The Bookie Puzzle: Auction versus Dealer Markets in Online Sports Betting

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1 The Bookie Puzzle: Auction versus Dealer Markets in Online Sports Betting Alper Ozgit Department of Economics, UCLA September 29, 2005 Abstract Both financial markets and online betting markets have recently converged to a hybrid structure where order-driven mechanisms (auction, betting exchanges) and quote-driven mechanisms (dealers, bookmakers) coexist and compete with each other for order flow. The absence of market consolidation in financial markets has been a puzzle because of lower transaction costs when auction mechanisms, or limit order books, are used. Parallel to this, the betting industry claims that odds offered on the exchange are more competitive and the bookmakers should be driven out of the market. I compile and analyze a dataset of National Basketball Association (NBA) games and find that both odds and net returns on the leading betting exchange (Betfair) are consistently higher than that of the two leading bookmakers (William Hill and Ladbrokes). These results are puzzling, since the bookmakers continue to be profitable. The bookie puzzle, the observation that bookies attract a lot of betting although better returns are available elsewhere is resolved through liquidity-based explanations. As the order size gets larger, I find that i)the return differences vanish rapidly, and ii) Order flow migrates to the bookmakers, thereby justifying the presence of and the need for bookmakers. Keywords: Auctions, Dealership, Market microstructure, Execution costs, Liquidity, Online betting. JEL Classification: D44 (Auctions), G14 (Information and Market Efficiency; Event Studies) 1

2 Betting exchanges will mean the end for bookmakers -Tab Limited, an Australian-based provider of entertainment services specializing in wagering and gaming 1 Introduction Trading mechanisms used in financial markets change over time. In the beginning of 1990 s, markets relied more exclusively on quote-driven regimes with Nasdaq and the London Stock Exchange being the two leading examples. Toward the end of the century, order-driven systems became more prevalent and most markets either adopted a pure order book or they moved to a hybrid structure where dealers and limit order book coexist. On Nasdaq, orders from the public now compete with dealer quotes. On the London Stock Exchange, the quote-driven SEAQ and the order-driven SETS supplement each other. The structure of the market, its effect on the price discovery process and final resource allocations has come to be an important research agenda and central to market microstructure literature. This research program has exploded in the last twenty years and deepened our understanding of the functioning of the financial markets. Madhavan (2000) provides an excellent survey. Betting markets bear many similarities with financial markets. In both markets, people with different beliefs trade with each other to make profits in a zero-sum setting. Moreover, large amounts of money are at stake. However, betting markets also have the additional advantage of price revelation. The price of a security is never known, but the price of a gamble is revealed in the long run as many similar events unfold. As a result, betting markets have been under scholastic radar for a while; they provide alternative venues to test theories in financial economics. In particular, the efficient market hypothesis has been regularly analyzed. Several studies presented anomalies against this hypothesis and questioned arbitrage opportunities (Ali, 1977; Snyder, 1978; Thaler and Ziemba, 1988; Gabriel and Marsden, 1990; Woodland and Woodland, 1994). The betting industry has also changed significantly. Interestingly, this transformation has been almost identical to that of the financial markets. Betting markets have traditionally been characterized by quote-driven mechanisms with bookmakers posting odds for selected events. These markets have now converged to a hybrid structure, where betting exchanges, essentially limit order books, cross trader-to-trader transactions and bookmakers, or dealers, supply liquidity to markets. Both markets coexist and compete with each other to attract order flow. In this paper I argue that the link between betting markets and financial markets is underutilized and propose that the market microstructure literature can use new insights from the current organization of betting markets. I draw a one-to-one map between two markets and attempt to understand the effects of the two most common trading mechanisms, auctions and dealership regimes, on the betting behavior. In contrast to previous studies that emphasize efficiency, I focus on execution costs on sportsbooks and 2

3 betting exchanges. The market microstructure literature has established that execution costs are usually lower on the exchanges. In betting markets, this would mean that betting exchanges offer higher returns. Indeed, the betting industry seems to accept this fact. To check the validity of this argument, I compiled a dataset based on online betting markets. I report the results of this natural experiment and show that both the odds and net returns are higher on the exchange. My dataset consists of National Basketball Association (NBA) games played between December 2004 and February Data are collected from the leading betting exchange, Betfair, and from the two biggest bookmakers, William Hill and Ladbrokes, all of which are registered in the UK. The results, in tandem with the increasing profitability of selected sportsbooks, are quite puzzling. The bookie puzzle refers to the observation that bookies attract a lot of betting although better returns are available elsewhere. As a matter of fact, the bookie puzzle can be seen as the betting counterpart of the network externalities puzzle and dealer puzzle in financial markets (See Madhavan (2000)). The former refers to the observation that markets do not tip to a single structure despite strong benefits to consolidation. The latter is about uncovering why dealers are valuable to the market. Suggested explanations include price discovery and stabilization as well as the provision of liquidity. Motivated by this, I come back full circle to the betting markets and empirically check whether the hybrid structure in betting markets can be explained by the developments offered in the finance literature. I find that significantly lower execution costs, or higher returns, on the exchange vanish rapidly as the orders become larger. Moreover, I provide evidence that whenever the exchange markets are thin, order flow migrates to the sportsbook thereby justifying the growing profitability of the latter. To that end, I demonstrate that the bookmaker revises the odds more frequently, when either the liquidity on the exchange is low and/or an unbalanced order flow is more likely to arrive to the book. In financial markets, dealers revise their quotations if their position is far from the desired inventory level. (Add References!) Therefore, the bookmaker behavior is is consistent with the inventory adjustments theories in financial economics. This paper has two important contributions. First, by reporting the results of a natural experiment in online betting markets, I present an empirical comparison of auction and dealership mechanisms. Empirical studies that compare different markets have been rare. Cohen et al. (1986) compare two specialist markets (NYSE and AMEX) to two non-specialist markets (Rio and Tokyo). Huang and Stoll (1996) compare NASDAQ and NYSE looking at execution costs using a matched sample. These studies have the apparent drawback that traded issues are different on selected exchanges. Amihud and Mendelson (1987) look at the differences between call auctions and continuous auctions within the NYSE. This removes the problem of different contracts but the comparison is not between auction and dealership regimes. Moreover, the call auction (or clearinghouse) and continuous auction (or double auction) institutions are close variants and they 1 In fact, the dataset will eventually cover the entire season. At the time of this writing, the analysis is carried out for three months and the paper reports these preliminary results. 3

4 yielded almost identical results in lab settings. 2 Closest to this paper is perhaps De Jong et al. (1995). They compare auction and dealer regimes by utilizing the fact that some French stocks trade on both exchanges. However, in their case the Paris Bourse is not an exclusive auction mechanism, but rather a hybrid where some shares are traded through call auction as well as bilateral search. Moreover, the entire limit book is not visible and some liquidity is hidden. In the present study, the entire book is common knowledge, all liquidity is committed and auction is the only mechanism used. The difficulty of empirical intermarket comparisons is perfectly summarized by Friedman (1993): Field data unfortunately rarely permit such clean [institutional] comparisons. This paper builds on one of these rare incidences. Second, using a unique dataset, I provide a detailed description of betting markets. To my best knowledge, this is the first paper that analyzes these markets from a market microstructure perspective. In similar vein, Levitt (2004) has analyzed gambling markets and demonstrated that the bookmakers are more skilled at predicting the outcomes than the bettors, which allows them to post non-market clearing prices and earn supranormal profits. Based on this conclusion, he claims that betting markets are organized differently from financial markets. However, he does not analyze betting exchanges. Therefore, although his paper offers an explanation why betting markets have evolved the way they did, it is silent about the current structure of betting markets. The present study differs from his and other related work by arguing that markets are quite similar in terms of their structure. Interestingly, the financial markets display a hybrid structure as a result of changes in regulation, whereas in betting markets, entrepreneurs played a game where the choice of the trading mechanism is endogenous. Roughly speaking, the financial markets correspond to the social planner outcome and the betting markets are characterized by decentralized profit maximization. The similarity of the structure in both markets can therefore imply that both markets are quite efficient. The rest of the paper is organized as follows. The next section summarizes the online sports betting market. Section 3 describes the data used in this study. Section 4 contains the main results. Section 5 concludes. 2 Friedman and Ostroy (1995) have documented this perfectly. One can think of DA being more efficient than the clearinghouse mechanism because of the continuity it possesses, in fact, it was exactly the position taken by one of the authors before they carried out the project. Although they ran experiments which are explicitly designed to produce different outcomes under different institutions, the two institutions fared equally well. 4

5 2 The Online Betting Market 2.1 Overview of the Industry Background The regulation of the gambling industry is an important policy problem. In this regard, the US and the UK are quite different. In the US, gambling is limited to certain states, Indian reservation areas and on-boat gambling. Online gambling is illegal. In a sharp contrast to this, gambling services are quite common in the UK. Gross stakes wagered in the UK in 2002 represent about five percent of the GDP. Naturally, providers of wagering services based in the UK have prospered and emerge as viable candidates of data sources. Betting is an important part of the gaming sector. Several wagering opportunities are available to those who want to bet on a certain outcome happening. Bets can be placed at betting shops where available, through phone, television systems or online. Bookmakers, or sportsbooks, may choose to offer some or all of the above. For example in the UK, the majority of the betting activity still comes from betting shops, but internet betting has been rising steeply. In contrast to this online wagering constitutes most or all of the betting activity on exchanges. Technically, betting exchanges can also offer wagering activities at shops, but I am aware of very few examples. Clearly, any meaningful comparison of the two market structures will necessarily rely on online units. The most comprehensive listing I could find specifies 640 domains hosted by sportsbooks worldwide although the number is believed to be approaching a thousand. 3 The same source lists 32 betting exchanges. In a world with numerous online sportsbooks and a growing number of exchanges, the main selection criterion in this article is the market share. Betfair is a betting exchange registered in the UK and is the clear market leader in the exchange market with an approximately 90% market share making it an obvious choice. The choice of the bookmaker is less obvious. Nevertheless, the bookmakers analyzed in this study, William Hill and Ladbrokes, are reasonable choices for two reasons: First, they are also registered in the UK, making the potential customer base more or less homogenous. 4 Second, they are the two biggest bookmakers in the UK, accounting for almost half of the total betting activity. Their online units together correspond to approximately 10 percent of the global online betting. 5 The introduction of betting exchanges is considered as a radical change in the gambling industry. According to BBC, The betting exchanges, Betfair, Betdaq and co. represent the greatest revolution in gambling in generations. (BBC, 17 August 2003). According to the popular belief, an exchange poses a serious threat to the bookmakers because it is able to offer much competitive odds. The quote in the very beginning of the 3 Source: 4 Even for online units, the bulk of the betting activity originates within the UK. 5 Gross revenues from these bookmakers are readily available from their annual reports. The estimates for the total size of the online betting industry vary, I use the widely cited figures by Christiansen Capital Advisors. 5

6 paper reflects the stance of a typical gaming provider. The prediction of the betting industry is a simple market consolidation argument; higher odds on the exchange will result in migration which will in turn make the odds more competitive and lead to further migration. Whether this is happening or not is an empirical question. The next subsection offers a closer look to company specifics and argues that this has not happened Company Specifics William Hill. William Hill is established in Its shares have been publicly traded on the London Stock Exchange since June It has recently acquired 624 shops of rival Stanley Leisue and became the largest operator in the UK with more than 2000 betting shops. These shops are still the biggest source of revenue but as a result of an increase in the use of the internet, the contribution of online gambling started to follow an upward trend. In 2004 (2003), the interactive unit has generated a gross revenue of (84.9) million pounds, up 25%, and profit of 51.7 (37.1) million pounds, up 39%. The number of interactive customers was 292,000 (247,000) in 2004 (2003). William Hill does not accept wagers from the US. Ladbrokes. Ladbrokes Limited is the betting and gaming division of the Hilton group. It has around 2000 betting shops in UK and has been the biggest operator in the UK until the recent acquisition of Stanley by William Hill. Its online gaming division has reported a gross revenue of 89.3 (63.7) million pounds in 2004 (2003). Its profits have risen from 14.2 million pounds in 2003 to 21.3 million pounds in The number of interactive customers was 306,000 (205,000) in 2004 (2003). Like William Hill, Ladbrokes does not accept wagers from the US. Betfair. Betfair is the leading betting exchange. It is established in 1999 and became operational in Soon after that, it merged with Flutter.com, the then-leading betting exchange. Betfair operates mostly on an online basis but it also provides its customers with the option of phone betting. In the year to 30 April 2005, Betfair s revenues increased by 61% to million pounds from 66.7 million pounds. Operating profits increased to 22.3 million pounds, up 87% from 11.9 million pounds. Its active users has increased to 95,000 from 65,000, and its registered users are estimated to be over 300, Betfair s business model is now widely recognized and respected, the company landed the Ernst and Young Emerging Entrepreneur of the Year Award in 2002 and the Queen s Award for Enterprise in Betfair, like its main competitors, does not accept bets from within the US. 7 6 An active user is someone who placed at least one bet in the last thirty days as Betfair defines it. The numbers for the bookmakers above also correspond to active users although the definition is unclear. It is somewhat curious that the proportion of active users on the exchange is about one third whereas at sportsbooks it is much higher. 7 They claim that they have access to a technology that is capable of locating the customers. Although these geolocation technologies might not be perfectly accurate, I was not allowed to activate my account when located in US, although I supplied a non-us address as well as a non-us credit card. 6

7 Discussion. The interactive division of William Hill and Ladbrokes include the online sportsbook, online casino and online poker. The online unit of Betfair includes the exchange itself and online poker. Segmental information is not reported, therefore one can argue that the growth of the bookmakers can be attributed to the casino and poker segments rather than the betting activities. I dismiss this claim on several grounds. First, the revenue figures from online poker, although not revealed, are estimated to be close for Betfair and William Hill. Ladbrokes has a stronger presence in poker, but they reported a 34% increase in the number of registered users, and a 49% increase in the number of active users in the sportsbook segment. The casino segment is more competitive and the growth figures have been significantly less, for example Ladbrokes reports a relatively small 7% increase in gross wins from the casino unit. In sum, different performance metrics reveal that there has not been a visible migration from top sportsbooks to the exchange despite the alleged differences in returns. The aggregate demand for online betting has increased, but the influx of bettors is not concentrated in one venue. This absence of migration might follow from misperceptions about returns or differences in market structure. The next section is devoted to a detailed summary of the market architecture. In fact, the current design of online betting strongly parallels that of the financial markets. 2.2 Market Architecture Traditional bookmakers are essentially dealership markets. They are characterized by quote-driven trading mechanisms; the bookie posts odds for a wide range of games and he takes the opposite side of every transaction. Limit orders are not allowed, the only possible transaction is hitting the market quote. Transparency is minimal, the odds are disseminated to the public, and nothing else. If a bettor makes the round trip, i.e. if he bets on both teams, he has to pay the vig, which is essentially a bid-ask spread. The vig is presumably the bookmakers compensation for making the market and bearing the risk of unfavorable outcomes. The market for a basketball game opens about half a day -less for games in the morning- before the start, and trading is continuous until the start. The bookmaker, just like dealers, has the right to change the odds whenever the market is open. However, basketball betting falls under the category of fixed-odds betting, i.e. the returns do not depend on subsequent price changes. 8 The tick size differs across bookmakers and not available at their websites. 9 The minimum bet that can be placed with William Hill is one cent. A betting exchange is an electronic limit order book. The market is order-driven; the bettors are allowed to post market and limit orders. In order for a trade to be executed, 8 Parimutuel betting is a system in which the total amount wagered is distrubuted to all the winning tickets. The main difference between parimutuel betting and fixed-odds wagering is the uncertainty of returns when placing a bet. 9 Compiling all announced odds throughout the year, however, is trivial, and the list is available from the author upon request. 7

8 a trader must hit the market quote. A variety of contracts are traded on exchanges, sports-related or otherwise. 10 To fix ideas, consider the following example in basketball: Back Lay Lakers 2.2 (100$) 2.21 (200$) Spurs 1.7 (50$) 1.71 (1000$) Backing a team is betting on the outcome that the team will win. The odds in the above figure represent gross returns for every dollar bet. The numbers in the parentheses correspond to the available quantity offered by the counterparty, who had posted a limit order. Laying a team is betting on the outcome that team will lose. Since there are only two teams and no possibilities of ties, a bettor who likes the Lakers has two options. 1. A bettor can back Lakers by hitting the market quote at 2.2 If the desired quantity is less than or equal to the quantity available at that price, here 100$, the order gets filled. If the former is greater, say 160$, part of the order is filled, and the rest becomes a limit order on the lay side of the market, leading to the following LOB. Back Lay Lakers 2.2 (60$) 2.21 (200$) Spurs 1.7 (50$) 1.71 (1000$) Thus, the order does not walk down the book, instead it goes to the other side of the book. This is reminiscent of the execution on the Paris Bourse. 2. Alternatively a bettor can lay Spurs at 1.71 up to the available quantity, here 1000$. A bettor who hits the market quote on the lay side essentially acts as a bookmaker, if Lakers win, he keeps the amount he laid, otherwise he is obligated to pay 71 dollars on every 100 dollars. If the amount laid is smaller, the transaction is executed immediately. If it is greater, say 1200 dollars, then the new LOB looks as follows: Back Lay Lakers 2.2 (100$) 2.21 (200$) Spurs 1.7 (50$) 1.71 (200$) Transparency is very high, the entire book is available to the public. (See the appendix). This includes all limit orders away from the market quotes, in other words all liquidity is committed and there is no hidden component. This is in contrast to, for example, Toronto Stock exchange, where only 5 orders away from the market quotes are visible to the traders on each side. The last contract price is available, but the quantity is not. However, the total quantities traded at each odds are revealed. A price trajectory 10 For an excellent survey of what type of contracts are traded on online exchanges, see Wolfers and Zitzewitz (2004) 8

9 supplements this information. The market is open more than a day and trading is continuous. Orders have price and time priority. Price improvement is possible and goes under the name best execution. It happens when either i) The quantity at best odds is small and the quantity at second best odds is large and a bettor demands liquidity at second best-odds. In that case, the small bet is matched at best odds. ii) If better odds become available, after a bet is placed, but before it is confirmed. In that case the user gets the better odds at the time of the matching. The tick size depends on the odds as in the Paris Bourse. It gets smaller, as the odds approach 1, i.e. as one of the teams becomes a heavy favourite. Unlike the bookmakers, a complete description of all tick sizes is available to the bettors at the website. It suffices to say here that the pricing grid is much thinner on the exchange. Any unmatched bet, or the unmatched part of an original bet can be cancelled without any charges. The minimum online bet is 4 dollars. 11 The betting exchanges serve as brokers. They facilitate trading by providing the platform on which bettors are matched. They do not take positions, instead they charge a commission on every transaction. Betfair charges 5 percent commission on net winnings. 12 If a winning bet of 100 dollars pays even money, the exchange pays out 195 dollars. Losing bets are not charged any commission. There is also an incentive scheme reminiscent of airlines frequent flyer programs. As bettors wager more on the exchange, the commission goes down and can be as low as 2 percent. But there is also a 15 percent weekly decay that is applied to bettors accumulated Betfair points, thus consistent betting is encouraged. In sum, the current structure of the entire online gambling is very similar to that of the financial markets. There are many bookmakers, corresponding to a set of dealers, who offer firm quotes and supply liquidity to the market. However, dealer quotations compete with public limit orders; bettors can post their own odds on the exchange. Bookmakers take positions regarding the outcome of the game, similar to dealers, and demand compensation for their market making activities by charging the vig, an implicit commission. The exchange facilitates trading by providing the betting platform and does not take any positions, instead a commission is charged on net winnings. 3 The Data The dataset consists of 623 National Basketball Association (NBA) games played between December 2004 and February For each game I manually collected odds from two bookmakers, William Hill and Ladbrokes and one betting exchange, Betfair twice a day. The first snapshot is taken randomly before the game, provided that there is at least 30 minutes and not more than five hours between the snapshot and the start of the game. With this procedure there is usually enough trade going on to make a meaningful analysis, 11 The issue of betting in smaller units has been raised in forums and it is claimed that bots, automated programs that can bet according to prespecified strategies, are allowed to place smaller bets. I could neither confirm nor refute this claim percent commission is more or less the industry standard, although smaller players in the exchange market charge lower commissions, or no commissions, with the hope of attracting bettors. 9

10 but there is also sufficient time to see the adjustment of the markets, late-betting, odds revisions by bookmakers and alike. The second snapshot is taken right before the start of the game. Betfair announces that the market gets suspended, after which no bets are allowed. A snapshot of this very moment is included in the appendix. 13 At William Hill and Ladbrokes I recorded the odds at each snapshot, which are potentially different due to odds revisions. At Betfair the entire limit order book is available. This includes all back and lay odds, the corresponding quantities (in dollars) as well as total quantity traded up to that point. When a trade is executed, say of 100 dollars, it is impossible to tell whether this is one big trade, or a few smaller trades. However, Betfair Developers Program, part of Betfair, decided to make some data available for its registered users on a monthly basis. Included in the data is the number of trades executed at each odds. Briefly, the dataset includes the following for each game: -The entire limit order book for both snapshots. -Quantity traded up to that point (first snapshot) and total quantity traded (second snapshot). -The time stamp of both snapshots (missing for some observations). -The number of transactions at every odds. -The odds at which the last trade is executed for both teams. -The odds at two bookmakers. The dataset has several shortcomings. First, whether trades are executed on the back side of the market or on the lay side is unknown. However, this is not a very important detail in answering the questions in hand. Second, NBA betting is not the universe of the betting on the exchange. Nevertheless it has the obvious advantage of providing a large sample. It would be interesting to analyze other markets. Third, the data used in this study is not high-frequency data. Some potentially valuable information might be lost because of this discreteness property. Fourth, I do not know the quantities traded at the bookmakers. Despite these apparent drawbacks, the data are rich enough to make a reasonably clean comparison of execution costs across different trading mechanisms. Although the data are not high-frequency, the first snapshot provides useful information about the subsequent trading activity on the exchange. And despite lack of information on quantities traded at the bookmaker, the odds revisions are observable. Therefore the revisions can be meaningfully tied to the state of the limit order book on the exchange. The number of observations falls short of all the games played. There are several reasons to this. Sometimes, bookmakers do not provide odds for all games played. On several occasions, the market was suspended well before the tip-off. At Betfair, some games turn in-play and therefore the market does not get suspended. 14 On some other 13 Odds are removed from William Hill at about the same time. Ladbrokes removes the odds five minutes before their competitors. 14 In-play betting is also called betting-in-the-run. If that option is available bettors can place bets until the game ends. 10

11 Table 1: Data Summary - December Mean Minimum Maximum 25th %tile Median 75th %tile First snapshot $12,375 $93 $71,635 $ $8,697.5 $15,654 Totals $24,220 $2,014 $130,322 $12, $18,429.5 $28, In-play games $29,866 $3,671 $63,116 $13, $23,431 $45,636.5 (1st snapshot) Note: Totals are based on the second snapshot at which the market is suspended. A total of $4,698,703 dollars are bet in 194 games. occasions data at the time of the suspension were not available. Technical problems at the websites or maintenance issues have prevented some data collection. Since almost all these factors are random, the exclusion of certain games should not affect the results substantially Summary statistics A total of 216 games were played in December In 15 of these games in-play betting was available. Excluding those along with 7 games on which information is missing leaves 194 games. Table 1 summarizes the characteristics of the data. Based on the data summary, it appears that the first snapshot, on average, roughly reflects, half of the betting activity. Also, games with in-play betting attract a lot of order flow. 4 Empirical Analysis 4.1 The Bookie Puzzle It is now well understood that there is no single measure that captures all the aspects of liquidity. The market microstructure literature has started out by focusing on bid-ask spreads and effective spreads. I will follow the same path and compare the exchange to the bookmaker on the basis of these metrics. In particular, I will report two measures of liquidity. I will demonstrate that the execution costs are much lower at the exchange based on these measures, at least for smaller orders. At the same time, this is hardly reflected in the profitability of the bookmaker. In tandem, these results seem puzzling. I will define the bookie puzzle as the fact that the market operates as a hybrid structure although identical contracts are traded at different costs. The first measure is called the overround. It is found by adding up the inverse odds and then subtracting 1 from that number. It represents the amount that need to be 15 I are not aware of any rules as to which games will turn in-play, but there is a high correlation between games that attracted a lot of betting and games for which in-play betting was made available. 16 This subsection will be updated. 11

12 invested in order to guarantee a sure return of a dollar. If the sum of inverse odds is less than 1, there is opportunity for arbitrage. The mark-up above one reflects the profit margin. I report this measure because this is simply the gambling counterpart of the bid-ask spread. It is an ex-ante measure and represents the execution costs if a trader wants to complete a round trip by buying and selling, or in gambling words, bets on both teams winning. I will also report a simple comparison of the winning bets. This measure represents the ex-post gains that are made at both venues and complements the overround, which is an ex-ante measure. It is useful for two reasons. First, it makes the comparison of net returns trivial. Net returns cannot be easily compared on the basis of the former measure because the commission is charged on net winnings only. Second, it resembles to the concept of effective spread, but one should be careful with this interpretation. In finance literature, the effective spread is useful complement to the ex-ante measure of quoted bid-ask spread, because the transaction prices can differ from the quoted ones. In online betting markets, the transaction price has to be equal to the quoted odds as the system is fully automated. Nonetheless, insights about the bookmaker behavior can be gleaned from this comparison. In Levitt (2004), bookmakers are better predictors than the bettors and therefore distort the odds to increase their profits. If this is true then this measure may differ from the overround. Consider the following situation. The odds on the exchange are 2-for-1 for both Lakers and Spurs. If the bookmaker s odds are 1.90-for-1 for both teams both measures are identical. But if the bookmaker s odds are 1.83-for-1 for Lakers and 2-for-1 for Spurs, and if Spurs always win, the second measure will suggest that the differences are not significant, whereas the first measure may suggest otherwise. Before proceeding to the results, several remarks are in order: 1. All orders in this market are executed against outstanding limit orders. The returns are calculated from the point of view of a trader who demands liquidity and has to hit the market quote for immediate execution. The returns could clearly be higher if a limit order is posted and subsequently hit. However, the data do not distinguish between these two and it is therefore almost impossible to estimate the uncertainty in execution probabilistically. The present method, in tandem with 5 percent commission, forms a firm lower bound for net returns on the exchange. 2. The exchange is different than the bookmaker in the sense that the total amount that could be bet on a team has two components, backing that team and laying the opponent. A strict analysis should take both components into account. In this section and the remaining of the paper, I will focus on backing only. There are two reasons that I ignore laying. First, it makes the data much easier to handle. Second, by doing so, I immediately reject a possible explanation to the puzzle, the claim that the products are different and the switching costs are high. This claim probably contains some element of truth in it, in my data the quantity available for backing is is significantly higher than that on the laying side. It may be an artifact of the data, but may also represent the 12

13 Table 2: Average Odds and The Frequency of Best Odds Website Observations Average Odds The Frequency Betfair (B) times (83.4%) William Hill (WH) times (10.7%) Ladbrokes (L) times (5.8%) Note: 1/n observations are awarded to the site if there is a n-way tie. reluctancy and/or confusion of people to be on a certain side Results On the exchange the average overround is (standard error 0.007) whereas at William Hill the average overround is (standard error 0.007). With a standard Vegas betting, the overround would be The results suggest that online betting odds are set parallel to offline odds. If one takes the (five percent) commission into account, then the overround on the exchange becomes approximately Still, a t-test of the null hypothesis that the overround is equal in both markets is rejected at all significance levels. Therefore, the results suggest that ex ante, execution costs are significantly lower on the exchange, at least for small bets. 19 As mentioned above, an alternative measure is directly comparing the odds and returns on winning bets. Table 2 depicts the average (back) odds on winning bets at Betfair, William Hill and Ladbrokes as well as the distribution of highest odds. 20 Table 2 explicitly reveals how the auction mechanism aggregates information perfectly, as one should expect the odds to converge to 2 over the long run. The natural next step is to test whether these differences are statistically significant. Table 3 summarizes the statistical results of the odds comparison analysis. The results are also depicted in Figure 1. As Table 3 reveals, the differences in odds are statistically significant at the 1 percent level. Therefore the results are in agreement with the industry prediction that competitive odds are offered on the exchange. Bookmakers, on the other hand, have the leverage of setting high profit margins. The significant differences in odds clearly do not tell the whole story. Since Betfair charges a commission on net winnings, the return differences between the exchange and bookmakers will be lower. Although the commission might be lower for heavy bettors, I 17 This apparent asymmetry is an important unanswered question in this research. It is possible that people think others will be reluctant to lay, so they will supply liquidity accordingly and it turns into a self-fulfilling prophecy. 18 With this structure you have to bet 11 units to win 10 units. 19 The overround at Ladbrokes is even higher and not reported here for brevity. 20 On a few occasions, odds were not reported by one of the three. These observations are still included in the sample. 13

14 2.3 Betfair William Hill Gross returns Weeks Figure 1: Differences in Odds will look at the limiting case of 5 percent commission. 21 Table 4 depicts the returns on a $1 bet for Betfair against the bookmakers, William Hill and Ladbrokes. As Table 4 shows, the return differences are also significant at the 1 percent level. These results are puzzling because the bookies still attract a lot of bettors as demonstrated in section Liquidity The previous section presented a conventional measure of liquidity for which trade size is irrelevant. In this section, a different path is taken. Useful information can presumably be gleaned from prices and depths beyond the bid-ask spread, therefore different versions of liquidity are worth to analyze. In fact, this is parallel to the development of the market microstructure literature. As limit-order books became more prevalent, the focus has shifted to measures that use the entire information in the limit-order book. (Biais et al. 21 It is believed that most bettors on Betfair are heavy bettors and the estimated average commission is 3 percent. 22 The results do not change if the second snapshot is used. Thereby the possibility that late betting might play a role is rejected. 14

15 Table 3: Average Odds on Winning Bets Observations B mean WH/L mean Difference t-value B vs. WH * (1.254) (1.090) (0.214) B vs L * (1.256) (0.986) (0.337) Note: Standard deviations are in parentheses. * significant at the 1 percent level Table 4: Average Winning Payouts per $1 Bet Observations B mean I WH/L mean Difference t-value B vs. WH * (1.192) (1.090) (0.168) B vs L * (1.194) (0.986) (0.285) Note: Standard deviations are in parentheses. * significant at the 1 percent level (1995), Irvine et al. (2000)). The main question in that literature is the following: Does the depth away from the quotes provide valuable information to traders? Order Book Shape Parallel to the developments in techonology and the prevalence of order book, an emerging literature analyzes the content and shape of the order book. The analysis here has its roots in Biais et al. (1995) and also very similar to Cao et al. (2004). The idea is to represent the limit order book using step functions as described below: 1. Define P 1 the as the outstanding back odds for the home team, and Q 1 the corresponding depth. P 2 and Q 2 are the next highest odds and corresponding quantities, P 3 and Q 3 are the ones further below in the book and so on. 2. The height of step i represents Q = Q i Q i The length of the step is defined as P = P i P i The heights and lengths on the side of the away team is defined analogously. Remark: Since the identity of the team is readily observable, this is a plausible distinction empirically. Another alternative would be the favorite-underdog distinction. Table 6 summarizes the shape of the order book. One empirical regularity in the dataset is the existence of limit orders away from the bid for either team. This is also depicted in Figure 2. This clustering is also documented in financial markets, notably in Paris Bourse (Biais et al. (1995) and Bouchaud et al. (2002)). This hump-shape of the limit order book is presumably an optimizing behavior of the uninformed traders. Posting 15

16 limit orders is essentially giving free options to informed traders, therefore uninformed traders want to protect themselves by clustering away from market prices. Rosu (2004) provides a dynamic model of limit order book. In his paper, this particular shape emerges in equilibrium when multi-unit orders are allowed. The present findings are therefore consistent with both the theoretical and empirical literature away home Number of Shares Price steps Figure 2: Shape of the Order Book Another observation is that little depth is provided at the outstanding market prices % of the depth is offered for the away team and only 9-11% of the depth is offered for the home team. Averaging across teams, the total depth at inside quotes corresponds to about 12%. In Toronto Stock Exchange, Australian Stock Exchange and Paris Bourse, this ratios are 25%, 22% and less than 20% respectively (Irvine et al. (2000), Cao et al. (2004), Biais et al. (1995). 23 This implies that i)a comparison of the exchange and the bookmaker at the inside quote fails to present the whole picture and ii)there is potentially useful information in the order book that can be utilized by the bettors, an issue I will revisit later in the section. 23 Since Cao et al. (2004) report the percentages for 10 deep, the percentages are recalculated for normalization purposes. Exact numbers are not reported in Biais et al. (2005), but an upper limit can be obtained. 16

17 Table 5: Order Book Statistics - Depth Away Home Ask Bid Dec Totals Jan (in thousand $) Feb Dec-Feb , Dec Averages Jan (in $) Feb Dec-Feb Dec Percentages Jan (%) Feb Dec-Feb A Liquidity Measure The measure that will be used here is inspired by Irvine et al. (2000). They suggest a measure called the cost of round trip and claim that it is is most useful, when committed liquidity is a big portion of the total liquidity that consists of committed and hidden liquidity. 24 In the present study, all liquidity is committed, therefore the measure is well-suited for the research questions in hand. As it is well understood, liquidity is a transaction size specific concept. I will proceed as follows: 1. Specify an amount D. 2. Define P 1 the as the outstanding back odds for a team, and Q 1 the corresponding depth. P 2 and Q 2 are the next highest odds and corresponding quantities, P 3 and Q 3 are the ones further below in the book and so on. 3. Calculate the average odds for D using the following: AO (D)= ( N i=1 P i 1 Q i 1 + (D N i=1 Q i 1 ) P i )/D if i s.t. N i=1 (Q i 1 ) < D and Ni=1 (Q i ) D The book is said to be not full for D otherwise. 4. Calculate the bid-ask spread based on 3. By construction, this bid-ask spread is equal to or greater than the quoted spread. This measure has a simple interpretation. The bettor who wants to bet D dollars on a team walks up the book until he spends all D dollars. Clearly, the book may not be full for larger amounts. Table 7 depicts the number of books that are not full, across home and away teams and for three months. The differences between home teams and away teams are naturally visible here, as the two measures are strongly correlated. The numbers are also consistent with the behavior of the aforementioned measure (Irvine et al. (2000)) for the Toronto Stock exchange. 24 Both in the Paris Bourse and on the Toronto Stock Exchange some liquidity is hidden. 17

18 Table 6: How full is the book? Away Home Amount (in $) ,000 5,000 10, ,000 5,000 10,000 Dec (210) Observations Jan (232) (# games) Feb (175) Dec-Feb (617) Dec Percentages Jan (%) Feb Dec-Feb Table 7: Average Gross Winning Payouts per $1 Bet When Different Amounts Are Bet Bet amount (in $) ,000 5,000 10,000 Payouts per $1 Bet What happens to the return differences as the order size gets larger? Table 8 demonstrates that higher returns on the exchange vanish very quickly with increasing orders. This is true although no attempt is made to correct the sample selection problem. Instead of assuming an perfectly inelastic supply at lower prices as Irvine et al. (2000) did, the observations are instead taken out of the sample when the book is not full. Even so, returns decline sharply with increasing order size. 25 Irvine et al. (2000) show that CRT is a useful measure because more liquid markets attract order flow. If bettors take the information in the entire limit order book into account, then liquidity should invite subsequent activity. 26 Moreover, if bettors base their decision of venue not only on the quoted spread but on the entire book, they should switch to the bookmaker less frequantly if liquidity is high on the exchange. Unfortunately quantity information at the bookmaker level is not available. Nevertheless, the number of revisions can be used as a proxy for volume. This scenario presents the idea behind the testable hypothesis that games for which odds are revised, are not random and are related to the state of the book on the exchange. Specifically, the odds are more likely to be revised if more people place bets with the bookmaker and this will be expected if liquidity is relatively low on the exchange. To test the above hypothesis, I give an identity to every game. The identity of a game is simply an ordered pair where the entries are the maximum amounts for which the book is full. For example, if the identity for a game is (500,1000), the interpretation is the book of the away team is full for 500 dollars, but not so for 1000 dollars. An identical argument holds for the home team. If liquidity matters then we should expect games where there is at least one team with betting possibilities of up to 10,000 dollars 25 One can also compare the returns by using the proper combination of the exchange and the bookmaker versus the bookmaker only. This is plausible as some people might be shopping around to find the best odds and can divide their orders. Even so, the bookmaker catches up quite easily. 26 Although not reported, preliminary analysis shows that this is indeed the case here. 18

19 Table 8: Contingency Table Based on Liquidity Liquid games Relatively illiquid games Revisions 20* 160 No Revisions * significant at the 1 percent level chi-square = 6.67 degrees of freedom = 1 p-value = to be revised less frequently. Indeed, a contingency table analysis (Table 9) shows this is the case. The results suggest that the revised games could not be the result of chance. The results suggest that bettors indeed take the depth of the limit order book into account. They are less likely to place bets with the bookmaker (proxied by the number of revisions) when liquidity is highh on the exchange. This together with sharply increasing execution costs provides an explanation for the hybrid structure in online betting markets. Betting exchanges (auctions) have found a successful niche, but bookmakers (dealers) provide immediate liquidity to bettors with high bankrolls. Betting exchanges may indeed mean the end for bookmakers, but for this to happen the liquidity on the exchange should increase quite significantly. A more plausible conjecture, then, is perhaps to expect both trading mechanisms survive and coexist, at least in the near future. 5 Discussion I will now discuss possible explanations and argue that none of them can be the main reason driving the results although they are possibly at work to some extent. Legal issues. Do the sportsbooks and exchanges have important differences in terms of legality? None of them accepts bets from the US, a claim which I verified. On the other hand, I managed to open an account with William Hill and place some bets by supplying a non-us credit card and address. As mentioned in footnote 7, the same procedure failed with Betfair. Potentially, if there are a lot of gambling addicts in US who have access to foreign credit cards, this might account for some of the betting activity with the bookmaker. This, however, does not seem very likely, not only because of the enormous profits made by the online sportsbook, but also there is no reason to believe that all these people choose William Hill, given that there are hundreds of online sportbooks. Moreover, most of these online venues are rather small and hoping to increase their market shares, they cannot afford rejecting bets from US, further diminishing the possibility to bet with William Hill in the absence of the option of betting with Betfair. Unawareness. Could it be the case that some bettors are simply not aware of the existence of Betfair? William Hill, for example, has been around since 1934 and when they started their online operation they were already very well known. Betfair started as 19

20 an internet startup. Although it is possible, it is hard to imagine, that bettors have never heard of betting exchanges, especially Betfair. First, it can be safely assumed that online bettors are sufficiently comfortable with the internet, and it is hard not to come across betting exchanges, especially with the rise of another group of websites, that provide a comparison of odds from many bookmakers and exchanges. Moreover, the youth is an important part of the betting crowd implying that not many bettors who wager online are switchers, who replaced betting offices with online units within the same bookie. Second the turnover in Betfair is already higher than any of the other three bookmakers and with its revolutionary business model Betfair has been highly publicized earning them several prestigious awards as mentioned before. All in all, unawareness does not emerge a satisfactory explanation. First Mover s Advantage/Switching Costs/Brand Loyalty. The traditional bookmakers clearly entered the market before betting exchanges and accumulated a large customer base. If the switching costs are high for the bettors and/or if there is some sort of brand loyalty, it might justify the observed results. However, the switching costs do not seem to be high. Both exchanges and bookmakers have similar designs and learning should be negligible. It might be the case that posting odds and laying teams require a considerable amount of learning but for our purposes this is irrelevant as only market orders are included in the analysis. As for the brand loyalty, some observations from other industries could be useful. For example, in the pharmaceutical industry, it has been observed that brand-name products keep selling at higher prices even after the patent is over. This might be a sustainable signalling equilibrium, the brand wants to signal that it is superior to generic products and consumers are convinced that this is indeed the case. However, signalling is less likely to work in the betting industry. The sports events are always the same, so the only relevant quality dimension is the possibility of financial trouble. It is still possible that consumers do not trust the exchange in financial terms yet with all the publicity and reputation Betfair has, such beliefs on the consumer side are hardly justifiable. Differences between the exchange and bookmaker. No two markets are exactly the same. The present case is no exception. There are some differences across the selected sportsbooks and the exchange, which might potentially contribute to the consumption value. On the exchange punters have the freedom of posting their own odds and laying a team. In-play betting is also available. 27 On the negative side, the minimum bet is $4 compared to one cent at William Hill and multiple bets are not allowed on the exchange It is worth to mention that in-play betting was only available on the exchange in the beginning, but William Hill started to offer this option to its bettors in January Two interesting observations: First, the in-play games at Betfair and William Hill mostly coincide. Second, whenever William Hill posts odds during the game, they are always inferior to pre-game odds. Presumably higher prices (lower odds) are required to compensate the additional risk. Interestingly, the price grid of these inferior odds coincide with Ladbrokes pricing grid. There may be some communication, if not collusion, between online venues as far as these games are concerned. 28 A multiple bet, or parlay, is placing a wager on any number of events simultaneously. Should all events have the desired outcome, the return is equal to the product of all odds, hence the returns can be 20