The Bookie Puzzle: Auction versus Dealer Markets in
Online Sports Betting
Alper Ozgit
Department of Economics, UCLA
ozgit@ucla.edu
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
“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
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 2005.1 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
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
2
The Online Betting Market
2.1
2.1.1
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: http://www.casinocity.com/
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.
4
5
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.
2.1.2
Company Specifics
William Hill. William Hill is established in 1934. Its shares have been publicly traded
on the London Stock Exchange since June 2002. 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
106.1 (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 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 2004. 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 2000. 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 107.1 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 300,000.6
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 2003.
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
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
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:
Lakers
Spurs
Back
2.2 (100$)
1.7 (50$)
Lay
2.21 (200$)
1.71 (1000$)
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
Lakers
Spurs
1.7 (50$)
Lay
2.2 (60$)
2.21 (200$)
1.71 (1000$)
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$. A bettor who hits the market quote on the “lay” side essentially acts as a bookmaker, if Lakers win, he keeps the amount he laid, otherwise he is obligated to pay 71
dollars on every 100 dollars. If the amount laid is smaller, the transaction is executed
immediately. If it is greater, say 1200 dollars, then the new LOB looks as follows:
Lakers
Spurs
Back
2.2 (100$)
1.7 (50$)
1.71 (200$)
Lay
2.21 (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
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 2005. 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.
12
5 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
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
Table 1: Data Summary
Mean Minimum Maximum
First snapshot $12,375
$93
$71,635
Totals
$24,220
$2,014
$130,322
In-play games $29,866
$3,671
$63,116
(1st snapshot)
- December
25th %tile Median 75th %tile
$5030.25
$8,697.5
$15,654
$12,320.75 $18,429.5 $28,325.75
$13,155.75 $23,431
$45,636.5
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.15
3.1
Summary statistics
A total of 216 games were played in December 2004.16 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
4.1
Empirical Analysis
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
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
Table 2: Average Odds and The Frequency of Best Odds
Website
Observations Average Odds
The Frequency
Betfair (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 William
Hill the average overround is 1.042 (standard error 0.007). With a standard 11-10 Vegas
betting, the overround would be 1.045.18 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 1.023. 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
2.3
Betfair
William Hill
2.2
2.1
Gross returns
2
1.9
1.8
1.7
1.6
1.5
1
2
3
4
5
6
Weeks
7
8
9
10
11
12
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 2.22
4.2
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
B vs. WH
B vs L
Table 3: Average Odds on Winning Bets
Observations B mean WH/L mean Difference t-Value
607
2.003
1.916
0.086
9.971*
(1.254)
(1.090)
(0.214)
607
2.004
(1.256)
1.853
(0.986)
0.150
(0.337)
11.020*
Note: Standard deviations are in parentheses.
* significant at the 1 percent level
B vs. WH
B vs L
Table 4: Average Winning Payouts per $1 Bet
Observations B mean I WH/L mean Difference t-Value
607
1.953
1.916
0.036
5.360*
(1.192)
(1.090)
(0.168)
607
1.954
1.853
(1.194)
(0.986)
Note: Standard deviations are in parentheses.
* significant at the 1 percent level
0.100
(0.285)
8.674*
(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?
4.2.1
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 P1 the as the outstanding back odds for the home team, and Q1 the corresponding 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 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
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.
1800
away
home
1600
Number of Shares
1400
1200
1000
800
600
400
200
1
2
3
Price steps
4
5
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 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
Table 5: Order Book Statistics - Depth
Away
Totals
(in thousand $)
Averages
(in $)
Percentages
(%)
4.2.2
Dec
Jan
Feb
Dec-Feb
Dec
Jan
Feb
Dec-Feb
Dec
Jan
Feb
Dec-Feb
88.4
80.4
69.0
237.8
410
347
394
382
16.1
21
14.1
16.7
121.9
77.0
108.5
307.5
564
332
620
494
22.2
20.1
22.2
21.6
138.8
97.4
122.9
359.1
643
420
702
577
25.2
25.5
25.1
25.3
Home
110.3
69.4
116.9
296.6
511
299
668
476
20.1
18.1
23.9
20.9
Ask
89.2
57.4
70.6
217.4
413
248
404
349
16.2
15
14.4
15.3
Bid
139.3
114.4
140.1
393.9
645
493
801
632
23.3
24.4
17.4
21.7
244.9
232.6
234.9
712.5
1134
1003
1343
1144
28
22.5
30.1
26.9
242.8
285.8
281.5
810.2
1124
1232
1609
1301
18.8
23.9
22.4
21.6
361.9
269.2
376.9
1,008.0
1676
1160
2154
1618
18.9
19.4
18.7
19
301.2
292.1
218.4
811.7
1395
1259
1248
1303
10.8
9.5
11.1
10.5
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 P1 the as the outstanding back odds for a team, and Q1 the corresponding
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.
3. Calculate the average odds for D using the following:
AO (D)= (
PN
i=1 (Qi ) ≥ D
PN
i=1
Pi−1 · Qi−1 + (D −
PN
i=1
Qi−1 ) · Pi )/D if ∃i s.t.
PN
i=1 (Qi−1 )
< D and
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
Table 6: How ”full” is the book?
Amount (in $)
Observations
(# games)
Percentages
(%)
Dec (210)
Jan (232)
Feb (175)
Dec-Feb (617)
Dec
Jan
Feb
Dec-Feb
100
209
232
174
615
99.5
100
99.4
99.6
500
146
174
145
465
69.5
75
82.8
75.3
Away
1,000
96
119
111
326
45.7
51.2
63.4
52.8
5,000
26
14
28
68
12.3
6
16
11
10,000
8
2
10
20
3.8
0.8
5.7
3.2
100
208
230
175
613
99
99.1
100
99.3
500
187
207
167
561
89
89.2
95.4
90.9
Home
1,000
152
161
143
456
72.3
69.3
81.7
73.9
5,000
61
58
70
189
29
25
40
30.6
10,000
28
32
33
93
13.3
13.7
18.8
15
Table 7: Average Gross Winning Payouts per $1 Bet When Different Amounts Are Bet
Bet amount (in $)
Payouts per $1 Bet
100 500
1.98 1.80
1,000
1.61
5,000
1.3
10,000
1.17
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
Table 8: Contingency Table Based on Liquidity
Revisions
No Revisions
Liquid games
20*
85
Relatively illiquid games
160
345
* significant at the 1 percent level
chi-square = 6.67
degrees of freedom = 1
p-value = 0.010
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
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.28
27
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 2005. 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
For example, if most of the betting at William Hill is in the form of multiple bets, the
observed results could be justified. However, this does not only require extreme risk-loving
attitide on the part of the bettors, it also requires the somewhat strong assumption that
the options at William Hill are more valuable to the punters than those offered by he
exchange. The betting crowd is probably heteregeneous enough and such differences are
likely to balance out.
Sampling issues. The lack of data on basketball market at the bookmaker level
can be considered as a shortcoming of this study. Indeed, one assumption implicit in the
paper is that all markets in the online unit attract a lot of betting. It could be argued
that the market I have chosen, the basketball market, does not have a high turnover and
the profitability of online unit relies on other markets. I tend to dismiss this explanation
for two reasons. As far as William Hill is concerned, in almost 30 percent of the games the
final odds were different than the first round of odds. On some occasions the odds have
changed more than once. Some games have seen large odd revisions. The rather frequent
modification 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 that
both odds and returns differences have been large. However my sample in these other
markets is rather small and the events are less frequent. Although the preliminary analysis
suggests that the results from American basketball market will carry over, future work
should definitely focus on other markets which might establish robustness and strengthen
the results.
6
Conclusions
The transformation of the betting industry has been quite similar to that of financial
markets. Both markets are now characterized by a hybrid structure where order-driven
mechanisms (auction/betting exchanges) compete with quote-driven mechanisms (dealers/bookmakers) for order flow. This regularity is not random in financial markets; dealer
are 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 competitive 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 February
2005, I show that the selected exchange, Betfair, offers significantly higher returns than
bookmakers, 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 to
analyze related concepts. I propose a measure which summarizes the information in the
limit order book. I find that liquidity matters, although the exchange offers significantly
higher 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, which
suggests that the bookmaker attracts order flow for large orders. Just like investors in
financial markets, bettors take the information in the limit order book into account.
The present study analyzes online betting markets, yet provides an empirical intermarket comparison which has been rare due to obvious limitations. The comparison is
reasonably clean; all trades are executed via a single mechanism and the entire limit order
book is public information. Moreover, the similarity of microstructure in both markets,
to my best knowledge, has not been analyzed in the literature. Gambling markets have
been regularly utilized from an efficiency perspective. With their current design, another
field in finance, market microstructure, could benefit from drawing on applications from
this parallel realm.
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23