odds lengthened. Following Thaler and Ziemba, research expanded beyond racetracks into other sports, many of which featured fixed-odds betting as opposed to parimutuel markets. In fixed odds bets, there is no consistent transaction cost levied on the pool, instead bookmakers must balance their expected payouts from an uncertain number of bets in order to turn a profit. As such, bookmakers offer odds that imply probabilities of certain outcomes that are higher than the true probability. As a result, when attempting to compute the implied probabilities of events occurring, using odds fixed by the bookmaker will give total probabilities for all possible outcomes that sum to more than 1, effectively implying total probabilities of greater than 100%. This excess probability, termed the overround, is a way for the bookmakers to consistently beat the public, as with an overround of, for example, 6%, the bookie can expect to take in 106 for every 100 it pays out in winnings. The size of the overround is largely determined by the ease of determining the true odds. If there is no uncertainty then the 3

4 4 bookmaker will be unable to levy an overround. Despite these complications, research into fixed odds markets has greatly expanded since Thaler and Ziemba. In a series of influential papers in the early 1990s, Shin[10][11][12] developed a model explaining the persistence of the overround despite the assumption of rational profit maximising gamblers. Shin argues that bettors are either insiders, with better knowledge of the outcome than the bookmaker, or outsiders, who are less informed. Given the expected losses to insiders, bookmakers sets a slate of odds that it expects to compensate it with profits made from the outsiders. An implication of the Shin model is that inefficiencies, such as the favourite-longshot bias, must be exploited by fixed odds bookmakers in order to remain in business. Some of the most prolific authors regarding the existence of the bias in fixed odds markets in general, and English football in particular, are Cain, Peel, and Law. In a wide ranging survey paper[2], the authors document evidence of the bias in leagues as diverse as the NFL and Sunday League Cricket, albeit with varying degrees of strength. The paper also notes that the literature and evidence amassed thus far is unclear as to whether the bias only manifests itself at the extreme ends of the probability spectrum, and how far these extremes extend. In a previous paper[1], the Cain et al. use data from the 1991/92 English Football League and find support for existence of the bias in markets for both simple result and final scores. Since the sample for this paper was taken, the size of the sports gambling industry, as well as the profile of English football, has grown enormously, and as a result it is instructive to revisit and replicate the tests carried out. III Data The data are compiled from the result of every English Premier League match from the last five completed seasons ( to ) for a total of 3800 matches. Over this period, twenty teams competed in the league each season, playing 38 matches each (home and away against every other team). A win was worth 3 points, a draw 1 and a loss 0. At the end of each season, the three teams finishing bottom of the league were relegated to the Championship, with three teams from that division promoted to replace them. Over the course of the five years in the sample, 29 different teams competed in the league. Unlike Cain, Peel, and Law[1] this paper examines one division, the Premier League, over five years, rather than four divisions in one season. This decision was taken due to the far larger differences in terms of the amounts bet on Premier League matches as opposed to League 2 (named Division 4 in 1991/2), as well as differences in media exposure and knowledge about teams. It is a reasonable assumption that the differences in these factors horizontally (year-to-year) in the Premier League is far smaller than the vertical (division-todivision) difference in a single season. The 1991/2 season was the last before the former First Division clubs breaking away to form the Premier League, a significant schism which has accelerated the differences between divisions thanks to inflows of television money and sponsorship to the top league. These differences were not as pronounced before the breakaway, and as such it is reasonable to account for this discrepancy by altering the sample collected. 4

5 5 Data is available at for every match played in the league for the past 25 seasons, consisting of the match result and assorted other statistics, as well as the fixed odds offered by the major bookmakers based in the UK. The data were accessed online, and transformed using R, before running regressions and generating graphics in Stata. The last five completed seasons were selected in order to minimise variations in other factors that could be at play (many of the aforementioned transformations in the League structure took several years to filter through) and could cause anomalies in the betting data if bookmakers or the gambling public absorbed and processed these changes at different rates. By 2008, relative stability in information terms can be assumed. 2 While most major bookmakers based in the UK are available, like Cain, Peel, and Law(2000)[1] this paper will use data from William Hill in order to proxy for the market as a whole. Selecting a single bookmaker is a reasonable proxy, as for most matches there will not be significant deviations in odds offered from one bookie to the next. This is partly because similar models of odds prediction are at work in most betting shops, but also because significant deviations could be exploited by gamblers to hedge and thus arbitrage away risk (Pope and Peel (1989)[8] do find such opportunities, however it is unclear if the greater information and lower transaction costs facilitated by internet gambling has allowed such instances to persist into the 21st century. Constantinou and Fenton[3] dispute this assumption, and argue that arbitrage opportunities exist thanks to the recent proliferation of bookmakers offering odds on English football. However, it is unclear that these opportunities are large enough to compensate for the transaction costs involved in such strategies. William Hill is the largest bookmaker in the UK, and boasts a considerable customer base abroad. The Gambling Commission estimates William Hill to hold a 25% UK market share, ensuring a liquid and popular market for Premier League bets, although the diversity the firm offers customers, by some estimates 3 500,000 events per week across 30 sports (though television advertisements put the numbers higher) as well as an online casino, could lead to complications regarding the companys portfolio value maximisation strategy. It is possible that the bookmaker offers generous odds to clients looking to gamble on the globally popular Premier League, with the intention of luring them into further wagers on other sports and business lines that are more profitable. However, given the size of the online soccer betting market and the competitive constraints put on William Hill, this paper will abstract away from such concerns, and assume the bookmaker is maximising the value of its match result fixed-odds book. IV IV- i Results Existence of the Bias In the first place, it must be determined that there exists some bias in bookmaker odds setting, and that the probabilities implied by the odds set ex-ante are not reflective of the true probabilities observed ex-post. As 2 For example, the purchase of Manchester City by Sheik al Mansour in 2008 altered the landscape of the Premier League, but both bookmakers and punters could look to the example of Roman Abramovic s takeover of Chelsea in 2003 for a precedent. Almost nothing of substance to alter the dynamics at work in the Premier League has happened since the early 2000s

6 6 the probabilities of these actual outcomes sum to unity, it is necessary to take account of the bookmaker s overround, and normalise the probabilities so that the predicted outcomes also sum to unity. Figure 1 shows the relationship between the overround and the spread between the raw home and away probabilities suggested by offered odds. It can be clearly seen that there is no relationship between the size of the overround and the spread. If bookmakers were explicitly exploiting the favourite-longshot bias when setting the overround, we would expect to see a positive relationship with the absolute value of the spread. As it is, no relationship is observable, with most matches featuring an overround of around 6%, similar to the findings of Cain et al.[2]. The selection of the overround appears to relatively arbitrary, with no trend observable when looking at a range of factors from the strength of the home team to time of the season. Overround Home-Away Spread (Absolute Value) Figure 1: Bookmaker s overround plotted against the home-away spread for the entire five-season sample. Given the absence of a relationship, no information regarding the bias is lost when normalising the probabilities such that q mi = p i i p mi, i {Home Win, Away Win, Draw} where p mi is the raw decimal probability of an outcome i in match m calculated from the bookmaker odds. Figure 2 (see appendix) shows the observed frequency of winning bets relative to the frequency of successful wagers predicted by the bookmaker odds. In the absence of bias, the fitted values should track the dashed 45 line (i.e. have a slope coefficient of one), as bets placed on outcomes with odds-implied probabilities of 0.2 should win about 20% of the time in reality if the market is efficient. In the presence of a classic favourite-longshot bias, it should be possible to reject the null hypothesis that the slope coefficient of the fitted line is less than or equal to unity. This is true of the entire five-year sample at the 5% level, as well as of (at a significance level of 5.11%), (at 7.41% significance) and (at 3.08% significance) shows no evidence of the bias, while seems to exhibit a reverse favourite-longshot bias. Neither of these seasons can be said to exhibit the bias at any reasonable level of significance using this test. However, it is noted in Constantinou and Fenton that [the] unexpected outcome observed during season is due to a high number of unexpected longshot outcomes observed in the EPL [3] and as such might be considered somewhat of an outlier season. While the simple linear regression is limited in its ability to find the precise properties of the bias (for example, the strength of the favoured team required for it to be undervalued by the bookmaker) this paper is 6

7 7 concerned primarily with demonstrating the bias s existence. Further analysis using probit or non-parametric regression techniques could be used to develop further insights as to the precise nature of the bias in a given season. IV- ii Weak Form Efficiency Having determined the existence of the favourite-longshot bias over the sample five-season period, it is possible to explore any potential profit opportunities that result. For the market to be considered weakly efficient, the expected value of all bets should be equal, given knowledge of current and past prices. If we assume bookmaker odds incorporate all publicly available information then we can extend these tests to cover semi-strong efficiency, however Shin and Cain et al. demonstrate that this assumption is too strong when looking at fixed odds markets. For example, injuries to key players sustained after the odds have been fixed will alter the true probabilities and thus create a wedge between the market price and the efficient price, which could be exploited by bettors. To satisfy weak form efficiency, technical analysis of previous trends and prices should not be able to produce a betting strategy with expected returns that are either positive or significantly different from those from other bets available. With odds-implied normalised probabilities of q i, all bets b i should satisfy equation 1. EV (b i q i ) = EV (b j i q j i ) 0 (1) In the presence of a favourite-longshot bias, it is unlikely that equation 1 will hold. The expectation would be that returns generated from betting on favourites would be greater than those from wagers on longshots. The implicit probabilities generated from the ex-ante odds data can be combined with the ex-post returns to determine whether significant differences exist at different price ranges. The results are collected in Table Price Range N Returns N Returns N Returns N Returns N Returns q i < q i < q i < q i < q i < q i < q i < q i < q i Total Table 1: Returns to a unit bet on match outcomes The patterns shown imply there is a considerable classic favourite-longshot bias at work, apart from in the anomaly season of Ex-post returns are consistently higher for bets placed on high probability outcomes relative to low probability outcomes. Even in , simply betting on outcomes with implicit probabilities of above 0.8 would have generated returns of 14%. This violates the key assumption of equation 1 that the expected value of all bets given available price information should be equal. However, the infrequency of opportunities to place such wagers suggests it would be hard to utilise this information to create a trading 7

8 8 rule that overcomes transaction costs. As such, it is not impossible that the expected value of any bet is less than or equal to zero, implying that the market may be somewhat weakly efficient. A potential source of error is the differences between bets on home wins, away wins, and draws. Deschamps and Gergaud[4] posit that the non-monotonicity observed in returns as implicit probabilities increase is largely a result of this factor s influence on pooled data such as that in Table 1. Table 2 shows the five-season returns decomposed by the type of bet, as well as the totals for the full five season sample. Home Draw Away Total Price Range N Return N Return N Return N Return q i < q i < q i < q i < q i < q i < q i < q i < q i Total Table 2: Returns to a unit bet on match outcomes by type, Contrary to Deschamps and Gergaud, there appears to be no evidence of a reverse favourite-longshot in draw odds(the most likely outcomes still generate higher returns than the least likely), and bets on home matches appear to exhibit a very weak bias overall, likely as a result of the exceptional results achieved by underdogs in almost exclusively coming at home. Away odds exhibit a near perfect favourite-longshot trend, with average losses at low probabilities far in excess of those at the high end. V Conclusion This study has added to and supported the literature documenting the favourite-longshot bias and its presence in fixed-odds betting markets. The English Premier League match results market continues to exhibit this deviation from efficiency. Returns on high implicit probability bets are systemically higher than those on unlikely wagers for one bookmaker, William Hill. Using a simple linear regression, it was possible to determine that in 3 out of the 5 seasons sampled, favourites won more often than was predicted by their odds, and vice versa for longshots. A more in-depth analysis would allow for variance in the level of surplus or deficit between the actual and predicted outcomes as odds lengthen. This analysis would be more conducive to developing a betting rule that exploits the favouritelongshot bias, as incidents of mispricing by bookmakers could be more precisely established. An anomaly was discovered in the season, but it is unlikely to be a persistent reversal of the bias. The literature is consistent with a variable strength bias, which occasionally reverses itself, merely thanks to an above average incidence of unlikely results. Especially in a low scoring game like football, where true probabilities are perhaps unable to impose themselves over the course of one match, such results are to be expected. Analysis over a longer time frame should support the conclusion that was an anomaly, and not a significant deviation from the norm. The effect of this season on the aggregate results had significant implications for testing weak form efficiency. 8

9 9 In addition to showing the continued presence of the favourite-longshot bias in general, examination of the data showed the clearest example of the bias in bets on away wins. Given the persistently strong effect of home-field advantage in soccer, it is likely that anomalous seasons like will manifest in abnormal home results, as underdogs are more likely to be able to pull of upsets in front of their own fans. The paper also disputed previous findings of a reverse bias in draw results, finding close to a classic fit. Despite the existence of the anomaly, it is unclear that profitable trading strategies can be formulated in response. Further research opportunities exist in accurately using the bias to predict bookmaker mispricing of odds and exploit such instances for profit. The bookmaker s overround appeared to show no relationship with the Home-Away spread, which increases with the favourite-longshot gap, implying that bookmakers do not exploit the bias to increase their balanced-book profit margin. While odds-setters may deliberately misprice to exploit bettors behaviour, they appear to maintain roughly the same overround of between 6% and 7% for most matches. This points to the bookmakers not capturing the bias in increased margins, but rather through simply mispricing the relative odds available. If such opportunities can be identified, they may be exploitable by informed bettors. The instances of abnormally high overround (of between 7% and 13%) do not seem correlated with any of the aggregate variables such as Home-Away spread or time of the season, and so may be determined by factors specific to individual matches. This also may prove a fruitful line of research. The key conclusion of this paper, that favourites are better value bets than underdogs, is valuable information for gamblers looking to improve their performance. It also provides researchers with an additional example of a market exhibiting the favourite-longshot bias. 9

10 10 Appendix Actual Outcome Actual Outcome β = ; p = β = ; p = Actual Outcome Actual Outcome β = ; p = β = ; p = All Seasons Actual Outcome β = ; p = β = ; p = Figure 2: Actual frequency of successful bets on outcomes against the frequency predicted by bookmaker odds. β is the slope of the solid regression line and p is the p-value of a one sided hypothesis test with H 0 : β 1; H 1 : β > 1. 10

11 11 References [1] Michael Cain, David Law, and David Peel. The favourite-longshot bias and market efficiency in uk football betting. Scottish Journal of Political Economy, 47(1):25 36, [2] Michael Cain, David Law, and David Peel. The favourite-longshot bias, bookmaker margins and insider trading in a variety of betting markets. Bulletin of Economic Research, 55(3): , [3] Anthony C Constantinou and Norman E Fenton. Profiting from arbitrage and odds biases of the european football gambling market. Journal of Gambling Business & Economics, 7(2), [4] Bruno Deschamps and Olivier Gergaud. Efficiency in betting markets: evidence from english football. The Journal of Prediction Markets, 1(1):61 73, [5] Richard M Griffith. Odds adjustments by american horse-race bettors. The American Journal of Psychology, [6] Donald B Hausch, William T Ziemba, and Mark Rubinstein. Efficiency of the market for racetrack betting. Management science, 27(12): , [7] Marco Ottaviani and Peter N Sørensen. The favorite-longshot bias: an overview of the main explanations. Handbook of Sports and Lottery Markets (eds. Hausch, DB and Ziemba, WT), North-Holland/Elsevier, pages , [8] Peter F Pope and David A Peel. Information, prices and efficiency in a fixed-odds betting market. Economica, 56(223):323 41, [9] Richard N Rosett. Gambling and rationality. The Journal of Political Economy, pages , [10] Hyun Song Shin. Optimal betting odds against insider traders. The Economic Journal, pages , [11] Hyun Song Shin. Prices of state contingent claims with insider traders, and the favourite-longshot bias. The Economic Journal, pages , [12] Hyun Song Shin. Measuring the incidence of insider trading in a market for state-contingent claims. The Economic Journal, pages , [13] Richard H Thaler and William T Ziemba. Parimutuel betting markets: Racetracks and lotteries. Journal of Economic Perspectives, 2(2): , [14] Martin Weitzman. Utility analysis and group behavior: An empirical study. The Journal of Political Economy, pages 18 26, [15] William T Ziemba and Donald B Hausch. Beat the racetrack. Harcourt Brace Jovanovich New York,