Can Punters win? Are UK betting markets on sporting events. efficiently aggregating information?

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1 Can Punters win? Are UK betting markets on sporting events efficiently aggregating information? Unlike in financial markets, the prices in betting markets are primarily set by bookmakers, not demand. This means that in order to be profitable bookmakers need to aggregate information more efficiently than punters. By looking at men s singles tennis matches from US Open tournaments and interpreting the data using regression analysis, I prove that because the bookmakers are efficient at aggregating information there exist no betting strategies that yield long-term profit when employed. 1.1 UK betting markets on sporting events are multi-million pound industries 1, and as a result it is essential that information is aggregated efficiently. If this doesn t happen then bettors will be able to exploit the inefficiencies by devising betting strategies that will yield significant profits. Due to the manner that UK betting markets are organized, the agents who are harmed by inefficiency are the bookmakers. It is essential for financial markets to be efficient, as the price of shares and options is set by the equilibrium of supply and demand. This means that the market price is self-set, and if a share is priced incorrectly then the ensuing flurry of trading will drive the price to its equilibrium level almost immediately. With betting markets efficiency is also vital, 1 Levitt reported that the top 4 English bookmakers turnover almost 10 billion in 2002.

2 and as bookmakers set the prices in betting markets, it is essential for them to aggregate all information efficiently. The definition of efficiency in price setting differs between the betting and financial markets. An efficient stock market is achieved when the price of a share is an unbiased view of the true value of the company, taking into account all factors that have an effect on it (forecasted dividend payouts, company expansion plans, etc.). An efficient betting market is slightly different however. When setting their prices (odds for an outcome) the bookmakers aren t actually trying to make an accurate prediction of the outcome and set a market clearing price, they are trying to equalize the amount of money wagered on each side of the bet. This ensures that regardless of the outcome the bookmaker will make a profit (equal to the commission that they charge). Using a game of football as an example, in order for a bookmaker to set their prices efficiently, not only do they have to aggregate information about the game, such as how big the home crowd is, both team s previous form, the effect of injuries to key players, and many more, but they have to take in to account information about punter s betting habits as well. Any strong local bias towards a team (such as English fans backing England to win the football World Cup and English players to win at Wimbledon) needs to be aggregated into the prices in order to ensure that the money on each side of the bet is equalized. Failure to do so could lead to a situation where bookmakers stand to make a profit in the event of one outcome, but make a loss in the event of another outcome 2, which does not suit them as they are risk averse. 2 On 7 th October 1996, the weekend that betting tax in the UK was abolished, British bookmakers were reported to have lost approximately $1 million when Frankie Dettori won the Prix de l Arc Triomphe riding

3 There have been many studies of efficiency in financial markets in economic literature, and due to some favourable characteristics there have also been several studies of betting markets as well. Unlike investing in shares, when an individual makes an investment in betting markets (places a bet) they are aware beforehand of the future asset payoffs, and, to an extent, the probability of the outcome happening. Due to the media interest in high profile sporting activities, most of the variables affecting the outcome are in the public domain. This enables punters to make highly informed bets (although there is a degree of information being asymmetric). 1.2 In my paper I am going to test whether UK betting markets aggregate information efficiently, and will be using data from professional men s tennis games. By analyzing the odds set by bookmakers, and the actual payoffs from the bets placed on events (which are now known), I will test various betting strategies. My definition of efficiency is that no single strategy can be detected in year N and used in ensuing years (year N+1, N+2, etc.) to create a sustained profit. The model I use makes the assumption that bettors are informed, risk-neutral, and don t have insider information. By using information exclusively in the public domain I will test the strategies of: betting on the favourite/underdog (taking into account degrees of favourite), betting on the higher ranked player 3 (taking into account the extent of the gap), and betting on different rounds of the competition. By regressing the returns against the odds offered by the bookmakers I will find out if any strategies are profitable, and can conclude whether the markets are efficient at aggregating information. My main hypothesis is that the market is efficient, and there won t be any strategies that can sustain a long-term profit when implemented. This is because betting markets would 3 Using the ATP World Rankings

4 not be such huge industries if strategies existed that made profits, as they would quickly become bankrupt. Even a small presence of gamblers who notice that bookmakers are mispricing events can turn out to be disastrous, as they could sell their tips on to other punters via telephone and Internet based services. I believe that a strategy of betting on the bookmaker favourite will be more successful than betting on the underdog, in that it will yield smaller losses. This is due to the positive long-shot bias that has been the subject of much economic research, with famous titles from Vaughan Williams and Paton (1997), and Shin (1992). I will explain this theory further in the literature review. I also predict that the strategy of betting on the higher ranked players when the gap between them and their opponent is large will yield more favourable results for punters. I expect that betting on the first round of the tournament could be more successful than later rounds, particularly on underdogs, as more asymmetric information is prevalent, possibly in the punter s favour. 1.3 In part 2 of my paper I will conduct a literature review, in which I explore current research relating to my topic, highlighting any methods that have a bearing on my work. In part 3 I will introduce my data, and in part 4 I will display and explain my empirical results, comparing them with any results from existing literature. In part 5 I conclude my study, summarizing any discoveries and opinions that have emerged from my research. 2.1 Financial markets are harder to test for efficiency than betting markets, as the market is constantly forming expectations of future events, and as a result betting markets are often studied in an attempt to further the understanding of financial market efficiency.

5 The paper Why are gambling markets organised so differently from financial markets? by Levitt (2004) demonstrates how the price-setting mechanism used by bookmakers in spread-betting markets to exploit bettor bias enables them to yield higher profits than if they simply named the market-clearing price. Levitt makes the point that with sporting events, bookmakers need to need to equalise the money placed on either side of the bet, unlike casino games such as roulette, where the law of large numbers dictates that the house will make a profit equal to their commission, meaning any bettor bias is irrelevant. Levitt s study is unique in the sense that he observes both prices and volumes of bets placed. This allows him to test both the bookmaker s strategies (such as equalising the quantities of money on each side of the bet) and bettor behaviour. Levitt discovers that in almost half the games he studied, at least two thirds of the bets fall on one side of the bet. This fails to satisfy the hypothesis that the bookmaker s prices are efficient in equalising the amount of money placed on each side of the wager. However his study does suggest that bias plays a strong role in the bettor s selections, and that the bookmaker set their prices in order to exploit this. The reason that this works is that the bookmakers skew the odds such that favourites and home teams (the two groups that bettor bias leans toward) win less than half the time, yet over 50% of the money is wagered on them. Levitt argues that this strategy enables the bookmaker to earn 20-30% higher profits than if they simply equalised the wagers on a bet, making the betting markets on American Football spread betting efficient. 2.2 A paper with similar objectives to my project is The efficiency of Australian Football betting markets, by Brailsford, Gray, Gray and Easton (1995). They analysed the spread betting markets using Probit and ordered probit models. While this method

6 helped Brailsford et al to test for betting strategies, it is not the ideal method for my data. Because they are testing that the spread is aggregating information efficiently, they needed a method that could analyse the effect that lots of different variables had. Due to the nature of my data this was largely unnecessary, as many of the variables Brailsford et al used were irrelevant to my study. One of the variables analysed in their study was the importance of key players to game outcomes. As tennis is an individual sport as opposed to a team sport this variable does not apply to my study. Likewise with momentum, as for a player to be playing in the quarter finals of a tournament they have to have won all their previous games in the tournament, which means in the latter stages of a tournament the individual s form will be identical. As the tournament progresses, the bookmakers will have less information to aggregate, as the player s form becomes more homogeneous. The only round where a player s previous result could differ to that of his opponent is the first round, as in order to reach round 2 both players will have had to win their previous game. Because of this I will test the effect the round has on the strategy of betting on the bookmaker favourite and underdog. 2.3 Much of the literature regarding the economics of gambling on individual outcomes (not spread betting) covers the longshot-bias anomaly. The biggest trend to have emerged from the available literature is that even though a strategy of betting on the short-odds favourite tends to yield higher returns, punters still tend to bet on the higher priced long-shot. Theories explaining this apparently inefficiency of punters relate to how they attain utility from betting. Betting on winning long-shots makes punters look like they are more skilled at betting, satisfying their desire to attain bragging rights over their peers (Thaler and Ziemba, 1988). Quandt (1986) points out that betting on higher priced

7 outcomes (long-shots) yields higher payoffs when successful, enabling punters to increase their utility of wealth at a faster rate. While I am not investigating long-shot bias myself, I found one of the papers to be of great help to my research. The paper Longshot bias: an insight from the betting market on men s professional tennis by Forrest and McHale (2004) attempts to prove that longshot bias is prevalent in the betting markets on men s tennis. Not only did they use a similar data sample to mine, but they also tested the efficiency of the market. They did this by investigating the returns on different betting strategies, and concluded that the market was weak form inefficient regarding betting on bookmaker favourites, meaning that a strategy could be identified in year 1 and used in following years to earn aboveaverage profit. As this was a fairly crude strategy, Forrest and McHale went on to investigate what effect the degree of favourite has on longshot-bias. For this they used probability odds: the stake that a bettor must place on a bet in order to return one unit (ie. 1). This was calculated by taking the reciprocal of the decimal odds (when decimal odds are 3.50 the probability odds are 0.286). Now each betting outcome had been assigned with probability odds, the data was separated into different odds ranges, defined at intervals of 0.1 in the probability odds. Each odds range was tested, and the conclusion was again made that the market failed to satisfy weak-form efficiency, as a strategy (betting on outcomes with probability odds of ) yielded above average profits. Forrest and McHale then went on to investigate the effect that different variables, such as what surface the games were played on, had on the efficiency of the markets. Although all my data comes from tournaments, and there is no deviation in the playing surface (as

8 all games are played on hard courts), I will also test to see what effect different variables have on the efficiency of my data. Although the ultimate aims of my project differs somewhat to those of Forrest and McHale, I will use many of the same analytical techniques as they do, and as a result will compare my results to theirs. 3.1 The data that I am analysing consists of 380 men s single tennis games from the last 3 US open tournaments (years 2003, 2004 and 2005) 4. There are many advantages to using this data. First of all, because of the excellent website I have access to the outcomes of every single game, as well as the final bookmakers odds prior to the game beginning (I have odds from the UK bookmakers: Ladbrokes, William Hill, Victor Chandler and the Internet based Bet365). This means that I have the outcome and return for 760 individual betting opportunities. 3.2 Using data from tennis matches has several advantages over other gambling markets, such as greyhound racing or football games. The level of uninformed betting is low, as tennis is primarily a spectator sport. The prices set in the betting markets mainly cater for informed bettors, and do not get distorted in order to account for recreational bettors 5. This enables the market to be more efficient. Also, transaction costs are 4 There were actually 381 games played in the three tournaments but there were no odds available for the Golmard vs. Labadze game in the first round of the 2004 tournament, meaning this result has been omitted. 5 Horse racing which exists almost purely to be gambled on. When people go to watch tennis they do so because they have a love of the sport and want to watch the game be played at a high standard, whereas when people go to watch horse racing they are mainly going for a day at the races, where the primary objective is to gamble on the horses. This means that a lot of the money wagered trackside at horse racing venues is by recreational punters, who are unlikely to have researched their picks thoroughly, and are unlikely to have taken into account all of the information widely available in the public domain. Bookmakers setting odds on horse racing need to set their prices with these punters in mind, whereas when setting prices on tennis matches they have to be more careful as they are primarily dealing with more professional, efficient gamblers.

9 relatively low, as the bookmaker commission rate charged is lower than other markets (at around 7-8%, whereas the commission on football is typically 10% and horse racing can be even higher). The main advantage to analysing tennis as opposed to analysing team sports such as football and rugby is that the herd-behaviour among punters isn t nearly as prevalent. The sentimentality some punters have towards certain teams could mean that they are unwilling to bet against them in any circumstances. When the team is a highly supported glamorous side, the betting patterns could be skewed dramatically. The only instance of this happening in tennis is English fans patriotically backing Englishmen to win the annual Wimbledon tournament. 4.1 Forrest and McHale reported that one of the benefits to studying the betting market on tennis is the relatively low commission charged by bookmakers. I decided that my first test would be to work out the approximate commission on my data, as according to the efficient market hypothesis outlined by both Forrest and McHale and Brailsford et al, in the event of the bookmaker setting prices in order to equalize the amount wagered on each side of the bet, the yield from all betting strategies should be negative and equal to the commission. By working out the probability odds (the reciprocal of the odds) for every player in every game, I had calculated an amount of money that would have to be staked on the player to return 1. For example, in the first round of the 2005 tournament, Baker played Gaudio. Table 1 shows the odds and probability odds for both players.

10 Table 1: Figures showing the calculation of the bookmaker s commission Player Average Odds Probability Baker B Gaudio G In order to guarantee a return equal to one unit, the punter has to stake on Baker, and pence on Gaudio. However, at 1.072, the cost of this strategy is more than one pound in total, meaning that the punter stands to lose regardless of the outcome. The sum lost by the punter when betting on all outcomes for a level stakes return is known as the commission. Over my whole sample the commission is equal to 7.9%, which supports Forrest and McHales point of the commission on tennis markets being lower than that on the markets for betting on football and Horse Racing. 4.2 The first measure of the bookmaker s efficiency at aggregating information was to see what the returns from two simple betting strategies would be: betting on the bookmaker s favourite and betting on the bookmaker s underdog. Table 2: Returns to betting on favourites and underdogs, all years All Years Yield t-stat Yield t-stat Yield t-stat Yield t-stat Favourite Underdog

11 My results in table 2 show that over the whole sample, neither betting on the bookmaker favourite or the bookmaker underdog accrues a long-term profit. In each timespan, and indeed overall, betting on underdogs yields significant losses, ranging from 11% in 2005 to as high as 40.6% in Over the whole sample betting on the underdog yields a loss of 18%, meaning that this is an extremely weak strategy. Betting on the bookmaker favourite is a better strategy, but only in the sense that the losses made by the punter are less significant, as over the whole sample, and in each subperiod, no profit is made. The only year that the strategy of gambling on favourites breaks even is in 2004, although the winnings are fairly insignificant (0.004). However, in the ensuing years, betting on the same strategy yields losses. Forrest and McHale s first test was also to investigate the returns from a strategy of betting on the favourites and the underdogs. My results for betting on underdogs are in line with theirs, as we both record a statistically significant overall loss. Also the minimum annual loss recorded by both papers was 11%, meaning that my data supports the existing research proving that always betting on the underdog yields large losses. My results for the strategy of betting on the favourite differ slightly to theirs however, as they yielded a small profit, whereas I yielded a small loss. I would not say that my results contradict those of Forrest and McHale, as my data is not statistically significant. Also if the results from 2003 are ignored, this strategy breaks even in 2004 and 2005, which is more in line with their results. The results shown in table 2 fail to support the hypothesis that by always betting on an underdog, or by always betting on a favourite, a profit can be made. My results do not

12 suggest that British Bookmakers aggregate this information inefficiently, as between 2003 and 2005, and indeed over the whole sample, betting on every single underdog/favourite fails to yield a profit for the punter. This is, however, an extremely crude strategy to test, and as a result I will be investigating the strategy of betting on favourites further. 4.3 Rather than simply dividing the players into two groups, favourite and underdog, I will analyse what effect the bookmaker s predicted probability has on the outcome. By that I mean that bookmakers have strong and weak favourites, which is reflected in how long and short the odds are that they offer on the outcome are. After calculating the probability odds, I analysed the same odds ranges as Forrest and McHale, increments of 0.1. By splitting the players into separate groups I analyse the results to see if there are any trends that can be exploited to formulate a winning betting strategy. Table 3: Returns on betting on different odds ranges over the whole sample Probability odds range Observations Yield Tstat Table 3 shows that there are only 2 probability groups that accrue significantly positive results. Betting on individuals in the probability range of yielded a profit of 2%,

13 and betting on matches in the odds range of yielded a profit of 12.7%. It appears that there may be a strategy which the punters could use in order to make a long-term profit from betting on tennis: always bet on players in these two odds ranges. However for this to be true the punter would have to identify the strategy in year 1, in order to place their bets in ensuing years. Because of this I separated the data into separate years in order to analyse it further. 4.4 Table 4: Returns to betting on different odds ranges over different subperiods Probability Odds Range Observations Yield t-stat Observations Yield t-stat Observations Yield t-stat Table 4 organises my data into different years. The data for 2003 shows that the odds ranges and yield positive returns, which means that a positive betting strategy can be identified in year 1 and employed in subsequent years, suggesting that the market is weak form inefficient. However there are two reasons why this theory can be disregarded. First of all, the data is not statistically significant, meaning that the sample was too small to draw any conclusive opinions. The second is that in 2003 the punter does not have the information that I have now: namely that the odds ranges and

14 are the only groups that yielded a profit. The punter s only way of determining which odds ranges to bet on are by analysing their data for 2003 and concluding a strategy from that. The 2003 data shows that betting on the odds ranges , , , and yielded a profit. This means that the punter would bet on all of these groups in the ensuing years, a strategy that would yield a profit when betting on the ranges and , but would yield a loss when betting on the ranges and Again my data fails to support the hypothesis that is a strategy of betting that makes a consistent profit against the bookmakers, so there is no evidence that the bookmakers are aggregating information inefficiently. Forrest and McHale found that a strategy of betting on strong favourites yielded positive results. My data is not entirely in line with theirs, as although my strongest strategy was betting on the odds range , betting on the range also yielded positive returns. However I did find that betting on genuine longshots produces spectacularly negative returns, which was also an observation of Forrest and McHale. Both studies calculated the returns from betting on outcomes in the range to be Forrest and McHale suggest that bettors who wish to become informed about tennis can do so relatively easy due to the World Ranking system, which aggregates a variety of information in an attempt to the relative quality of players. Each player is assigned a unique World Ranking position, calculated by using a complicated formula based on the player s past results. The best player in the World is ranked number 1,

15 second best number 2, etc. Therefore in a match, the player with the higher World ranking (lower number) is the better player of the two contestants. However in my sample, only 85% of the players with a higher ranking begin the match as the bookmaker s favourite. Because of this I decided to test the strategy of always betting on the better player, ie. the player with the higher World ranking. Table 5: Returns to betting on the higher and the lower ranked player, all years Obs. Yield t-stat Obs. Yield t-stat Higher W.Rank Lower W.Rank All Years Obs. Yield t-stat Obs. Yield t-stat Higher W.Rank Lower W.Rank Table 5 shows that betting on the lower ranked player yields a statistically significant loss of 20.5% over the whole sample, being almost 50% in Betting on the higher ranked player is barely better, as it still yields a statistically significant loss of 10.4% over the whole sample, despite yielding a profit in The downside to this strategy is that in matches where there is only a difference of a few places in the world rankings, the players are practically of the same standard, yet one is being labelled the better player. There is likely to be more effect when the gap in the world rankings is greater. This leads me to my next test, to see if betting on a player when there is a greater gap in the World rankings makes a difference. 4.6 I will separate the events into four different groups:

16 group 1 50 places or greater lower in the rankings. group 2 between 1 and 49 places lower in the rankings group 3 between 1 and 49 places higher in the rankings group 4: 50 places or greater higher in the world rankings Table 6: Returns to betting on differences in World Rankings, all years Group Observations Yield t-stat Observations Yield t-stat All Years Group Observations Yield t-stat Observations Yield t-stat Table 6 shows the data for each period and over the whole sample. As expected, the returns are more positive, despite still yielding losses, when betting on the player with the higher ranking. Although the results from the whole sample fail to suggest that a strategy of betting on any group will yield a profit, the returns from betting on players in group 4 are far better than any others. Over the whole sample betting on group 4 yields a loss of 4%, yet in 2004 a profit of 6.4% is made, and in 2005 a profit of 1.7% is made. This is logical, as players at least 50 places higher in the World Rankings than their opponents are largely expected to win. The stand out result from table 6 is that the largest loss comes from betting on group 2 (26.2%), as I had fully expected it to come from the strategy of betting on group 1 outcomes. However, in spite of the yield from betting on

17 group 1 over the whole sample being 12.1%, the largest loss yielded by betting on any group was group 1 in 2003, with returns being 46.2%. Again this strategy has its failings, as the World rankings don t adjust during tournaments, and could be incorrect, particularly in the later stages of tournaments. An expansion of this was to investigate whether the bookmakers aggregate information efficiently in each round of tournaments. 4.7 Different rounds of tournaments tend to have different characteristics. For example, in earlier rounds, particularly the first round, there are likely to be several players who are relativley unknown to bookmakers, making it hard for them to price the match efficiently. There are a variety of reasons for this, such as it being a young player starting out in the game, or a local player (in my study it would be a US national) who gained entry to the tournament via the extra places being allowed to home nationals 6. Bookmakers are in a difficult position, as the information about these players is asymetric (enabling people who have worked with them, and therefore hold more information regarding the player than the bookmaker, hold an edge over the bookmakers). Young rising stars of the game can be the hardest to price, because although the seeding and world rank difference between them and their opponent suggests that the established player should be the favourite, this may not infact be the case. This leads me to my next test: betting on the bookmaker underdog and favourite in different rounds of the tournaments to decide if there is a strategy of betting that beats the bookmaker. 6 In 2005 tournament, Andrew Murray, in his first year as a proffessional tennis player and world rank 312, gained entry to the Wimbledon tournament through a wild card (he is likely to have gained priority over other players due to being British). In the second round he defeated Radek Stepanek, the current world 13 and 14 th seed

18 Table 7: Returns to betting on favourites in different rounds, whole sample Favourite Underdog Round Obs. Yield t-stat Obs. Yield t-stat *Note there are no results for round 7 (the final) as the sample was to small. The results displayed in table 7 fail to suggest that a profit can be made by always betting on the underdog in any single round. In rounds 2 through to 6, the punter makes a loss of between 20.1% and 47.8% by betting on the underdog in different rounds. If the punter bets on the favourite in rounds 2, 3, 4 and 6, they will make a loss of at least 6.7%. The strategy of betting on favourites in round 5 yields a positive return of 19.5%. The results from round 1 were interesting, as betting on favourites yielded a profit of 2.8%, and betting on the underdog broke even 7. This supports my hypothesis that the bookmakers would the first round the hardest round to aggregate information for. 5.1 All my hypotheses were supported by my results. The hypothesis that betting on the bookmaker favourite would be a better strategy then betting on the underdog was supported by my results throughout the paper. Betting on favourites over the whole sample gives the punter returns of -1.8%, whereas betting on underdogs yields a loss of 7 Although a loss is actually made, it is less than 1%, therefore in line with forrest + mchale definition of breaking even

19 18%. Often my results for betting on the underdog yielded a loss which was considerably larger than the bookmaker s commission. The degree of favourite made a difference as well, and despite not being as conclusive, my results were in line with those of Forrest and McHale s in suggesting that a positive betting strategy could emerge from betting on outcomes in the probability range. My hypothesis that the market might be less efficient at aggregating information in the first round of the competition is also supported by my results. When backing underdogs in round 1 the punter almost breaks even, yet in all subsequent years the punter makes a loss of at least 20.1%. 5.2 After analysing my findings it appears that my results fail to support the theory that UK betting markets are even weak form inefficient. My definition of inefficiency in the market was thus: if a betting strategy could be identified in year N, and then implemented in subsequent years in order to sustain a profit the market is inefficient. My findings fail to suggest any form of inefficiency in the markets. When analysing my sample as a whole (not separating into subperiods) I did not identify one strategy that yielded a profit and was statistically significant. Although my results stated that betting on individuals in the probability odds range yields a profit, to take this as a fact and state that betting markets inefficiently aggregate information when setting odds would be short-sighted and foolish. The t-statistic for this result was only 0.92, making my results more likely to be an exception than a trend. 5.3 The aim of my paper was to analyse whether UK betting markets on sporting events were efficient. I decided to concentrate on one market as this would allow me to gather large volumes of data for one subject, such as Forrest and McHale did with their

20 data, as opposed to gathering small amounts of data on a wide variety of sports, similarly to Cain, Law and Peel (2003). This was because Forrest and McHale s study returned more conclusive results than the study by Cain, Law and Peel, as the high volume of data gave their findings more credibility. However, most of my results, particularly when I investigated data from individual years, wasn t statistically significant. This is because despite being larger than Cain, Law and Peel s sample, my data set was relatively small when compared to that of Forrest and McHale. If I were to improve this study I would definitely require a larger amount of data. A further extension would be to analyse the effect that different variables had on the bookmaker s efficiency. Not only would this enable me to test different strategies, such as betting on clay court games, or only betting on non-tournament games, but it would enable me to analyse the data by using the ordered probit model, similar to Brailsford et al. 6. Bibliography Economics Papers -Brailsford, T., Easton, S., Gray, P., Gray, S., (1995) The Efficiency of Australian Football Betting Markets, Australian Journal of Management 20, pg Cain, M., Law, D. and Peel, D (2003) The Favourite-Longshot bias, Bookmaker Margins and Insider Trading in a variety of Betting Markets, Bulletin of Economic Research 55:3, pg Forrest, D. and McHale, I. (2005) Longshot bias: Insights from the betting market on men s professional tennis, Information Efficiency in Financial and Betting Markets, Cambridge University Press, pg

21 -Levitt, S., (2004) Why are Gambling Markets Organised so Differently from Financial Markets?, The Economic Journal 114, pg Quandt, R., (1986) Betting and Equilibrium, Quarterly Journal of Economics 101, pg Shin, H. (1992) Prices of State Contingent Claims with Insider Traders, and Favourite- Longshot bias, Economic Journal 102, pg Thaler, R. and Ziemba, W.T., (1988) Anomalies Parimutual Betting Markets: Racetracks and Lotteries, Journal of Economic Perspectives 2, pg Vaughan Williams, L. and Paton, D. (1997) Why is there a Favourite-Longshot bias in British Racetrack Betting Markets?, Economic Journal 107, pg Websites - For all information about tennis results and odds.