The Bookie Puzzle: Auction versus Dealer Markets inOnline Sports Betting

Alper OzgitDepartment of Economics, UCLA

ozgit@ucla.edu

September 29, 2005

Abstract

Both financial markets and online betting markets have recently converged to ahybrid structure where order-driven mechanisms (auction, betting exchanges) andquote-driven mechanisms (dealers, bookmakers) coexist and compete with eachother for order flow. The absence of market consolidation in financial marketshas been a puzzle because of lower transaction costs when auction mechanisms,or limit order books, are used. Parallel to this, the betting industry claims thatodds offered on the exchange are more competitive and the bookmakers should bedriven out of the market. I compile and analyze a dataset of National BasketballAssociation (NBA) games and find that both odds and net returns on the leadingbetting exchange (Betfair) are consistently higher than that of the two leadingbookmakers (William Hill and Ladbrokes). These results are puzzling, since thebookmakers continue to be profitable. “The bookie puzzle”, the observation thatbookies attract a lot of betting although better returns are available elsewhere isresolved through liquidity-based explanations. As the order size gets larger, I findthat i)The return differences vanish rapidly, and ii) Order flow migrates to thebookmakers, thereby justifying the presence of and the need for bookmakers.

Keywords: Auctions, Dealership, Market microstructure, Execution costs, Liq-uidity, Online betting.

JEL Classification: D44 (Auctions), G14 (Information and Market Efficiency;Event Studies)

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“Betting exchanges will mean the end for bookmakers”

-Tab Limited, an Australian-based provider of entertainment services specializing inwagering and gaming

1 Introduction

Trading mechanisms used in financial markets change over time. In the beginning of1990’s, markets relied more exclusively on quote-driven regimes with Nasdaq and theLondon 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 pureorder book or they moved to a hybrid structure where dealers and limit order bookcoexist. On Nasdaq, orders from the public now compete with dealer quotes. On theLondon Stock Exchange, the quote-driven SEAQ and the order-driven SETS supplementeach other. The structure of the market, its effect on the price discovery process and finalresource allocations has come to be an important research agenda and central to marketmicrostructure literature. This research program has exploded in the last twenty yearsand 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 havethe 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 providealternative venues to test theories in financial economics. In particular, the efficientmarket hypothesis has been regularly analyzed. Several studies presented anomaliesagainst 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 transforma-tion has been almost identical to that of the financial markets. Betting markets havetraditionally been characterized by quote-driven mechanisms with bookmakers postingodds for selected events. These markets have now converged to a hybrid structure, wherebetting exchanges, essentially limit order books, cross trader-to-trader transactions andbookmakers, or dealers, supply liquidity to markets. Both markets coexist and competewith each other to attract order flow.

In this paper I argue that the link between betting markets and financial markets isunderutilized and propose that the market microstructure literature can use new insightsfrom the current organization of betting markets. I draw a one-to-one map betweentwo markets and attempt to understand the effects of the two most common tradingmechanisms, auctions and dealership regimes, on the betting behavior. In contrast toprevious studies that emphasize efficiency, I focus on execution costs on sportsbooks and

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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 exchangesoffer higher returns. Indeed, the betting industry seems to accept this fact. To check thevalidity of this argument, I compiled a dataset based on online betting markets. I reportthe results of this natural experiment and show that both the odds and net returns arehigher on the exchange. My dataset consists of National Basketball Association (NBA)games played between December 2004 and February 2005.1 Data are collected from theleading betting exchange, Betfair, and from the two biggest bookmakers, William Hilland Ladbrokes, all of which are registered in the UK.

The results, in tandem with the increasing profitability of selected sportsbooks, arequite puzzling. The bookie puzzle refers to the observation that bookies attract a lotof betting although better returns are available elsewhere. As a matter of fact, thebookie puzzle can be seen as the betting counterpart of the network externalities puzzleand dealer puzzle in financial markets (See Madhavan (2000)). The former refers to theobservation that markets do not tip to a single structure despite strong benefits to consol-idation. The latter is about uncovering why dealers are valuable to the market. Suggestedexplanations 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 checkwhether the hybrid structure in betting markets can be explained by the developmentsoffered in the finance literature. I find that significantly lower execution costs, or higherreturns, on the exchange vanish rapidly as the orders become larger. Moreover, I provideevidence that whenever the exchange markets are thin, order flow migrates to the sports-book thereby justifying the growing profitability of the latter. To that end, I demonstratethat the bookmaker revises the odds more frequently, when either the liquidity on theexchange is low and/or an unbalanced order flow is more likely to arrive to the book. Infinancial markets, dealers revise their quotations if their position is far from the desiredinventory level. (Add References!) Therefore, the bookmaker behavior is is consistentwith the inventory adjustments theories in financial economics.

This paper has two important contributions. First, by reporting the results of a nat-ural experiment in online betting markets, I present an empirical comparison of auctionand dealership mechanisms. Empirical studies that compare different markets have beenrare. Cohen et al. (1986) compare two specialist markets (NYSE and AMEX) to twonon-specialist markets (Rio and Tokyo). Huang and Stoll (1996) compare NASDAQand NYSE looking at execution costs using a matched sample. These studies have theapparent drawback that traded issues are different on selected exchanges. Amihud andMendelson (1987) look at the differences between call auctions and continuous auctionswithin the NYSE. This removes the problem of different contracts but the comparisonis not between auction and dealership regimes. Moreover, the call auction (or clearing-house) and continuous auction (or double auction) institutions are close variants and they

1In fact, the dataset will eventually cover the entire season. At the time of this writing, the analysisis carried out for three months and the paper reports these preliminary results.

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yielded almost identical results in lab settings.2 Closest to this paper is perhaps De Jonget al. (1995). They compare auction and dealer regimes by utilizing the fact that someFrench stocks trade on both exchanges. However, in their case the Paris Bourse is not anexclusive auction mechanism, but rather a hybrid where some shares are traded throughcall auction as well as bilateral search. Moreover, the entire limit book is not visible andsome liquidity is hidden. In the present study, the entire book is common knowledge, allliquidity is committed and auction is the only mechanism used. The difficulty of empir-ical intermarket comparisons is perfectly summarized by Friedman (1993): “Field dataunfortunately rarely permit such clean [institutional] comparisons.” This paper builds onone 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 marketmicrostructure perspective. In similar vein, Levitt (2004) has analyzed gambling marketsand demonstrated that the bookmakers are more skilled at predicting the outcomes thanthe bettors, which allows them to post non-market clearing prices and earn supranormalprofits. Based on this conclusion, he claims that betting markets are organized differentlyfrom financial markets. However, he does not analyze betting exchanges. Therefore,although his paper offers an explanation why betting markets have evolved the waythey did, it is silent about the current structure of betting markets. The present studydiffers from his and other related work by arguing that markets are quite similar interms of their structure. Interestingly, the financial markets display a hybrid structureas 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, thefinancial markets correspond to the “social planner” outcome and the betting marketsare characterized by decentralized profit maximization. The similarity of the structurein 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 onlinesports betting market. Section 3 describes the data used in this study. Section 4 containsthe main results. Section 5 concludes.

2Friedman and Ostroy (1995) have documented this perfectly. One can think of DA being moreefficient than the clearinghouse mechanism because of the continuity it possesses, in fact, it was exactlythe position taken by one of the authors before they carried out the project. Although they ran exper-iments which are explicitly designed to produce different outcomes under different institutions, the twoinstitutions fared equally well.

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2 The Online Betting Market

2.1 Overview of the Industry

2.1.1 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 sharpcontrast to this, gambling services are quite common in the UK. Gross stakes wagered inthe UK in 2002 represent about five percent of the GDP. Naturally, providers of wageringservices 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 opportunitiesare available to those who want to bet on a certain outcome happening. Bets can beplaced 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 examplein the UK, the majority of the betting activity still comes from betting shops, but internetbetting has been rising steeply. In contrast to this online wagering constitutes most orall of the betting activity on exchanges. Technically, betting exchanges can also offerwagering activities at shops, but I am aware of very few examples. Clearly, any meaningfulcomparison of the two market structures will necessarily rely on online units. The mostcomprehensive listing I could find specifies 640 domains hosted by sportsbooks worldwidealthough the number is believed to be approaching a thousand.3 The same source lists 32betting exchanges. In a world with numerous online sportsbooks and a growing numberof exchanges, the main selection criterion in this article is the market share. Betfair isa betting exchange registered in the UK and is the clear market leader in the exchangemarket with an approximately 90% market share making it an obvious choice. The choiceof 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 alsoregistered 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 ofthe total betting activity. Their online units together correspond to approximately 10percent of the global online betting.5

The introduction of betting exchanges is considered as a radical change in the gam-bling 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 bookmakersbecause it is able to offer much competitive odds. The quote in the very beginning of the

3Source: http://www.casinocity.com/4Even for online units, the bulk of the betting activity originates within the UK.5Gross 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 CapitalAdvisors.

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paper reflects the stance of a typical gaming provider. The prediction of the betting in-dustry is a simple market consolidation argument; higher odds on the exchange will resultin migration which will in turn make the odds more competitive and lead to further mi-gration. Whether this is happening or not is an empirical question. The next subsectionoffers a closer look to company specifics and argues that this has not happened.

2.1.2 Company Specifics

William Hill. William Hill is established in 1934. Its shares have been publicly tradedon the London Stock Exchange since June 2002. It has recently acquired 624 shops ofrival Stanley Leisue and became the largest operator in the UK with more than 2000betting shops. These shops are still the biggest source of revenue but as a result of anincrease in the use of the internet, the contribution of online gambling started to followan upward trend. In 2004 (2003), the interactive unit has generated a gross revenue of106.1 (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 theUK until the recent acquisition of Stanley by William Hill. Its online gaming division hasreported a gross revenue of 89.3 (63.7) million pounds in 2004 (2003). Its profits haverisen from 14.2 million pounds in 2003 to 21.3 million pounds in 2004. The number ofinteractive 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 2000. Soon after that, it merged with Flutter.com, the then-leading bettingexchange. Betfair operates mostly on an online basis but it also provides its customerswith the option of phone betting.

In the year to 30 April 2005, Betfair’s revenues increased by 61% to 107.1 millionpounds from 66.7 million pounds. Operating profits increased to 22.3 million pounds, up87% from 11.9 million pounds. Its active users has increased to 95,000 from 65,000, andits registered users are estimated to be over 300,000.6

Betfair’s business model is now widely recognized and respected, the company landedthe Ernst and Young Emerging Entrepreneur of the Year Award in 2002 and the Queen’sAward for Enterprise in 2003.

Betfair, like its main competitors, does not accept bets from within the US.7

6An 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 whereasat sportsbooks it is much higher.

7They claim that they have access to a technology that is capable of locating the customers. Althoughthese geolocation technologies might not be perfectly accurate, I was not allowed to activate my accountwhen located in US, although I supplied a non-US address as well as a non-US credit card.

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Discussion. The interactive division of William Hill and Ladbrokes include theonline sportsbook, online casino and online poker. The online unit of Betfair includes theexchange itself and online poker. Segmental information is not reported, therefore onecan argue that the growth of the bookmakers can be attributed to the casino and pokersegments 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 forBetfair and William Hill. Ladbrokes has a stronger presence in poker, but they reporteda 34% increase in the number of registered users, and a 49% increase in the number ofactive users in the sportsbook segment. The casino segment is more competitive and thegrowth figures have been significantly less, for example Ladbrokes reports a relativelysmall 7% increase in gross wins from the casino unit.

In sum, different performance metrics reveal that there has not been a visible mi-gration 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 notconcentrated in one venue. This absence of migration might follow from misperceptionsabout returns or differences in market structure. The next section is devoted to a detailedsummary of the market architecture. In fact, the current design of online betting stronglyparallels that of the financial markets.

2.2 Market Architecture

Traditional bookmakers are essentially dealership markets. They are characterized byquote-driven trading mechanisms; the bookie posts odds for a wide range of games andhe takes the opposite side of every transaction. Limit orders are not allowed, the onlypossible transaction is hitting the market quote. Transparency is minimal, the odds aredisseminated to the public, and nothing else. If a bettor makes the round trip, i.e. ifhe 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 bearingthe risk of unfavorable outcomes. The market for a basketball game opens about halfa day -less for games in the morning- before the start, and trading is continuous untilthe start. The bookmaker, just like dealers, has the right to change the odds wheneverthe market is open. However, basketball betting falls under the category of fixed-oddsbetting, i.e. the returns do not depend on subsequent price changes.8 The tick size differsacross bookmakers and not available at their websites.9 The minimum bet that can beplaced with William Hill is one cent.

A betting exchange is an electronic limit order book. The market is order-driven; thebettors are allowed to post market and limit orders. In order for a trade to be executed,

8Parimutuel betting is a system in which the total amount wagered is distrubuted to all the winningtickets. The main difference between parimutuel betting and fixed-odds wagering is the uncertainty ofreturns when placing a bet.

9Compiling all announced odds throughout the year, however, is trivial, and the list is available fromthe author upon request.

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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 LayLakers 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 theabove figure represent gross returns for every dollar bet. The numbers in the parenthesescorrespond to the available quantity offered by the counterparty, who had posted a limitorder. Laying a team is betting on the outcome that team will lose. Since there are onlytwo 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 desiredquantity is less than or equal to the quantity available at that price, here 100$, the ordergets filled. If the former is greater, say 160$, part of the order is filled, and the restbecomes a limit order on the “lay” side of the market, leading to the following LOB.

Back LayLakers 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 thebook. 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, here1000$. A bettor who hits the market quote on the “lay” side essentially acts as a book-maker, if Lakers win, he keeps the amount he laid, otherwise he is obligated to pay 71dollars on every 100 dollars. If the amount laid is smaller, the transaction is executedimmediately. If it is greater, say 1200 dollars, then the new LOB looks as follows:

Back LayLakers 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 ap-pendix). This includes all limit orders away from the market quotes, in other words allliquidity is committed and there is no hidden component. This is in contrast to, forexample, Toronto Stock exchange, where only 5 orders away from the market quotes arevisible to the traders on each side. The last contract price is available, but the quantityis not. However, the total quantities traded at each odds are revealed. A price trajectory

10For an excellent survey of what type of contracts are traded on online exchanges, see Wolfers andZitzewitz (2004)

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supplements this information. The market is open more than a day and trading is contin-uous. Orders have price and time priority. Price improvement is possible and goes underthe name “best execution”. It happens when either i) The quantity at best odds is smalland the quantity at second best odds is large and a bettor demands liquidity at secondbest-odds. In that case, the small bet is matched at best odds. ii) If better odds becomeavailable, after a bet is placed, but before it is confirmed. In that case the user gets thebetter odds at the time of the matching. The tick size depends on the odds as in the ParisBourse. It gets smaller, as the odds approach 1, i.e. as one of the teams becomes a heavyfavourite. Unlike the bookmakers, a complete description of all tick sizes is available tothe bettors at the website. It suffices to say here that the pricing grid is much thinneron the exchange. Any unmatched bet, or the unmatched part of an original bet can becancelled without any charges. The minimum online bet is 4 dollars.11

The betting exchanges serve as brokers. They facilitate trading by providing theplatform on which bettors are matched. They do not take positions, instead they charge acommission 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. Losingbets are not charged any commission. There is also an incentive scheme reminiscent ofairlines’ frequent flyer programs. As bettors wager more on the exchange, the commissiongoes down and can be as low as 2 percent. But there is also a 15 percent weekly decay thatis 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 ofthe financial markets. There are many bookmakers, corresponding to a set of dealers,who offer firm quotes and supply liquidity to the market. However, dealer quotationscompete 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, anddemand compensation for their market making activities by charging the vig, an implicitcommission. The exchange facilitates trading by providing the betting platform and doesnot 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 betweenDecember 2004 and February 2005. For each game I manually collected odds from twobookmakers, 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 30minutes 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,

11The issue of betting in smaller units has been raised in forums and it is claimed that bots, automatedprograms that can bet according to prespecified strategies, are allowed to place smaller bets. I couldneither confirm nor refute this claim.

125 percent commission is more or less the industry standard, although smaller players in the exchangemarket charge lower commissions, or no commissions, with the hope of attracting bettors.

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but there is also sufficient time to see the adjustment of the markets, late-betting, oddsrevisions by bookmakers and alike. The second snapshot is taken right before the startof the game. Betfair announces that the market gets suspended, after which no betsare allowed. A snapshot of this very moment is included in the appendix.13 At WilliamHill and Ladbrokes I recorded the odds at each snapshot, which are potentially differentdue to odds revisions. At Betfair the entire limit order book is available. This includesall back and lay odds, the corresponding quantities (in dollars) as well as total quantitytraded up to that point.

When a trade is executed, say of 100 dollars, it is impossible to tell whether this isone big trade, or a few smaller trades. However, Betfair Developers Program, part ofBetfair, 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 importantdetail in answering the questions in hand. Second, NBA betting is not the universe ofthe betting on the exchange. Nevertheless it has the obvious advantage of providing alarge sample. It would be interesting to analyze other markets. Third, the data used inthis study is not high-frequency data. Some potentially valuable information might belost because of this discreteness property. Fourth, I do not know the quantities traded atthe bookmakers.

Despite these apparent drawbacks, the data are rich enough to make a reasonably cleancomparison of execution costs across different trading mechanisms. Although the data arenot high-frequency, the first snapshot provides useful information about the subsequenttrading activity on the exchange. And despite lack of information on quantities tradedat the bookmaker, the odds revisions are observable. Therefore the revisions can bemeaningfully 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 severalreasons to this. Sometimes, bookmakers do not provide odds for all games played. Onseveral occasions, the market was suspended well before the tip-off. At Betfair, somegames turn in-play and therefore the market does not get suspended.14 On some other

13Odds are removed from William Hill at about the same time. Ladbrokes removes the odds fiveminutes before their competitors.

14In-play betting is also called betting-in-the-run. If that option is available bettors can place betsuntil the game ends.

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Table 1: Data Summary - DecemberMean Minimum Maximum 25th %tile Median 75th %tile

First snapshot $12,375 $93 $71,635 $5030.25 $8,697.5 $15,654Totals $24,220 $2,014 $130,322 $12,320.75 $18,429.5 $28,325.75In-play games $29,866 $3,671 $63,116 $13,155.75 $23,431 $45,636.5(1st snapshot)

Note: Totals are based on the second snapshot at which the market is suspended. A totalof $4,698,703 dollars are bet in 194 games.

occasions data at the time of the suspension were not available. Technical problems atthe websites or maintenance issues have prevented some data collection. Since almostall these factors are random, the exclusion of certain games should not affect the resultssubstantially.15

3.1 Summary statistics

A total of 216 games were played in December 2004.16 In 15 of these games in-playbetting was available. Excluding those along with 7 games on which information ismissing leaves 194 games. Table 1 summarizes the characteristics of the data. Based onthe data summary, it appears that the first snapshot, on average, roughly reflects, half ofthe 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 aspectsof liquidity. The market microstructure literature has started out by focusing on bid-askspreads and effective spreads. I will follow the same path and compare the exchange tothe bookmaker on the basis of these metrics. In particular, I will report two measuresof liquidity. I will demonstrate that the execution costs are much lower at the exchangebased on these measures, at least for smaller orders. At the same time, this is hardlyreflected 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 structurealthough identical contracts are traded at different costs.

The first measure is called the overround. It is found by adding up the inverse oddsand then subtracting 1 from that number. It represents the amount that need to be

15I are not aware of any rules as to which games will turn in-play, but there is a high correlationbetween games that attracted a lot of betting and games for which in-play betting was made available.

16This subsection will be updated.

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invested in order to guarantee a sure return of a dollar. If the sum of inverse odds isless than 1, there is opportunity for arbitrage. The mark-up above one reflects the profitmargin. I report this measure because this is simply the gambling counterpart of thebid-ask spread. It is an ex-ante measure and represents the execution costs if a traderwants to complete a round trip by buying and selling, or in gambling words, bets on bothteams winning.

I will also report a simple comparison of the winning bets. This measure representsthe ex-post gains that are made at both venues and complements the overround, whichis an ex-ante measure. It is useful for two reasons. First, it makes the comparison ofnet returns trivial. Net returns cannot be easily compared on the basis of the formermeasure because the commission is charged on net winnings only. Second, it resemblesto the concept of effective spread, but one should be careful with this interpretation. Infinance literature, the effective spread is useful complement to the ex-ante measure ofquoted 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 asthe system is fully automated. Nonetheless, insights about the bookmaker behavior canbe gleaned from this comparison. In Levitt (2004), bookmakers are better predictorsthan the bettors and therefore distort the odds to increase their profits. If this is truethen this measure may differ from the overround. Consider the following situation. Theodds on the exchange are 2-for-1 for both Lakers and Spurs. If the bookmaker’s odds are1.90-for-1 for both teams both measures are identical. But if the bookmaker’s odds are1.83-for-1 for Lakers and 2-for-1 for Spurs, and if Spurs always win, the second measurewill suggest that the differences are not significant, whereas the first measure may suggestotherwise.

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 hitthe market quote for immediate execution. The returns could clearly be higher if a limitorder is posted and subsequently hit. However, the data do not distinguish betweenthese two and it is therefore almost impossible to estimate the uncertainty in executionprobabilistically. The present method, in tandem with 5 percent commission, forms afirm lower bound for net returns on the exchange.

2. The exchange is different than the bookmaker in the sense that the total amountthat could be bet on a team has two components, backing that team and laying theopponent. A strict analysis should take both components into account. In this sectionand the remaining of the paper, I will focus on backing only. There are two reasons thatI ignore laying. First, it makes the data much easier to handle. Second, by doing so, Iimmediately reject a possible explanation to the puzzle, the claim that the products aredifferent and the switching costs are high. This claim probably contains some element oftruth in it, in my data the quantity available for backing is is significantly higher thanthat on the laying side. It may be an artifact of the data, but may also represent the

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Table 2: Average Odds and The Frequency of Best OddsWebsite Observations Average Odds The FrequencyBetfair (B) 623 2.000 520 times (83.4%)William Hill (WH) 623 1.916 67 times (10.7%)Ladbrokes (L) 623 1.851 36 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.17

4.1.1 Results

On the exchange the average overround is 1.011 (standard error 0.007) whereas at WilliamHill the average overround is 1.042 (standard error 0.007). With a standard 11-10 Vegasbetting, the overround would be 1.045.18 The results suggest that online betting oddsare set parallel to offline odds. If one takes the (five percent) commission into account,then the overround on the exchange becomes approximately 1.023. Still, a t-test of thenull hypothesis that the overround is equal in both markets is rejected at all significancelevels. Therefore, the results suggest that ex ante, execution costs are significantly loweron the exchange, at least for small bets.19

As mentioned above, an alternative measure is directly comparing the odds and re-turns 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 stepis to test whether these differences are statistically significant. Table 3 summarizes thestatistical results of the odds comparison analysis. The results are also depicted in Figure1.

As Table 3 reveals, the differences in odds are statistically significant at the 1 percentlevel. Therefore the results are in agreement with the industry prediction that competitiveodds are offered on the exchange. Bookmakers, on the other hand, have the leverage ofsetting high profit margins.

The significant differences in odds clearly do not tell the whole story. Since Betfaircharges a commission on net winnings, the return differences between the exchange andbookmakers will be lower. Although the commission might be lower for heavy bettors, I

17This apparent asymmetry is an important unanswered question in this research. It is possible thatpeople think others will be reluctant to lay, so they will supply liquidity accordingly and it turns into aself-fulfilling prophecy.

18With this structure you have to bet 11 units to win 10 units.19The overround at Ladbrokes is even higher and not reported here for brevity.20On a few occasions, odds were not reported by one of the three. These observations are still included

in the sample.

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1 2 3 4 5 6 7 8 9 10 11 121.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

Weeks

Gro

ss r

etur

nsBetfairWilliam Hill

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 demonstratedin section 2.22

4.2 Liquidity

The previous section presented a conventional measure of liquidity for which trade size isirrelevant. In this section, a different path is taken. Useful information can presumably begleaned from prices and depths beyond the bid-ask spread, therefore different versions ofliquidity are worth to analyze. In fact, this is parallel to the development of the marketmicrostructure literature. As limit-order books became more prevalent, the focus hasshifted to measures that use the entire information in the limit-order book. (Biais et al.

21It is believed that most bettors on Betfair are heavy bettors and the estimated average commissionis 3 percent.

22The results do not change if the second snapshot is used. Thereby the possibility that late bettingmight play a role is rejected.

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Table 3: Average Odds on Winning BetsObservations B mean WH/L mean Difference t-Value

B vs. WH 607 2.003 1.916 0.086 9.971*(1.254) (1.090) (0.214)

B vs L 607 2.004 1.853 0.150 11.020*(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 BetObservations B mean I WH/L mean Difference t-Value

B vs. WH 607 1.953 1.916 0.036 5.360*(1.192) (1.090) (0.168)

B vs L 607 1.954 1.853 0.100 8.674*(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: Doesthe depth away from the quotes provide valuable information to traders?

4.2.1 Order Book Shape

Parallel to the developments in techonology and the prevalence of order book, an emergingliterature analyzes the content and shape of the order book. The analysis here has itsroots in Biais et al. (1995) and also very similar to Cao et al. (2004). The idea is torepresent the limit order book using step functions as described below:

1. Define P1 the as the outstanding back odds for the home team, and Q1 the corre-sponding depth. P2 and Q2 are the next highest odds and corresponding quantities, P3

and Q3 are the ones further below in the book and so on.2. The height of step i represents ∆Q = Qi −Qi−1.3. The length of the step is defined as ∆P = Pi − Pi−1.4. 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 dis-

tinction 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 alsodepicted in Figure 2. This clustering is also documented in financial markets, notably inParis Bourse (Biais et al. (1995) and Bouchaud et al. (2002)). This ”hump-shape” of thelimit order book is presumably an optimizing behavior of the uninformed traders. Posting

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limit orders is essentially giving free options to informed traders, therefore uninformedtraders 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 emergesin equilibrium when multi-unit orders are allowed. The present findings are thereforeconsistent with both the theoretical and empirical literature.

1 2 3 4 5200

400

600

800

1000

1200

1400

1600

1800

Price steps

Num

ber

of S

hare

s

awayhome

Figure 2: Shape of the Order Book

Another observation is that little depth is provided at the outstanding market prices.14-16% of the depth is offered for the away team and only 9-11% of the depth is offeredfor the home team. Averaging across teams, the total depth at inside quotes correspondsto 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 etal. (2004), Biais et al. (1995).23 This implies that i)A comparison of the exchangeand the bookmaker at the inside quote fails to present the whole picture and ii)There ispotentially useful information in the order book that can be utilized by the bettors, anissue I will revisit later in the section.

23Since Cao et al. (2004) report the percentages for 10 deep, the percentages are recalculated fornormalization purposes. Exact numbers are not reported in Biais et al. (2005), but an upper limit canbe obtained.

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Table 5: Order Book Statistics - Depth

Away HomeAsk Bid

Dec 88.4 121.9 138.8 110.3 89.2 139.3 244.9 242.8 361.9 301.2Totals Jan 80.4 77.0 97.4 69.4 57.4 114.4 232.6 285.8 269.2 292.1

(in thousand $) Feb 69.0 108.5 122.9 116.9 70.6 140.1 234.9 281.5 376.9 218.4Dec-Feb 237.8 307.5 359.1 296.6 217.4 393.9 712.5 810.2 1,008.0 811.7

Dec 410 564 643 511 413 645 1134 1124 1676 1395Averages Jan 347 332 420 299 248 493 1003 1232 1160 1259

(in $) Feb 394 620 702 668 404 801 1343 1609 2154 1248Dec-Feb 382 494 577 476 349 632 1144 1301 1618 1303

Dec 16.1 22.2 25.2 20.1 16.2 23.3 28 18.8 18.9 10.8Percentages Jan 21 20.1 25.5 18.1 15 24.4 22.5 23.9 19.4 9.5

(%) Feb 14.1 22.2 25.1 23.9 14.4 17.4 30.1 22.4 18.7 11.1Dec-Feb 16.7 21.6 25.3 20.9 15.3 21.7 26.9 21.6 19 10.5

4.2.2 A Liquidity Measure

The measure that will be used here is inspired by Irvine et al. (2000). They suggest ameasure called the cost of round trip and claim that it is is most useful, when committedliquidity is a big portion of the total liquidity that consists of committed and hiddenliquidity.24 In the present study, all liquidity is committed, therefore the measure iswell-suited for the research questions in hand. As it is well understood, liquidity is atransaction size specific concept. I will proceed as follows:

1. Specify an amount D.

2. Define P1 the as the outstanding back odds for a team, and Q1 the correspondingdepth. P2 and Q2 are the next highest odds and corresponding quantities, P3 and Q3 arethe ones further below in the book and so on.

3. Calculate the average odds for D using the following:

AO (D)= (∑N

i=1 Pi−1 ·Qi−1 + (D −∑Ni=1 Qi−1) · Pi)/D if ∃i s.t.

∑Ni=1(Qi−1) < D and∑N

i=1(Qi) ≥ 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 isequal to or greater than the quoted spread.

This measure has a simple interpretation. The bettor who wants to bet D dollars ona team walks up the book until he spends all D dollars. Clearly, the book may not befull for larger amounts. Table 7 depicts the number of books that are not full, acrosshome and away teams and for three months. The differences between home teams andaway teams are naturally visible here, as the two measures are strongly correlated. Thenumbers are also consistent with the behavior of the aforementioned measure (Irvine etal. (2000)) for the Toronto Stock exchange.

24Both in the Paris Bourse and on the Toronto Stock Exchange some liquidity is hidden.

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Table 6: How ”full” is the book?Away Home

Amount (in $) 100 500 1,000 5,000 10,000 100 500 1,000 5,000 10,000Dec (210) 209 146 96 26 8 208 187 152 61 28

Observations Jan (232) 232 174 119 14 2 230 207 161 58 32(# games) Feb (175) 174 145 111 28 10 175 167 143 70 33

Dec-Feb (617) 615 465 326 68 20 613 561 456 189 93

Dec 99.5 69.5 45.7 12.3 3.8 99 89 72.3 29 13.3Percentages Jan 100 75 51.2 6 0.8 99.1 89.2 69.3 25 13.7

(%) Feb 99.4 82.8 63.4 16 5.7 100 95.4 81.7 40 18.8Dec-Feb 99.6 75.3 52.8 11 3.2 99.3 90.9 73.9 30.6 15

Table 7: Average Gross Winning Payouts per $1 Bet When Different Amounts Are Bet

Bet amount (in $) 100 500 1,000 5,000 10,000Payouts per $1 Bet 1.98 1.80 1.61 1.3 1.17

What happens to the return differences as the order size gets larger? Table 8 demon-strates 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. In-stead 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 marketsattract order flow. If bettors take the information in the entire limit order book intoaccount, then liquidity should invite subsequent activity.26 Moreover, if bettors basetheir decision of venue not only on the quoted spread but on the entire book, they shouldswitch to the bookmaker less frequantly if liquidity is high on the exchange. Unfortunatelyquantity information at the bookmaker level is not available. Nevertheless, the numberof revisions can be used as a proxy for volume. This scenario presents the idea behindthe testable hypothesis that games for which odds are revised, are not random and arerelated to the state of the book on the exchange. Specifically, the odds are more likelyto be revised if more people place bets with the bookmaker and this will be expected ifliquidity is relatively low on the exchange.

To test the above hypothesis, I give an identity to every game. The identity of agame is simply an ordered pair where the entries are the maximum amounts for whichthe book is full. For example, if the identity for a game is (500,1000), the interpretationis the book of the away team is full for 500 dollars, but not so for 1000 dollars. Anidentical argument holds for the home team. If liquidity matters then we should expectgames where there is at least one team with betting possibilities of up to 10,000 dollars

25One can also compare the returns by using the proper combination of the exchange and the book-maker versus the bookmaker only. This is plausible as some people might be shopping around to findthe best odds and can divide their orders. Even so, the bookmaker catches up quite easily.

26Although not reported, preliminary analysis shows that this is indeed the case here.

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Table 8: Contingency Table Based on Liquidity

Liquid games Relatively illiquid gamesRevisions 20* 160

No Revisions 85 345

* significant at the 1 percent levelchi-square = 6.67degrees of freedom = 1p-value = 0.010

to be revised less frequently. Indeed, a contingency table analysis (Table 9) shows this isthe 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 intoaccount. They are less likely to place bets with the bookmaker (proxied by the number ofrevisions) when liquidity is highh on the exchange. This together with sharply increasingexecution 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 indeedmean the end for bookmakers, but for this to happen the liquidity on the exchange shouldincrease quite significantly. A more plausible conjecture, then, is perhaps to expect bothtrading 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 mainreason driving the results although they are possibly at work to some extent.

Legal issues. Do the sportsbooks and exchanges have important differences in termsof legality? None of them accepts bets from the US, a claim which I verified. On the otherhand, I managed to open an account with William Hill and place some bets by supplyinga non-US credit card and address. As mentioned in footnote 7, the same procedurefailed with Betfair. Potentially, if there are a lot of gambling addicts in US who haveaccess to foreign credit cards, this might account for some of the betting activity with thebookmaker. This, however, does not seem very likely, not only because of the enormousprofits made by the online sportsbook, but also there is no reason to believe that all thesepeople 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 withWilliam 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 theexistence of Betfair? William Hill, for example, has been around since 1934 and whenthey started their online operation they were already very well known. Betfair started as

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an internet startup. Although it is possible, it is hard to imagine, that bettors have neverheard of betting exchanges, especially Betfair. First, it can be safely assumed that onlinebettors are sufficiently comfortable with the internet, and it is hard not to come acrossbetting exchanges, especially with the rise of another group of websites, that provide acomparison of odds from many bookmakers and exchanges. Moreover, the youth is animportant part of the betting crowd implying that not many bettors who wager online areswitchers, who replaced betting offices with online units within the same bookie. Secondthe turnover in Betfair is already higher than any of the other three bookmakers andwith its revolutionary business model Betfair has been highly publicized earning themseveral prestigious awards as mentioned before. All in all, unawareness does not emergea satisfactory explanation.

First Mover’s Advantage/Switching Costs/Brand Loyalty. The traditionalbookmakers clearly entered the market before betting exchanges and accumulated a largecustomer base. If the switching costs are high for the bettors and/or if there is some sortof brand loyalty, it might justify the observed results.

However, the switching costs do not seem to be high. Both exchanges and bookmakershave similar designs and learning should be negligible. It might be the case that postingodds and laying teams require a considerable amount of learning but for our purposesthis is irrelevant as only market orders are included in the analysis.

As for the brand loyalty, some observations from other industries could be useful. Forexample, in the pharmaceutical industry, it has been observed that brand-name productskeep selling at higher prices even after the patent is over. This might be a sustainablesignalling equilibrium, the brand wants to signal that it is superior to generic productsand consumers are convinced that this is indeed the case. However, signalling is lesslikely to work in the betting industry. The sports events are always the same, so the onlyrelevant quality dimension is the possibility of financial trouble. It is still possible thatconsumers do not trust the exchange in financial terms yet with all the publicity andreputation Betfair has, such beliefs on the consumer side are hardly justifiable.

Differences between the exchange and bookmaker. No two markets are exactlythe same. The present case is no exception. There are some differences across the selectedsportsbooks and the exchange, which might potentially contribute to the consumptionvalue. On the exchange punters have the freedom of posting their own odds and layinga team. In-play betting is also available.27 On the negative side, the minimum bet is $4compared to one cent at William Hill and multiple bets are not allowed on the exchange.28

27It is worth to mention that in-play betting was only available on the exchange in the beginning, butWilliam Hill started to offer this option to its bettors in January 2005. Two interesting observations:First, the in-play games at Betfair and William Hill mostly coincide. Second, whenever William Hillposts odds during the game, they are always inferior to pre-game odds. Presumably higher prices (lowerodds) are required to compensate the additional risk. Interestingly, the price grid of these inferior oddscoincide with Ladbrokes’ pricing grid. There may be some communication, if not collusion, betweenonline venues as far as these games are concerned.

28A multiple bet, or parlay, is placing a wager on any number of events simultaneously. Should allevents have the desired outcome, the return is equal to the product of all odds, hence the returns can be

20

For example, if most of the betting at William Hill is in the form of multiple bets, theobserved results could be justified. However, this does not only require extreme risk-lovingattitide on the part of the bettors, it also requires the somewhat strong assumption thatthe options at William Hill are more valuable to the punters than those offered by heexchange. The betting crowd is probably heteregeneous enough and such differences arelikely to balance out.

Sampling issues. The lack of data on basketball market at the bookmaker levelcan be considered as a shortcoming of this study. Indeed, one assumption implicit in thepaper is that all markets in the online unit attract a lot of betting. It could be arguedthat the market I have chosen, the basketball market, does not have a high turnover andthe profitability of online unit relies on other markets. I tend to dismiss this explanationfor two reasons. As far as William Hill is concerned, in almost 30 percent of the games thefinal odds were different than the first round of odds. On some occasions the odds havechanged more than once. Some games have seen large odd revisions. The rather frequentmodification of the odds reflects that the basketball market has been active. Second,a quick look at the other markets, including soccer, golf and horse racing, reveals thatboth odds and returns differences have been large. However my sample in these othermarkets is rather small and the events are less frequent. Although the preliminary analysissuggests that the results from American basketball market will carry over, future workshould definitely focus on other markets which might establish robustness and strengthenthe results.

6 Conclusions

The transformation of the betting industry has been quite similar to that of financialmarkets. Both markets are now characterized by a hybrid structure where order-drivenmechanisms (auction/betting exchanges) compete with quote-driven mechanisms (deal-ers/bookmakers) for order flow. This regularity is not random in financial markets; dealerare valuable because they are immediate suppliers of liquidity along with other functions,which results in fragmented markets.

The betting industry (rightly) pointed out that betting exchanges will offer compet-itive odds and (wrongly) predicted that the bookmakers will be driven out of business.Utilizing a unique dataset of NBA games played between December 2004 and February2005, I show that the selected exchange, Betfair, offers significantly higher returns thanbookmakers, William Hill and Ladbrokes. Since the bookmakers continue to be profitable,it is important to understand why migration has not occurred.

Since both venues are quite similar in terms of market microstructure, it is natural toanalyze related concepts. I propose a measure which summarizes the information in thelimit order book. I find that liquidity matters, although the exchange offers significantlyhigher returns for small orders, execution costs rise sharply as the order size gets larger.

enormous. If one event is not correctly guessed the returns are zero.

21

Moreover, odds revisions are more frequent when books on the exchange lack depth, whichsuggests that the bookmaker attracts order flow for large orders. Just like investors infinancial markets, bettors take the information in the limit order book into account.

The present study analyzes online betting markets, yet provides an empirical inter-market comparison which has been rare due to obvious limitations. The comparison isreasonably clean; all trades are executed via a single mechanism and the entire limit orderbook is public information. Moreover, the similarity of microstructure in both markets,to my best knowledge, has not been analyzed in the literature. Gambling markets havebeen regularly utilized from an efficiency perspective. With their current design, anotherfield in finance, market microstructure, could benefit from drawing on applications fromthis parallel realm.

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