Department of Economics Information and Efficiency: Goal Arrival in Soccer Betting Department of Economics Discussion Paper 11-01 Karen Croxson J. James Reade Information and Efficiency: Goal Arrival in Soccer Betting∗ Karen Croxson† J. James Reade‡ January 21, 2011 Abstract In an efficient market news is incorporated into prices rapidly and completely. Attempts to test for this in financial markets have been undermined by the possibility of information leakage unobserved by the econometrician. An alternative is to switch to laboratory condi- tions, at the price of some artificiality. Potentially, sports betting markets offer a superior way forward: assets have terminal values and news can break remarkably cleanly, as when a goal is scored in soccer. We exploit this context to test for efficiency, applying a novel identification strategy to high-frequency data. On our evidence, prices update swiftly and fully. JEL Classification: G14, D0, C01. Keywords: Information, market efficiency, gambling. 1 Introduction A matter of considerable importance in economics and finance is how relevant information becomes impounded in market prices. The significance of the topic derives partly from its theoretical pertinence: the efficient functioning of the price mechanism requires that a security’s price at all times reflect its true fundamental value. It also has much to do with practical interests: traders with superior information may secure gains at the expense of the less well informed. The efficient markets hypothesis predicts that asset prices will incorporate relevant information, and in the ∗We are grateful to anonymous referees for valuable feedback on a previous version of this paper. In addition, wewishtothankseveralcolleaguesfortheirinterestandcomments,particularlyPeteKyle,KevinSheppard,David Myatt, Paul Klemperer, Andrea Prat, Ian Jewitt, David Hendry, Andrew Patton, Neil Shephard, Clare Leaver, MarkusEberhardt,ThomasFlury,andNathanielFrank. VersionsofthepaperwerepresentedattheSymposiumof theSouthernEconomicJournalonGambling,PredictionMarketsandPublicPolicy,the28thAnnualInternational SymposiumonForecasting,theOxford-ManInstituteofQuantitativeFinance,NuffieldCollege,OxfordUniversity’s Economics department, the Conference in Honour of David Hendry, and the IMA’s First International Conference on Mathematical Modelling in Sport. We received many helpful comments at these events. Both authors have benefittedfromthefinancialassistanceoftheEconomicandSocialResearchCouncilandtheEconomicsDepartment at Oxford. Croxson also gratefully acknowledges support from the Oxford-Man Institute of Quantitative Finance and from New College, Oxford. An earlier version of this paper formed part of Croxson’s doctoral dissertation. †DepartmentofEconomicsandNewCollege,UniversityofOxford,andtheOxford-ManInstituteofQuantitative Finance. Email: [email protected] ‡Corresponding author. Department of Economics, University of Birmingham. Email: [email protected] 1 simplest interpretation, will do so immediately and completely.1 Extensive efforts have been made to put matters to the test. Fama (1970) popularized the idea of considering efficiency in relation to subsets of the totality of information, focusing on three differently stringent tests. The first and most lenient test is for weak form efficiency. It requires the current price to reflect all information contained in historical prices.2 A second test deals with semi-strong form efficiency. In a market that is semi-strong form efficient prices completely and immediately update to new information, provided that this very obviously is publicly available.3 Finally, and most stringently, there is the notion of strong form efficiency, according to which price must at all times reflect all available information, even where this is held privately.4 Applying efficiency tests in the real world, most investigations have centered on conventional financial markets.5 For instance, and regarding public information (the second form of test), a number of researchers have scrutinized the response of share prices to corporate events such as stock splits (Fama 1969), the release of company results (Ball 1968, Beaver 1968), merger announcements (Asquith 1983), as well as to announcements about economic variables such as the money supply (Waud 1970, Chen et al. 2003). Some investigations find support for the view that prices update efficiently but a number of others have uncovered some evidence of post-news price drift, described in the finance literature as “the tendency of individual stocks’ performances following major corporate news events to persist for long periods in the same direction as the return over a short window [...]” (Jackson and Johnson 2006). For instance, in the study by Patell and Wolfson (1984) profitable trading opportunities arise following public announcements about dividend and earnings and take five to ten minutes to dissipate. Meanwhile, Chan (2003) examines returns to a subset of stocks after public news about them is released and finds evidence of post-news drift.6 Somewhat problematically considering the objective of such enquiries, it can be hard to tell when news actually breaks in financial markets—it is difficult to rule out information leakage not observed by the econometrician.7 There is also the difficulty of defining normal returns. It is hard to interpret cleanly the results of tests for efficiency in financial markets as any test must assume an equilibrium model that defines normal security returns. If efficiency is rejected, this 1The efficient markets hypothesis is most commonly associated with Eugene Fama (1965; 1970; 1998). Its early originscanbetracedbacktotheworkofLouisBachelier,whoin1900studiedthedynamicsofstockpricebehavior (Bachelier 1900). 2For illustration, weak-form efficiency rules out the possibility that technical analysis techniques could be used to produce excess returns, though analysis of fundamentals still might. 3Byimplication, undersemi-strongformefficiencynotonlytechnicalanalysisbutalsofundamentalanalysiswill be powerless to deliver abnormal returns. With regard to the speed and completeness of updating, the definition of semi-strong form efficiency given in the text is the strictest interpretation. Less strict formulations exist whereby it is sufficient for efficiency that it not be possible to trade upon the relevant subset of information in such a way as to earn above-normal profits. 4In a market that is efficient in the strong form sense no one can earn excess returns, not even with privileged information. 5Vaughan-Williams (2005) offers a comprehensive review of the academic literature which has investigated in- formation efficiency in financial markets. 6The literature contains ambiguous findings in terms of the sign of any inefficient reaction to news. De Bondt andThaler(1985)findevidencethatNYSEtradersoverreacttoinformationduetoacognitivebias. Abarbanelland Bernard(1992)andChanetal.(1996),meanwhile,arguethattradersinfinancialmarketsadapttonewinformation slowly—they underreact. The literature contains several useful reviews of the evidence regarding post-event price drift (Kothari and Warner 1997, Fama 1998, and Daniel et al. 1998). 7Some market participants may be party to the content of announcements (or some part of this content) before these “go public” (Jarrell and Poulson 1989). See Worrell et al. (1970) for an illustrative discussion of leakage in the context of layoff announcements. 2 could be because the market is inefficient or because the postulated equilibrium model is incorrect. This problem—known as the joint hypothesis problem—means that market efficiency as such can never be rejected. Responding to these complications, some investigators have preferred to analyze markets in the laboratory, where conditions such as the information structure can be tightly controlled (Chamberlain 1948, and more recently, Plott and Sunder 1988, and List 2004). But while experimental settings can eliminate some concerns their artificiality raises others: what trading experience do subjects (typically students) have? Are they appropriately motivated?8 Potentially, sports betting markets offer a superior lens for efficiency studies, especially where news arrival is the focus. Unlike laboratory experiments, these are real markets with participants that are well motivated and often experienced. Contracts on sports outcomes (unlike equities and other financial securities) have well-defined terminal values and converge to these over a short pe- riod of time. Moreover, and most importantly, major sports news often breaks remarkably cleanly. For instance, once a soccer game has kicked off the most significant innovation in information con- cerns the scoring of a goal, and this event becomes common knowledge at a single identifiable point in time. This is particularly so where a game is televised, as many now are. Until very recently it was impractical to base efficiency studies around sports news; wagering was tightly controlled by traditional bookmakers (dealers), who posted prices, updated these infrequently, allowed bet- ting only up until kick-off, and due to their business model (betting against their own customers) guarded data particularly fiercely. But from 2000, widespread Internet penetration facilitated a development in betting which would transform the industry landscape (and research possibilities) radically: the emergence of online betting exchanges. Inspired by electronic financial exchanges, a small number of entrepreneurs began to offer web-based order-driven betting markets, enabling prospective punters to bet against each other through a live order book, with intermediation by the exchange to guarantee anonymity and remove counterparty risk. For the first time, customers could buy and sell bets at current market prices (which typically were keener prices than offered by bookmakers), submit their own limit orders, and do all this ‘in-running’ (as play unfolds).9 The development proved popular with many customers and in a few short years the leading exchanges had become serious betting markets. The dominant betting exchange, Betfair (www.betfair.com), now sees trading comparable in intensity (if considerably smaller in volume) to activity on the world’s leading financial exchanges. Betfair was one of the very first betting exchanges onto the market and has grown to be overwhelmingly the largest; its turnover of over $50m per week accounts for 90% of all exchange-based betting activity worldwide and it currently has over two million registered users. Two million trades a day—six times the number of trades on the London Stock Exchange—are processed through Betfair markets, and the exchange now covers a vast variety of events, mostly sporting.10 From an academic perspective, the success of Betfair presents an attractive research oppor- tunity. We exploit data extracted from the exchange at high frequency to conduct a novel and remarkably clean test for semi-strong form efficiency. The data comprise second-by-second snap- shots of Betfair’s live order book for professional soccer games, featuring in-running prices and volumes related to betting on the outcomes of 1,206 matches. Included in the sample are recent 8See Levitt and List (2007) for a recent consideration of factors affecting the generalizability of laboratory findings, including the extent to and manner in which subjects are scrutinized in their decision-making. 9A limit order is a speculative order to place a bet at a price not worse than some specified ‘limit’ price and for a stated volume. The price specified is more attractive than the current market price and the order will be ‘filled’ only if the market moves in a favorable direction. 10“Betfair Makes Online Odds on AC Milan, Hillary Clinton, Weather,” Bloomberg News, September 6, 2005. Article available online at: http://quote.bloomberg.com/apps/news?pid=nifea&&sid=a8Y11XQeIcyY 3 English Premiership matches (547), games played as part of the Euro 2008 Championships (101), games from the Champions League (165), the Scottish Premiership league (64), the UEFA Cup (249), the Intertoto Cup (14), the Asian Cup (24), and a number of international friendlies (42). The average match is heavily traded, with over $6m bet in total, and half of this in-running. The major news in a soccer match concerns the arrival of goals. Goals arrive infrequently and tend to be material to match outcomes. If the betting markets in our sample are semi-strong form efficient then prices should respond immediately and completely to such news. The paper implements a complementary set of tests to investigate. Immediacy of reaction implies a jump in price, and it is straightforward to test for this. We carry out disaggregated analysis on our full sample and confirm that prices jump when a goal is scored; on average the scorer’s win probability jumps up by 22 points. Drilling into the sample, the size of initial jump can be considerably smaller or larger than this depending intuitively on such factors as the precise stage of play (later goals tend to have a greater impact) and the realized scoreline (goals that change the default match outcome have the biggest effect on prices). Toascertainwhetheraninitialjumprepresentscompleteupdatingormerelythestartofamore sluggish updating process is somewhat less straightforward. Consider that, once a soccer match is underway, participants should update to major news such as a goal, but also to the continual flow of more minor news inherent in the ticking down of the playing clock, the arrival of cards for offences, free-kicks, and injuries. As playing time elapses efficient betting prices should drift continually, therefore, reaching their terminal values (1 or 0 in probability terms) by the end of the game. By implication, properly identifying inefficient drift in a betting price during minutes of play would require positing some model of ‘efficient’ drift. But quite what efficient drift looks like will be match specific, depending on such factors as the teams competing, the new scoreline, and time left on the clock. We implement three complementary approaches to testing for efficiency in this setting. Our first approach introduces an identification strategy which allows us to study the incor- poration of major news in individual contracts whilst side-stepping the potential complication of ‘efficient’ drift. Our strategy involves exploiting the (virtually) newsless window provided by the half-time interval in play. Soccer games feature two periods of play—a first half and a second half, each of 45 minutes plus a few minutes of ‘injury time’ (added on by the referee to compensate for stoppages). Between these periods the match stops completely for 15 minutes, but betting related to the match outcome continues apace. We exploit this window as an opportunity to iden- tify potential inefficient goal-related drift simply and cleanly. Concretely, we study the reaction to goals that arrive on the cusp of half time. Our sample features 160 goals that arrive within five minutes of the precise end of the first half. Looking more closely at these ‘cusp goals’, 53 are scored in the final minute of first half play. These goals provide the basis for a particularly strong test for semi-strong form efficiency. Focusing on the reaction of half-time prices to these goals, we implement both a test for statistical efficiency, using regression methodology, and a test for economic efficiency. Our test for economic efficiency asks whether a hypothetical trader could make money during the half-time interval by exploiting goal-related price drift during the break. We are unable to reject the efficiency hypothesis that a cusp goal immediately shifts price but does not cause this to drift during the interval: prices update so swiftly and completely that the news of a goal is fully digested by the time the break commences, even where the goal occurs just moments before the end of play. The key strengths of this test are simplicity and cleanness. A potential weakness relates to the potential for any efficiency finding to be specific to the half-time interval. One might suspect, for instance, that our inability to detect sluggishness in updating over the break could be due to 4 a lull in trading during this time. We deal with this concern by tracking and reporting half-time trading activity; betting interest remains healthy during the break, and certainly half-time trading is strong in games which feature cusp goals.11 One might worry that the half-time finding does not generalize to minutes of play for other reasons: different trader types could be active during half time or goals might interact with the arrival of more minor news when the match is in progress. For robustness, therefore, and capitalizing on the richness of our data set, we deploy two further testing strategies. Both are intended to provide a more direct look at the incorporation of news during minutes of play. The first exploits our large sample size in exploring whether average in-play prices display inefficient drift. An informationally efficient asset price should satisfy the martingale property—the current price should be the market’s best guess of the price next period. Yet, as noted already, individual in-play contracts will display almost continuous drift, regardless of the efficiency of the underlying contracts. Consequently, testing for a martingale in the price series for an individual contract, or a small set of contracts, cannot yield meaningful conclusions. The particular importance of sample size in this context can be understood by recognizing that a test for absence of drift in in-play prices is a close relation to the standard calibration tests now familiar to readers of the prediction markets literature (for instance, Wolfers and Zitzewitz 2004 and references therein). Like most prediction markets contracts (for example, ‘Obama to Win’), the Betfair ‘match outcome’ contracts that we study have a binary payoff structure—they pay out 1 in the event of a win, and 0 otherwise. This means that it is never possible to tell whether an individual binary contract priced at say, 0.6, was priced efficiently. It is, however, possible to consider a sample of such contracts priced at, say, 0.6, and provided the sample is large enough test meaningfully for efficiency by asking whether these ‘win’ (have a final price of 1) 60% of the time. This is a standard calibration test. It is equivalent to asking whether the average final price is 0.6—or whether on average the contract prices do not drift between now and the end of the event. Hence, such a test can be considered a special case of a martingale test where the future price considered happens to be the final price. Typicallythoseconductingstandardcalibrationtestsplotcontractprices(inprobabilityterms) against ‘win’ frequency, and carry out standard diagnostic tests to assess closeness of fit to the 45–degree line. In an efficient market all the data points should lie on the 45–degree line. But if the sample of contracts is too small then the fit to the 45–degree line will be poor, regardless of efficiency. In the extreme, imagine a calibration test conducted on a sample that includes only ten contracts, one in each of ten price intervals: (0–0.1), [0.1–0.2) . . . , [0.8–0.9), [0.9–1). Each of these ten contracts must go on to win or lose. With a single contract in the interval [0.4–0.5), either 100% or 0% (but never 40–50 %) of the contracts in this bracket will ‘win’. Thus, for a small sample like this, it is very easy to see how the results (evidence for efficiency) will have little meaning.12 Similarly, tests for average post-goal drift will have little bite unless the sample is sufficiently large, providing good coverage of the various price points. With a large enough sample we should find that for those contracts priced efficiently at 0.9 immediately following a goal the 11Weak half-time trading is observed in a few exceptional cases. For instance in the Premiership match between Wigan and Liverpool, the latter had built up a virtually unassailable 4–0 lead by half time. This early domination appears to have killed interest in the match odds market. 12See, for instance, Christiansen (2007) for a practical illustration of the problems of conducting standard cali- bration tests on a small sample of prediction markets. His sample featured 39 markets trading contracts related to theoutcomesofrowingcontests. Standardcalibrationonthesedata,usingintervalsoftenpercentagepoints,shows a relatively poor calibration curve. The poor calibration is due to the small number of data points in each interval. For example, only one contract in his sample had a price (probability) of over 80% (a contract on a previously unbeaten Great Britain boat to win a Henley Regatta) but that contract lost, undermining the overall calibration (see his Figure 2). 5 average price in the next minute or so is 0.9. Indeed the average price should remain at 0.9 for the remainder of the game. We utilize the large size of our sample to implement such a test in the paper, focusing on the stability of the average price series in the fifteen minutes following goals. We are unable to find signs of significant in-play drift in average prices following goals and so fail to reject the hypothesis that these markets update efficiently during minutes of play. Our second approach to testing efficiency in-play is more elaborate; it involves modelling in- running match outcome probabilities in order to estimate ‘efficient’ time-related drift for each match. Concretely, we begin by ‘reverse engineering’ the goal arrival process from historical match data. The bivariate Poisson model suggested in Karlis and Ntzoufras (2003) provides a natural starting point for this exercise. Following this, we combine the fitted goal arrival model with a multinomial model to back out ‘efficient’ in-running match outcome probabilities for the games in our sample. The final step is to compare the two series—our ‘efficient’ price series and actual observed Betfair prices—with a view to drawing inferences regarding efficiency. We find that the probabilities implied by Betfair prices closely track those implied by the selected Poisson process, which suggests that most of the in-play drift we observe can be ascribed to efficient updating to the clock. There are some differences between the two series and we discuss these further in the paper. This form of efficiency analysis is notably less clean than our half-time identification: the joint hypothesis problem is severe as our test relies on the ability of the posited Poisson model (which cannot incorporate in-play developments unobservable to the econometrician) to describe ‘efficient’ in-play returns. Nevertheless, the modelling exercise offers an insightful and again more direct perspective on efficiency during minutes of play. Inadditiontopreviousworkonefficiencyinfinancialmarkets,ourstudyisrelatedtoacollection of earlier studies of efficiency in sports betting markets. The vast majority of previous betting analysesarebasedonlowfrequencyprices(typicallybookmakerodds)sampledpriortothestartof a live event (betting in-running being a very recent development). For instance, studies by Golec and Tamarkin (1991), and Gray and Gray (1997) both examine efficiency in the NFL betting markets using the closing spreads of Las Vegas sportsbooks. Closing spreads are the final prices quotedbythebookmakersshortlybeforegametime. Vaughan-Williams2005providesarecentand thoroughreviewofpreviousworkonbettingandefficiency. Initsexploitationofin-runningbetting exchange data, and its focus on goal arrival in soccer betting, our work is most closely related to a recent paper by Gil and Levitt (2007). Gil and Levitt analyze data from the Intrade exchange (www.intrade.com), which until recently operated markets for sports-related bets.13 Considering fiftymatchesfromthe2002SoccerWorldCup, theauthorsimplementanevent-studymethodology to look at updating to goals during minutes of play. They report that Intrade prices, though they respond strongly to a team scoring, trend for ten to fifteen minutes after the goal is registered. On the face of it, this drift appears reminiscent of the post-news drift found in some financial market studies. Gil and Levitt (2007) interpret the drift they observe in Intrade’s markets as evidence of informational inefficiency—prices, they suggest, update sluggishly to the news of a goal. The analysis in their paper is insightful in many ways (for one, the data come disaggregated at the individual trader level, and the authors are able to document the endogenous emergence of market makers), butasatestforsemi-strongformefficiencyitsuffersseverelimitations. Themainconcern relates to data quality: Intrade soccer markets attract very few traders (on average just 75 per game); these people make very infrequent trades (an average game attracts 100–200 trades and 13To avoid difficulties with US law, which considers wagering on sports to be gambling, Intrade-Tradesports, a single operator at the time of the 2002 World Cup, has since split into two separately registered companies with different activities: Tradesports deals with sports betting, whereas Intrade now operates as a prediction market focused exclusively on non-sports events. 6 features several minutes in which trades do not occur); and betting volumes typically are low (just $1.5m is traded in total across the full set of fifty matches). The first of our own in-play efficiency tests, which applies a comparable regression methodology to a large sample of Betfair markets, fails to reject the efficient market hypothesis. We can conceive of a few possible explanations for the apparent discrepancy in our respective findings. It could be that the Intrade markets Gil and Levitt (2007) study are inefficient, perhaps because of cognitive biases on the part of traders or simply because of the markets are very thin. An alternative explanation is that this particular test for efficiency—being a test for whether there is drift in average in-running prices—is not robust to their relatively small sample size, for the reasons discussed above. We conclude our study by using the dataset to take a closer look at whether and how liquidity affects a market’s ability to aggregate information. This issue stands at the heart of an important and unresolved debate in the finance literature. It has considerable academic but also practical rel- evance, perhaps most obviously in the field of prediction markets design.14 A number of theoretical articles establish that liquidity is related to the informational efficiency of markets but the sign of the relationship is disputed. In the first view, increased liquidity lowers the transaction cost (price impact) for informed arbitrageurs and creates greater incentives to acquire information, leading to improved informational efficiency. In the second view, liquidity is a proxy for non-informational trading (noise trading), which may harm informational efficiency (De Long et al. 1990). A fur- ther possibility is that liquidity and informational efficiency are unrelated. Whilst some empirical studies have lent support to the first view, that securities mispricing is greater in illiquid markets (Kumar and Lee 2006; Sadka and Scherbina 2007; and Chordia, Roll, and Subrahmanyam 2008), some other investigations appear to support the idea that liquidity worsens mispricing (Tetlock 2007, Hartzmark and Solomon 2008). Tetlock’s (2007) empirical analysis utilizes asset prices sam- pled at thirty minute intervals from the online prediction market TradeSports. As he points out in his paper, the advantage of working with such a data set is that the assets traded have short lives and so reach their terminal values quickly. He finds “strong empirical support for the hypothesis that the prices of illiquid securities converge more quickly toward their terminal cash flows,” so supporting the second strand of theoretical work. A limitation of the study, from the perspective of semi-strong form efficiency, is that the author does not directly observe event-relevant information. Across our dataset as a whole, we observe considerable variation in liquidity per game, with betting volume of over $50m in the most heavily traded match, compared with just over $0.05m in the least traded. We exploit this variation, together with the clean and observable arrival of event-relevant information, to offer a new perspective on the link between liquidity and efficiency. Our preliminary investigations would appear to support the view that liquidity and informational efficiency are not strongly related in these markets, at least over the liquidity range we observe. Liquidity can be defined in a number of ways, and in the current analysis, we use in-play trading volume as our proxy. Future work could deploy more sophisticated liquidity measures. It would be of further interest to investigate the effect of news arrival on intra-match liquidity. The rest of our paper is organized as follows. The next section provides further background on 14Recent years have seen a growth in real-world interest in the topic of prediction markets, and considerable hype about the potential for markets to revolutionize forecasting and decision making. Yet the formal literature on prediction markets is very underdeveloped and has yet to investigate with sufficient rigor whether the information such markets generate can be relied on for decision making. Whilst evidence from some existing studies (many of the Iowa Election markets) is encouraging, and several researchers have recently emphasized the ability of markets to improve decisions (Hanson 2002, Hahn and Tetlock 2005, and Sunstein 2006, among others), considerably more work is needed. For further information the reader is referred to the recent survey article by Wolfers and Zitzewitz 2004 and to Hahn and Tetlock Eds., an excellent compendium of papers on information markets. 7 the betting industry and discusses Betfair in more detail, whilst Section 3 describes the data set used in this study. Section 4 discusses estimationstrategy and presents the mainfindings regarding market efficiency. Section 5 briefly investigates the possible link between informational efficiency and liquidity. Concluding remarks are set out in Section 6. Section 7 is an Appendix containing supplementary materials referred to in the main text. 2 Betting and the Betfair Exchange Traditionally, betting markets have been run by a closed community of licensed dealers, known as bookmakers. Bookmakers are similar to market makers in financial markets; they establish and maintain liquid markets by quoting prices at which they will deal. In betting, the prices are termed “odds” and the most common type of bet is known as a fixed-odds bet. Suppose party A wishes to back (bet on) some outcome and party B wishes to lay (bet against) the same. Then under a fixed-odds bet, A agrees to pay B a certain amount (the backer’s “stake”) if the outcome fails to materialize, and B agrees to pay A the same stake multiplied by pre-agreed (hence “fixed”) odds if instead it does. For example, A might stake $100 at odds of 3 : 1 (‘three to one’) that Argentina will win the World Cup. In this case, she collects $300 from B if Argentina succeed, but otherwise B keeps her $100 stake. When betting with bookmakers, customers are restricted to backing outcomes only; the bookmaker plays the role of party B, taking the lay side to every bet. Odds relate inversely to the probabilities associated with particular outcomes.15 For instance, odds of 3 : 1 imply a view that Argentina is three times more likely to fail than to succeed (a 25% probability of Argentine victory).16 Bookmakers rely on in-house gambling experts to assess the likelihood of different outcomes and to compile a set of odds accordingly. As the event draws closer the odds can be adjusted, reflecting the arrival of relevant information and the bookmaker’s desire to maintain a balanced book. Odds are described as “fair” when the implied probabilities sum to one, but built into the set of prices offered by the bookmaker is a return for liquidity services (known in betting circles as the “overround” or “vigorish”) such that the sum of probabilities exceeds one. In 1999, this bookmaking model was still the only model of betting, and bookmakers belonged to an exclusive and profitable club. In the UK, one of the world’s key betting markets, it was illegal for anyone other than a licensed bookmaker to accept bets and a handful of major players (William Hill, Ladbrokes, Coral) dominated the market. The overround stood at a healthy twenty two per cent.17 Thearrivalin2000ofonlinebettingexchangesmarkedarevolutionintheindustry. Theleading exchanges are essentially order-driven markets in fixed-odds bets, allowing individual punters to bet with each other directly, thereby disintermediating the bookmaker. This means that exchange bettors can and do lay individual outcomes, contrary to the standard bookmaking model. In addition, exchanges allow customers to place bets “in-running,” once an event is underway. This is felt to have created a significantly more exciting betting experience. Typically, customers are charged a small commission for exchange betting services, but the exchange does not otherwise impose any overround. Compared with bookmakers’ odds, exchange prices, at least for popular 15The interpretation of betting prices as probabilities is a somewhat debated area. The interested reader is referred to Wolfers and Zitzewitz (2006) and the articles cited therein, particularly Manski (2006). 16In this example, the odds are quoted in so-called fractional form. An alternative is to quote decimal odds, in which case the stake is included in the quoted multiple, so that 3 : 1 becomes 4. This is convenient because the implied probability is then obtained simply by inverting the decimal odds and normalizing. 17Merrill Lynch Research, 17 January 2006. 8 events, have tended to be highly competitive.18 The real hurdle for exchanges has been to achieve sufficientliquidity. Betfairwasoneofthefirstexchangestomarket, andisnowbyfarthelargest. It leviesastandardcommissionof5%onwinningbets, fallingto2%fortheheaviestusers.19 Betfair’s early entry into the market and its decision to run with a model much closer to a standard financial exchange than some of its competitors (notably Flutter.com) are thought to have been pivotal its success.20 Volumes on the exchange are estimated to have doubled from $5.23bn to $11.06bn between 2003 and 2004, and almost doubled again between 2004 and 2005.21 These growth rates are well ahead of those for the gambling market generally. Figure 1 benchmarks Betfair to the world’s largest financial exchanges in terms of trade frequency.22 Betfair processes around two million trades a day—six times the number of trades on the London Stock Exchange. And in the past few years the search term ‘betfair’ has overtaken ‘FTSE’ in popularity on google.co.uk (Figure 2). The selection of markets Betfair offers is vast and covers most sporting events of popular interest, together with many non-sporting events (such as key political events and reality TV). Horse racing dominates exchange turnover, followed by soccer. Within soccer betting, customers can place bets related to the ‘Outright Winner’ of a particular league or tournament, or the ‘Top Scorer’ of the competition, for instance. Meanwhile, ‘Match Odds’ markets allow betting on the outcome of individual games, by backing (betting on) or laying (betting against) the ‘Home Win’, ‘AwayWin’, or‘Draw’. Forthosewithlessconventionalbettingpreferences, therearemarketssuch as ‘Over 2.5 goals,’ ‘Half-Time Score’ and exotic bets, such as Asian Handicaps and Multipliers. SupposeauserwishedtobetontheoutcomeofarecentPremiershipencounterbetweenArsenal and Manchester United. Figure 3 shows the order book shortly before kick off.23 Theorderbookindicates, amongotherthings, thatshouldshewishtobackManchesterUnited, she might immediately stake up to $16,784 at odds of 3.3, and up to a further $53,140 at slightly 18The dominant exchange, Betfair, claims its prices are on average 20% more generous than bookmakers’. Ozgit (2005)confirmsthecompetitivenessofBetfair’spricingintheBasketballmarkets, althoughhedoesdrawattention tothefailureofexchangesometimestooffersufficientliquidityatinside(best)prices. Henotesthatpunterswishing to place large bets can be better off taking their custom back to bookmakers rather than “walking down the order book” at the exchange, accepting increasingly unattractive prices to get large orders filled. 19On the 8th of September 2008 Betfair announced the introduction from 22nd September of an extra “Pre- mium Charge” to be paid by those customers whose winnings over the preceding 60 weeks have reached a certain threshold. Such gamblers will be required to pay 20% of their profits to Betfair in commission or other charges. The stipulated winnings threshold was set so high that the vast majority of Betfair users have so far been en- tirelyunaffectedbythisinnovationtothechargingscheme. Neverthelessthedevelopmenthasprovedcontroversial: http://www.guardian.co.uk/sport/2008/sep/16/horseracing 20Flutter.com, founded in February 1999 by American management consultants, was the first person-to-person betting site. Des Laffey (2005) analyzes some of the operational and marketing differences likely to have led to Betfair’s dominance over (and eventual merger with) its main rival, despite the Flutter managing to attract a comparatively huge amount of financial backing for its launch: “Flutter believed that they could thrive by facilitatingsocial betsbetweenfriends, forexample aboutwho would wina gameofgolf, andalso limited thevalue and frequency of bets allowed.” “Flutter’s website was not based around the Betfair idea of matching pools of money from backers and layers, instead requiring a complete match between a single backer and a single layer. Multiple transactions on an event by a punter on Flutter were also treated separately which led to inefficiency whilst the Betfair model recognised mutually exclusive outcomes.” 21Merrill Lynch Research, 17th January 2006. 22ThisfigureisbasedonanalysisundertakenbyStephenRoman, Analyst, FXCM,NewYork, commissionedand reported by prediction markets blog midas.org. 23The standard view of the Betfair order book shows the best three prices (and corresponding available volumes) on the back and the lay side. By clicking on the team name it is possible to view the full order book showing any prices and volumes available beyond the first three steps of the book, along with historical prices charts for each selection. 9