Globalisation and Efficiency in the Fixed-odds Soccer Betting ... - Istituti

Address for correspondence:
Globalisation and Efficiency in the
Fixed-odds Soccer Betting Market
by
David Forrest
and
Robert Simmons
Centre for the Study of Gambling and Commercial Gaming
University of Salford
December, 2001
Dr David Forrest
Centre for the Study of Gambling and Commercial Gaming
University of Salford
Salford
M5 4WT
e-mail: d.k.forrest@salford.ac.uk
telephone: + 44 161 295 3674
telefax: + 44 161 295 2130

ABSTRACT
The paper analyses patterns of odds in the British soccer betting market over four seasons from
1997. It uncovers limited evidence for home-away and favourite-longshot bias identified in
previous research. It also considers the hitherto unexplored issue of the extent to which odds set
by bookmakers reflect the different numbers of supporters that different football clubs have.
However, by the end of the period, the growth, from 1999, of a significant offshore sector with
tax-free betting opportunities and greater competition had moved the market strongly towards
efficiency.
JEL Classification: L83
1

1. Introduction
A voluminous literature, comprehensively surveyed by Sauer (1998) and Vaughan Williams
(1999), concerns itself with efficiency in betting markets. The core question addressed is
whether and to what extent the terms of bets on horse races or sports events capture accurately
the objective probabilities of the possible outcomes. Given the size of wagering turnover in
many jurisdictions, the question is interesting in itself; but most authors give it further and wider
significance by portraying these specialised financial markets (where bettors are purchasing state
contingent claims on ‘winnings’) as offering opportunities for learning general lessons about the
ability of economic agents to process information and about how successfully the information is
transmitted into market prices.
The largest number of studies relates to horse racing in the United States. 1 There, betting
is organised on a pari mutuel (or pool) basis such that the relative odds of the competitors in a
race depend only on the relative amounts wagered on each horse. Relative prices are therefore
entirely demand-determined. If observed prices are inefficient in the sense of failing to reflect
objective probabilities, this can be attributable only to bettor behaviour: either bettors suffer
systematic misperceptions (uncorrected by arbitrageurs) or the explanation lies in their
preferences (e.g. the well-known favourite-longshot bias may be generated by utility functions
characterisable as risk-loving).
A second way in which betting may be organised is in a bookmaker market. This is the
dominant form of gambling on horse races in Britain, Ireland and many Commonwealth
countries and is also favoured for wagering on team sports in the United States. In these
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markets, a bookmaker announces the terms on which bets may be made (these may be
summarised either by a quotation of the odds or, in the cases of American football and
basketball, by points spreads). Clients may strike a bet at whatever terms are offered at the time
but these terms will be adjusted in light of any subsequent bets as bookmakers receive guidance
from the weight of money wagered on the various outcomes. The ‘prices’ observed at the end of
the betting period will therefore reflect interaction between the demand and supply sides of the
market. Any ‘inefficiency’ observed in the closing odds (or points spread) could be the result of
bettor behaviour (as in pari mutuel markets) but authors such as Shin (1993) have drawn
attention to the potential for sources of inefficiency alternatively to lie on the supply side (where
bookmakers may, e.g. be responding to concern over insider trading).
There is however, a third and unusual form of betting market, which is the focus of this
paper. In ‘fixed-odds betting’ on British football (soccer), bookmakers offer odds at the
beginning of the trading period (which is of several days duration) and these are then available
up to the time of the game, regardless of bettors’ response to the terms offered. Prices are purely
supply-determined (though, of course, the bookmakers may take into account predicted client
response to different odds). We examine this market to assess the degree of efficiency exhibited
by the odds. In a sense, this is a particularly challenging market on which to test an efficiency
hypothesis: where the odds are allowed to move, as in pari mutuel or in conventional bookmaker
markets, price is influenced by diverse sources of information driving the trading decisions of
bettors; these extra sources of information are unused in fixed-odds betting where bookmakers
must rely on their own expertise (and perhaps their experience of patterns of demand).
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Section 2 outlines the main features of the football betting market in the United
Kingdom, Section 3 considers the small but growing body of previous literature and Section 4
describes our data. In Sections 5 and 6, we propose and implement tests for specific biases in
odds and include consideration of a previously ignored issue, whether odds reflect levels of
interest in and support for particular football clubs and whether this ‘sentiment’ in the market can
be exploited for wagering gain. Section 7 offers interpretation and concludes.
2. Betting on UK soccer matches
All large British bookmakers offer odds on the possible outcomes (home team win, away team
win, draw) of all games played under the auspices of the English (as well as the Scottish)
professional leagues. 2 The bulk of matches are played on Saturday afternoons between August
and May and a typical Saturday may feature sixty such games in England and Scotland. 3 The
odds setters of an individual bookmaking firm meet at the beginning of the week (Sharpe, 1997)
and the odds they decide are printed on to entry forms (known as coupons) which are then
available all week. Bets may be made right up to the start of the relevant match(es) by visiting
the bookmaker’s shop or, in most cases, by telephone or internet, using a credit card. Such
betting has been increasingly popular. Mintel Intelligence Report (2001) commented that
“football betting is the fastest-growing form of gambling in the UK”. Global Betting and
Gaming Consultants (2001) cite an opinion poll in 1998 that indicated nearly four million adults
betting weekly on sports and claimed annual UK turnover of sports betting to be about £2bn.
The huge majority of this turnover will relate to football though the figure includes not only
betting on results but also wagering on other aspects of the game such as the identity of the first
scorer in a match.
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Crafts (1985), in a paper on insider trading in horse betting markets, remarked that the
willingness of bookmakers to commit themselves to ‘fixed-odds’ in respect of soccer games is
testimony to the low relevance of inside information in the sport. We would not necessarily
share this interpretation. Bookmaker betting grew during the 1980s to compete with an
alternative form of betting on football, the pools, at that time a mass-participation long-odds (and
pari mutuel) gambling medium where the idea was to select a group of games likely to end in
draws. It was natural that bookmakers would challenge the pre-existing competition by aping
their entry forms. 4 Printing bookmaker coupons similar to those of the pools necessitated fixing
the odds in advance of the betting period. However, giving up the right to shift the odds in
response to demand was only feasible and prudent because of alternative rules available to
bookmakers to protect themselves against the exploitation of inside (or just new) information.
The rules to which we refer constitute an important feature of the market, only
occasionally and incidentally mentioned in previous academic studies of football betting: it is not
normally possible to bet on the outcome of a single match. Only combination bets have
traditionally been allowed. 5 This rule had its origin with the football authorities themselves
which licensed use of the fixture lists and imposed a prohibition on single game bets in order to
protect the integrity of the sport against temptations of match fixing. However, bookmakers
have imposed more restrictive rules than the Football Association requires (and, moreover, differ
from each other in the severity of their restrictions on types of bet) and their rules must therefore
be understood as a part of business strategy rather than something imposed exogenously.
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With some exceptions (e.g. televised matches), bookmakers have not normally permitted
anything less than a ‘treble’ bet. Such a rule is protection against those with inside or new
knowledge. If one knew, as if with certainty, that team A would defeat team B, one could only
be sure of using the knowledge to make a winning bet by choosing two other matches and
making a series of treble bets in each of which A was wagered to win but each time with a
different pair of forecasts from the other two games. The expense would normally make it
impossible to take a position where a profit was certain and, even taking the risk of covering only
some of the combinations of outcomes of the other two games, expected profit would be eroded
or eliminated altogether.
An alternative to betting on three or more matches has, however, emerged in recent years.
Bookmakers permit ‘double’ bets on a single game where the two halves of the bet relate to (i)
the half-time score in the game (home, away, draw) and (ii) the full-time score in the game
(again home, away or draw). Each bookmaker will offer the chance of such a double on any
match on the coupon. The odds are not fixed match-by-match but are linked to the odds quoted
for the chosen team on the main entry form.
As a typical example, suppose the odds against home team A defeating away team B are
6/4. Corresponding to these odds, a bookmaker offers bets including the following:
A leads at half-time, A leads at full-time 7/2.
Draw at half-time, A leads at full-time 9/2.
B leads at half-time, A leads at full-time 22/1.
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Were a single bet permitted on A at 6/4, one would need to spend £0.40 to receive £1 in
the event of an A victory. By employing the device of betting on the three combinations which
can end in a win for A, one can ensure a pay-back of £1 for a spend of £0.447. 6 This represents a
shading of the odds by 17.7% from 1.5 to 1 to 1.24 to 1. We interpret this 17.7% as a sort of
insurance premium to protect bookmakers against insider dealing: if a client wants to bet on a
single match he can do so but, in case his wishes are inspired by the possession of fresh news or
inside information, he must accept odds approximately 18% less favourable than the published
odds.
The significance of the ‘insurance premium’ is that it reduces the likelihood that any bias
identified in the published odds can be exploited via the formulation of appropriate trading rules.
For such betting to have been profitable in the past, the bias would have had to be sufficiently
pronounced that bets could overcome not only the 9% tax and the (approximately) 10.5%
bookmaker’ take 7 but also the implicit charge of 18% associated with being allowed to wager on
a single game. The total take-out rate accounting for all three deductions, (1-(0.91*0.823)) +
0.105, is 35.6%, which is not much less than the figure of 50% for the UK National Lottery.
Transactions costs in soccer betting have, however, been falling. From May, 1999, a
number of large British bookmakers set up offshore betting firms in jurisdictions such as
Gibraltar and Guernsey to permit wagers to be placed via telephone or internet without any
liability to betting duty. Moreover, competition amongst offshore operations eroded the severity
of restrictions on single bets so that, e.g., it is now possible to make a single bet on any Premier
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League fixture. In response to the move of bookmaking offshore, betting duty was removed in
the United Kingdom in October, 2001. This fall in transactions costs would be expected to
diminish the extent to which bookmakers could deliberately bias their odds without attracting the
attention of professional bettors seeking opportunities to make positive expected profits.
3. Previous studies of UK soccer betting
In view of the novelty of the market, there have been surprisingly few academic studies until
very recently. Pope and Peel (1989) employed data from the 1981/2 football season and
regressed the outcome of the match (defined by a binary variable equal to one for a named result)
on the bookmaker odds quoted for that result. In the case of home wins and away wins, the
coefficient on the bookmaker odds was never significantly different from one (at the 5% level)
indicating that there was no statistically significant bias in odds-setting.
Pope and Peel next estimated regressions in which measures of newspapers tipster
forecasts were included as additional explanatory variables. Though tips had only low
informational content, there was some indication that bettors could use them to reduce their
expected losses and it was also possible for bettors to benefit by studying the odds set by
different bookmakers, the pooling of information unsurprisingly assisting in the identification of
games where a ‘fairer’ bet might be made at a selected bookmaker. However, a 10% betting tax
was noted to be an impediment to profitable trading rules, so that that market appeared to be
weak-efficient in the Thaler-Ziemba (1988) sense of there being no opportunity to find bets with
positive expected value. Our comment that one should take account of the worsening of odds
implicit in restrictions against single bets would reinforce their conclusion. One should also note
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that the data analysed by Pope and Peel are now nearly 20 years old and pertain to a period when
betting volumes were negligible compared with their present importance (Jackson, 1994).
Bookmakers now have much more incentive to pay for the specialised talent necessary to ensure
accuracy in odds setting. Conceivably therefore, any tendency to inefficiency may have been
eliminated since Pope and Peel’s pioneering contributions.
Dixon and Coles (1997) adopt a model proposed by Maher (1982) to forecast the results
of football games played over the 1992-95 period. The score of each team is modelled as an
independent Poisson distribution with mean determined by the past goal-scoring record of that
team and the past goal-conceding record of the opposing team. 8 Probabilities of home, away and
draw outcomes are extracted from the estimated model and a simulation performed for a filter-
betting strategy whereby a bet is placed on any outcome for which the probability indicated by
the model exceeds (by a nominated margin) the probability implicit in the bookmaker’s odds.
With the required ratio of model probability to bookmaker probability set at 1.2, the
expected return to such betting is reported as “borderline significantly different from –0.11, the
expected return to a random betting strategy”. This constitutes evidence against strong
efficiency in odds to the extent that some bets indeed appear to yield higher expected returns
than other bets. Whether there is sufficient evidence of a potentially profitable betting strategy is
more open to question. From the authors’ figure 4, allowing for the worse odds associated with
betting on a single match would require the filter ratio to be raised to about 1.3 for the expected
return to become positive. Figures are not presented on the number of bets that can be made in a
season at each value of the filter ratio but it is a familiar feature of horse betting that ‘winning’
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strategies require considerable effort and data analysis while identifying frustratingly few
occasions on which a bet should be placed (Crafts, 1994).
Kuypers (2000), Dobson and Goddard (2001) and Goddard and Asimakopoulos (2001)
follow similar procedures to Dixon and Coles in that they employ a forecasting model to identify
matches where the bookmaker probability in respect of one of the possible outcomes has been
underestimated to some specified degree. However, they employ ordered profit models which
can encompass a variety of historic information beyond just the goal scoring record of each team.
Kuypers was able to identify a limited number of profitable bets in season 1994-5 using a model
estimated for 1993-4 but only when the forecasting model included not only team quality data
but also odds data (i.e. he exploited a combination of fundamental and technical analysis). The
research reported in Dobson-Goddard and Goddard-Asimakopoulos draws on a very rich
forecasting model estimated over ten seasons to select value bets in 1998-9 and 1999-2000.
They find positive profit opportunities from using the model but only late in the season when the
forecasting model can include much more current season information and can also benefit from
the use of a dummy variable that highlights teams for whom a particular match has strong
promotion or relegation significance. The positive profit depends, however, on being able to bet
on single matches and on not having to pay tax. Goddard and Asimakopoulos remark that tax is
now indeed abolished; but, of course, bookmakers may now for that reason alone reduce the
extent to which they will offer ‘biased’ odds.
Dixon and Pope (1996) point to indications of a degree of inefficiency in the football
betting market associated not with a failure of the odds to capture information on the
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performance in the past of particular teams but with patterns in the odds across matches.
Evidence related to three bookmakers and their odds in English football games over 1992-6
suggested that appreciably lower losses would accrue to bettors backing home wins or draws
rather than away wins. Further, an examination of returns related to different ranges of odds
pointed to a reverse favourite-longshot bias: wagers on outcomes with the shortest odds (i.e. the
highest bookmaker probability) attracted the largest losses. Cain, Law and Peel (2000), on the
other hand, however, noted superior (though still negative) returns accrued to bets on strong
favourites; but their evidence was drawn from only one year, 1991-2.
The evidence presented by Dixon and Pope in support of the proposition that odds
underestimated the chances of home teams and underdogs is highly suggestive. However, we
prefer to assess the existence and magnitude of these and other possible biases by multivariate
regression analysis. A comparison of returns to backing short- and long-odds teams may for
example generate misleading estimates of the size of any bias if odds are correlated with whether
or not a team enjoys home advantage. Thus, the superior return to betting on strong favourites,
noted by Cain, Law and Peel, may in fact be generated by home-away bias in betting odds since
strong favourites are almost always playing at home. 9 As implied by work from Golec and
Tamarkin (1991) on American football points-spread betting, the detection and estimation of
favourite-longshot bias (or its reverse) requires a multivariate approach to ensure that any
estimation is not contaminated by the presence of a simultaneous home-away bias. In this paper,
we test for these biases and also for a possible bias linked to disparity in fan-betting volumes
when opposing teams have very unequal numbers of supporters.
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4. Data
Our model was estimated for each of four football seasons from 1997-8 to 2000-1. For each
season, we attempted to include all matches in the English professional leagues (i.e. the FA
Premier League and Divisions One, Two and Three of The Football League) that were played on
a Friday, Saturday or Sunday (these are the days whose fixtures are included on bookmakers’
weekly coupons). The outcome of each match was noted from the relevant volume of The
Rothman’s Football Year Book.
Betting odds used in this study are for Super Soccer. Super Soccer odds are those
supplied by a specialist odds-setting firm and adopted by nearly all the small, independent
bookmakers of the United Kingdom (coupons carry both the name Super Soccer and the name of
the local bookmaker who has subscribed to the service). The four largest national bookmaking
firms quote their own individual odds. However, these are highly correlated with each other and
with Super Soccer’s: we collected data from all five sources for the first of our seasons, 1997-8,
and replicated the work reported below using, in turn, the odds from each of the other four firms.
The pattern of our results was very similar irrespective of which bookmaker was used and we are
therefore confident that our findings for Super Soccer are representative of the sector as a whole.
1998-9 and 1999-2000 Super Soccer odds were obtained directly from entry forms
(coupons); a small number of coupons were missing from our set and matches for these weeks
are excluded from the sample. For 1997-8 and 1998-9, we collected Super Soccer odds from
archive copies of the daily betting newspaper, The Racing Post. Both on the coupons and in the
newspaper, odds against any team i winning were quoted in the traditional form, a/b. We
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converted these odds so that they were expressed in the alternative form of probability-odds such
that the probability-odds of a win for team i became b/(a+b). For example, with quoted odds of 4
to 1, probability-odds were 1/5 or 0.20: one would have to spend £0.20 to secure a payout of £1
in the event of team i winning. 0.20 would, however, not be the implicit bookmaker-probability
of a win for team i because the sum of the probability-odds of the three possible outcomes (win,
loss or draw for team i) is always greater than one. Therefore, the bookmaker-probability of i
winning is obtained by dividing the probability-odds for team i by the sum of the probability-
odds of the three possible outcomes.
A problem here is that the Racing Post, on which we relied for data from two of our four
seasons, did not report odds for a draw but only for a home win and for an away win. However,
in the two years for which we had coupons quoting odds on each of the three possible results, the
sum of probability-odds was always close to 1.117, a figure reported by other authors for other
bookmakers and one that indicates a nominal bookmaker take of 10.5%. 10 For the matches for
which the data source was the Racing Post, we therefore estimated the bookmaker-probability of
a team winning a particular match by dividing its probability-odds by the fixed number of 1.117.
Thus in our example, the 4 to 1 team would have been attributed a bookmaker-probability of
0.20/1.117 or 0.179. This was then the figure used in empirical analysis.
5. Model
Authors such as, most recently, Goddard and Asimakopoulos (2001) demonstrate that –
occasionally (in their case, in the closing weeks of the season) – sophisticated forecasting models
might capture more fundamental information than is encapsulated in bookmaker’s odds. But,
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given the growing volume of betting in recent years, bookmakers have had an increasing
incentive to hire talent able accurately to process team quality and form information and it is
therefore unsurprising that these authors find (Table 2) that in general bookmaker odds perform
similarly as well as forecasting models in predicting on-the-field outcomes.
That is not to say, however, that the fixed odds betting market may be expected to be
‘efficient’ consistently. A bookmaker’s function is not to provide odds that are objectively
‘correct’ but to maximise profit. Accordingly odds may be biased if this allows the bookmaker
to take advantage of bettors’ misperceptions or preferences. For example, a consistent favourite-
longshot bias (positive or negative) may emerge if bettors have preferences such that they behave
as if they were risk-loving or risk-averse. Sentiment (as it is termed by Avery and Chevalier
(1999)) may likewise play a role in the market. Most crucially perhaps, sports betting markets
differ from typical financial markets in that many investors view the expenditure not just as an
investment but as a vehicle for becoming more of a stakeholder in the team for which they cheer
either in the stadium or more passively; bookmakers may price bets to take account of the
likelihood that the reservation price (odds) of such potential bettors will be influenced by their
degree of attachment to their team as well as by their assessment of the ‘true’ probability of
victory.
Studies of wagering markets have generally been disciplined by treating them as just
financial markets which happen to be convenient to study because of such well-cited
characteristics as the unambiguous termination point at which the value of the asset becomes
definitively measurable. Generally, there has been no recognition that a large proportion of
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participants in the market may choose between possible bets not primarily in terms of their value
as financial assets but as consumer goods complementary to the sport itself. This has led to a
tendency to search for, but not explain, biases in the odds and has perhaps limited the dimensions
of bias for which empirical evidence has been sought.
Kuypers (2000) is an exception to the extent that he (importantly) sought to build a model
where a profit maximising bookmaker sets (fixed) odds in the context of a market where there is
a mixture of ‘neutral’ bettors (who share the (objectively correct) bookmaker assessment of the
probabilities attached to each possible outcome from the match) and ‘committed’ bettors (whose
views are coloured by their support for a particular team and are over-optimistic with regards to
its probability of a win). This appears a useful framework to represent the soccer betting market
though we prefer to think of the ‘fan’ bettors as capable of assessing win-probabilities
objectively even though behaving as if they had misperceptions: we interpret their willingness to
wager as taking account of utility obtained from ‘supporting’ their team in the betting market as
well as in the stadium.
In his numerical example, Kuypers has ten supporters who have decided to bet and will
wager on a particular outcome according to their perception of the value offered by each of the
(three) possible bets. Four of the bettors are neutral and six are fans of Manchester United,
Britain’s most heavily supported club. Their opponents in Kuyper’s hypothetical match are
Liverpool. He has no committed Liverpool fans in the betting market but this is not damagingly
unrealistic to the extent that the same results would have been obtained had he posited a mix of
committed fans whose average assessment of a Manchester United victory was over-optimistic.
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In other words, what he is really examining is the effect of net ‘stakeholder’ support in favour of
one of the two teams.
Kuypers demonstrates in this context that the bookmaker’s expected profit is increased by
moving from ‘efficient’ odds to ‘inefficient’ odds (that implicitly overstate the probability that
Manchester United will win the match). This has some intuitive appeal since the bookmaker is
able to take advantage of the eagerness of Manchester United supporters to back their team by
offering them a lower pay-out in the event they win. However, the formal model and the
numerical example may suffer from excessive simplicity to the extent that it assumes that the
number of bettors is fixed. Kuypers justifies this by modelling the bookmaker as varying the
odds for each outcome within the context of a fixed over-round (which itself is realistic): he sees
‘price’ as embodied in the over-round and therefore fixed across the experiment. But if
Manchester United fans were modelled as interested in betting only on their team and were odds-
sensitive with regard to making that particular bet, it is conceivable that (depending on
elasticities) it would be worthwhile for the bookmaker to offer fairer rather than less fair odds in
respect of a United win.
It is surprising that Kuypers’ empirical investigation included no test of his implied,
innovative hypothesis that the probability that a bet wins will be a function of bookmaker
probability and relative supporter numbers for the teams in the match. We attempt such a test
here. We also test for bias in the home-away dimension; the rationale is similar to the extent that
a significant proportion of potential bettors (especially on minor games) may be spectators who
would consider betting (depending on value) to give themselves more of a stake in the outcome.
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This should add to their excitement at the match. Bookmakers would again be expected as part
of their profit-maximising decision to take account of how odds-sensitive this segment of the
market (mainly home fans, betting (if at all) on home teams) is likely to be.
We also test for favourite-longshot bias. The result is likely to be of interest in that
evidence on favourite-longshot bias in American team sports appears to be that it is in the
opposite direction from that widely observed in horse and dog racing (see Woodland and
Woodland (1994 and 2001) on baseball and hockey respectively). If we were similarly to find
negative favourite-longshot bias in this market, we might start to discern the beginning of a
pattern in which sets of odds in team sports consistently displayed different characteristics from
those in horse and dog betting.
The earliest study of the fixed odds market, Pope and Peel (1989), estimated a linear
probability model where the outcome of a bet (win or not) was regressed on the bookmaker-
probability associated with the bet. We adopt this model and also follow their procedure of
estimating by weighted least squares (with weights derived from fitted values of the dependent
variable, obtained using preliminary OLS estimation) in recognition of the likelihood of a
heteroscedasticity problem from ordinary least squares. However, we expand the regression to
test for home-away bias and for bias associated with relative fan numbers of the teams in a
match. Our model is therefore
PROBWINi = ∀ + ∃1 BOOKMAKER-PROBABILITYi + ∃2 (HOMEi)*(BOOKMAKER-
PROBABILITYi) + ∃3 HOMEi + ∃4 DIFFATTEND
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where PROBWINi is the probability that focus team i will win the game, BOOKMAKER-
PROBABILITYi is the win probability implied by the Super Soccer odds, HOMEi is a dummy
variable taking the value one if team i is playing at home and DIFFATTEND, included to proxy
relative numbers of committed fans, is the mean home game attendance of team i (calculated in
thousands for the previous season from information in The Rothmans Football Yearbook) minus
the mean home game attendance of its opposing team (similarly calculated). Each match is
included once only in the estimation with the identify of the focus team i selected by random
process. The test for efficiency is that the estimated values for ∀ and ∃2, ∃3 and ∃4 should be
each zero and that for ∃1 should be one.
The advantage of following Golec and Tamarkin (1991) in the context of odds-based
soccer betting (as opposed to in their setting of points-spread NFL betting) by randomly selecting
focus teams for inclusion in the sample is that this procedure permits separate evaluation of
possible biases in the favourite-longshot and home-away dimensions. Suppose one always
adopted the home team as focus. Ignoring DIFFATTEND, one would then have as the criterion
for testing efficiency the joint hypothesis that ∀ = 0 and ∃1 = 1. A non-zero estimate on the
intercept team would not necessarily imply home-away bias because if favourite-longshot bias
were present, this would be reflected in both the slope and intercept values.
A problem with Golec-Tamarkin randomisation is, however, that in addition to sampling
matches from a population, it is further sampling a set of bets (those on teams picked out in the
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andom process). Estimating the regression equation once only would therefore be misleading
because of the unreliability of the standard errors.
Accordingly, we estimate each equation twenty times using twenty different
randomisations. The statistical significance of the coefficients can then be examined using a
procedure outlined in Snedecor and Cochran (1967). We count the number of cases in the
twenty trials where a particular coefficient is significant at the 5% level. A normal
approximation can be used to test the null hypothesis that the “true” proportion of cases where
the coefficient is not equal to zero is 5%. If the null is true, the observed proportion of
rejections, R1 is distributed approximately normally with mean r and standard deviation
s = (r (1-r)/n) ½ , where n is the sample size, here 20. The normal deviate, with a correction for
continuity, is z = (|R – r| - (2n) -1 )/s. The critical value for this test statistic is 2.33 at a
conservative 1% significance level. If there are four significant (at 5%) coefficients out of
twenty in our trials, the value of z is 2.57 which exceeds our 1% critical value, so where there are
four or more significant coefficients amongst twenty trials, we conclude that the particular
coefficient is significantly different from zero (or one as appropriate).
6. Results
Table 1A reports our results for the whole sample in each of our four seasons. The values shown
are mean coefficient estimates across twenty trials. The figures in parentheses indicate in how
many trials the particular coefficient estimate was significantly different from the value specified
by the null (zero or one). Where this number is four or more, we can reject the null hypothesis.
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Tables 1B and 1C display disaggregated results by division. We have two subsamples,
one relating to the Premier League (PL) and Division One (D1) of the Football League, the other
to Divisions Two and Three (D2 and D3) of the Football League. These two groupings may
fairly be represented as capturing a divide between high- and low-profile football. Nearly all the
large market football clubs play in the Premier League or Division One. We review now the
principal findings embodied in these Tables.
Favourite-Longshot Bias
There is a hint in the data of the reverse favourite-longshot bias noted for American team
sports by Woodland and Woodland (1994 and 2001) and by previous researchers on soccer
(Dixon and Pope (1996)) to the extent that the mean estimated coefficient on bookmaker-
probability in our all matches samples is always less than one. Moreover, even when this point
estimate is adjusted by the interaction term between ‘home’ and bookmaker probability, this
remains true. On the basis of point estimates, bookmakers appear to offer less unfair odds on
longer-odds teams, home or away.
However, the coefficient is only significantly different from one in a single season, 1998-
9. The result for that particular season is consistent with a finding from Dobson and Goddard
(2001, p.408). Dobson and Goddard concern themselves primarily with applying a forecasting
model (including football data but not odds) to identify favourable betting opportunities. But for
that one season, 1998-9, they analyse in addition the profitability of purely technical trading rules
(i.e. rules based only on patterns in the odds themselves). They report an advantage to “betting
long” on away teams. That this strategy yielded superior returns would have been predicted by
our regression results. Our coefficient on bookmaker-probability is significantly less than one
20

ut adjustment for home teams from the interaction term moves the estimate substantially back
towards one. Hence, a reverse favourite-longshot bias in the odds can be detected fairly
confidently but only in respect of away teams.
We note, however, that there is no statistically significant (reverse) favourite-longshot
bias detectable in the odds in any of the other three seasons analysed here. We suspected
therefore that the Dobson and Goddard trading rule that one should “bet long” on away teams
was one whose success would have been ephemeral. This proved to be the case. In our sample
for that season, 1998-9, exactly 30% of away teams had posted odds longer than 3 to 1. A unit
bet in support of each of these teams would have involved 459 bets and yielded a better than
normal return of +2.37% (ignoring tax and restrictions against singles). Implementing the same
strategy in the following season would have generated 520 bets for a return of –14.9%, which is
worse than the benchmark loss suggested by the size of bookmaker over-round.
Disaggregation into upper- and lower-divisions does little to modify our conclusions. In
the PL/D1 results, significant bias in the favourite-longshot dimension is found only at the
beginning of the period (1997-8) and then only for away teams. Indeed, by the last season
(2000-1), the point estimate on bookmaker-probability is very close to one. In D2/D3, there is
again only one season (1998-9) for which bias was statistically significant. We conclude that
even if there were favourite-longshot bias present at the beginning of the period, it was not
sufficiently stable or durable to be the basis of reliable wagering rules.
21

Home-away Bias
That it is more financially rewarding to bet on home than on away teams has been noted before
(Dixon and Pope (1996)) but the implied bias in odds setting is revealed here to have been
extinguished after our first season. For that season, the coefficient on ‘home’ in the full sample
and in the D2/D3 sample is positive and significant. In PL/D1, home-away bias is also present
once one combines the effects of the coefficients on the home dummy and the home
dummy/bookmaker-probability interaction term. The extent of bias was sufficient that there
would have been very divergent returns from strategies of backing all home or all away teams in
1997-8. A unit bet on all home teams and all away teams (in all divisions) would have yielded
returns of +1.01% and –23.95% respectively (using quoted odds and ignoring tax). The
comparisons for PL/D1 and D2/D3 are +0.22% versus –13.00% and +1.59% versus –32.4%. In
that particular season, as for earlier times examined by Dixon and Pope (1996), home bets were
much better bets than away bets. However, in neither the all divisions case nor in either of the
disaggregations is there any evidence of statistically significant bias after 1997-8. Indeed, for the
PL/D1 case in 2000-1, once one combines the point estimates of coefficients on the two relevant
variables, then a home team with average bookmaker probability of victory has a zero difference
in winning compared with that implied by the odds. Once again, over our data period, early
signs of inefficiency consistent with those noted for earlier times by other authors, disappear
completely by 2000.
Relative Fan Support
A novel feature of this paper is that it tests the proposition that bookmakers will vary odds in
response to the presence in the market of sentiment-driven demand for wagering. Kuypers
(2000) proposed a model of a profit-maximising bookmaker who would exploit the backers of
22

well-supported teams by offering them odds more than averagely unfair. His model is
restrictive, however, in that it assumes the decision to participate in the wagering market on a
particular game is determined independently of relative odds. It is quite possible that if
sentimental demand is elastic with respect to odds, bookmakers will aim to raise turnover by
favouring larger teams in terms of the generosity of odds.
In fact, the evidence here is that Kuypers is correct in expecting bookmakers to take
account of the net direction of fan demand but the direction of the bias is opposite to that which
he proposed. The coefficient on DIFFATTEND is positive and significant in the all-matches
sample in each of the first three of our seasons. In the disaggregated results, the coefficient is
positive and significant in 1997-8 and 1998-9 in PL/D1 and positive and significant in all four
seasons in D2/D3. The magnitude of the coefficient is typically large. In the most recent season
in the lower divisions, a difference in mean home attendance of 3,000 in favour of one team is
estimated to raise the probability that a bet on that team will be successful by in excess of five
percentage points relative to a given bookmaker-probability.
In contrast to the findings on favourite-longshot and home-away bias, some residual
‘inefficiency’ therefore remains in the market (at least for D2/D3) even at the end of our period.
A betting strategy of wagering on teams with greater support than their opponents (in D2/3)
would have yielded superior returns even in 2000-1. In that season, our data revealed 264 bets
where one team had mean home attendance more than 2,000 greater than the opposition; a unit
bet on each of these 264 teams at posted odds and ignoring tax would have yielded a return of
–4.96% (a smaller loss than that accruing to random betting). But if the filter were raised to
23

3,000, one would have bet 131 times to yield a return of +12.37%; and even at a 4,000 filter, one
would have found 71 bets and earned a profit of 9.15%. In the lower divisions, tax-free betting
would therefore have yielded a profit from a strategy of following teams with significantly
greater support providing that one could have made singles bets. Restrictions on singles may of
course make it perfectly rational behaviour for bookmakers to seek to attract large groups of fans
by offering better than fair odds on ‘their’ team so long as they know the gain will in fact be
dissipated by these bettors being forced to make more random wagers in compulsory matching
bets on at least two other games.
Our finding that bookmakers court or have courted large groups of fans by posting
‘attractive’ odds on their teams in some sense contrasts with the findings of the paper by Avery
and Chevalier (1999) on American football betting. They use proxies to identify ‘glamorous’
clubs likely to have large followings (e.g. the conference to which they belong, their success in
winning championships) and establish that the terms of bets on such teams overstate their likely
superiority in a given match. In that context, a plausible wagering strategy would be contrarian,
i.e. bet in the opposite direction to sentimental demand. That such a result holds is consistent
with American bookmakers (Vegas casinos) aiming at a balanced book (equal liabilities to
bettors irrespective of game outcome) on each match, i.e. with the market behaving as if pari-
mutuel. Such behaviour appears unlikely to be expected profit maximising though Avery and
Chevalier discuss reasons (such as regulatory concern that the casino should be disinterested in
game outcome) why balancing the book may nevertheless be the basis of odds setting.
24

Our evidence specifically implies that bookmakers in Britain are not so extremely risk-
averse as to balance the book on each individual game. This is unsurprising. Bookmakers offer
odds on thousands of football and other sports events each year and scope for risk-pooling is
therefore so great that, even if risk-averse, they would have no reason to depart from expected
profit maximising behaviour in setting the odds on any individual fixture. If sentimental demand
is sufficiently elastic with respect to odds, our DIFFATTEND bias will reflect appropriate
behaviour by odds setters.
Betting Simulations
Regression-based tests for market efficiency can suggest bets which offer abnormal returns but
the relevant strategies can be successful only if the biases investors observe from the pattern of
odds and results in one period prove stable across time. Accordingly, in this section, we test
whether a regression model estimated from one season’s data is capable of being used in the
following season to select a set of bets that will earn superior returns. The bets we examine are
those which would have been made whenever the probability of a win as estimated from the
previous season’s model is more than one-fifth greater than that implied by the bookmaker odds.
Table 2 displays the results. The number of bets recommended by the model in any one
season may be interpreted as reflecting the degree of inefficiency embodied in the regression
results for the previous year. The success of those bets will then depend on whether or not any
biases continue to characterise odds setting behaviour in the current year.
Both aggregate and disaggregated results for 1997-98 revealed the presence of several
specific biases in the pattern of odds. The model accordingly generates a large number of bets
25

passing the 1.2 filter ratio for season 1998-9. The biases in 1998-9 proved sufficiently congruent
with those for 1997-8 for the betting strategy to be successful. At the aggregate and for PL/D1
and D2/D3 separately, returns were sharply higher than the –10.5% implied by the level of over-
round. Indeed, in D2 and D3 the level of return calculated at posted odds was sufficiently high
(22.14%) to cover the extra commission (17.7%) charged for the privilege of betting on a single
match via the device of a half-time/full-time double. The strategy would therefore have been
profitable but for tax. In any case, the levels of return in 1998-9 available from assuming the
continuation of biases noted for 1997-8 may fairly be described as ‘abnormal’ and the market
therefore ‘inefficient’.
However, we find in the regression results for particular seasons, a distinct trend towards
efficiency since 1999. In PL/D1, very few bets (22) are recommended in 1999-2000 and the
impressive profit cannot be regarded as significant because it depended on a very small number
of long-odds wins. In D2/D3, the pattern of odds the previous season generated 197
recommended bets in 1999-2000; 162 of these were on away teams and only 35 on home teams.
Here, it was still possible to make a bare positive profit (without accounting for tax and
restrictions on singles bets). Some evidence of an inefficient market remained therefore in the
lower divisions. The rather poor result from applying the ‘all divisions’ model probably reflects
that the previous season, 1998-9, had seen a gap opening between the upper and lower tiers in
terms of the degree of efficiency exhibited in the odds: this is evident from the regression results
(Tables 1B and 1C) and therefore the application of an aggregated model was by 1999-2000
inappropriate.
26

The most telling illustration of the extent to which the market was moving towards
efficiency is that application of 1999-2000 regression results to betting in 2000-1 yielded not one
recommended bet whether one used an aggregate model or two disaggregated models. By 1999-
2000, no specific biases (other than DIFFATTEND) appeared to be present in the odds and so
‘value’ bets were hard to obtain in 2000-1 if relying on a regression model for guidance. As
noted above however, gains still accrued to those following a simpler strategy based on only one
indicator, DIFFATTEND. Overall, the betting simulations point to inefficiency in the market
being close to eliminated over our four year study period.
7. Interpretation and Conclusions
The literature on efficiency in wagering markets has overwhelmingly been motivated from the
perspective of finance and financial economics. That has led others to expect patterns of odds to
display efficiency in the sense that all bets should be equally good (or, more strictly, bad) bets.
The perspective ignores that, with sufficient transactions costs to deter professional arbitrage, the
wagering market in sports may be more usefully represented as a consumer good market where
potential consumers have preferences on what bets they make that go beyond expected financial
return. In that framework, it is easier to understand biases in the odds as reflecting price
discrimination across groups of potential bettors. Price is here identified not (as is traditional)
with the bookmaker over-round for the event but rather as the expected bettor loss on each
possible unit bet (home, draw, away).The profit maximising price may differ in respect of each
result because of customer preferences and this will manifest itself in biases in the odds.
27

Bookmakers have strong incentives to be (or to hire) sophisticated odds setters. This is
particularly so in a market such as that on British soccer where they have eschewed the right to
vary the odds during the betting period. In fact, they do display a high level of expertise.
Goddard and Asimakopoulos (2001) acknowledged that there is very little difference in
forecasting performance between bookmaker odds and their own very rich and detailed statistical
model drawing on past team performance and many years of soccer information data. If odds
setters are so skilled as to be able to match very advanced statistical forecasting models, it is
reasonable to assume that biases in the odds in the dimensions studied in this paper are, if
present, there by design rather than accident and that they should be viewed as a means to
maximizing profit. Specific biases should be viewed not as aberrations but as examples of price
discriminating strategy. Any reverse favourite-longshot bias could be interpreted merely as odds
setters taking due account of bettor risk aversion. 11 The similarly familiar home-away bias could
be interpreted as a response to perceived elasticity of demand amongst bettors who attend a game
and consider betting to show support for their local team (they often indeed place the bet in the
stadium itself). And our DIFFATTEND bias is readily interpretable along the same lines of
demand being driven by the utility of a bet including non-financial elements (the fun is greater if
betting on one’s ‘own’ team) and odds setting recognising that.
Biasing the odds as a strategy may, however, be constrained by the potential presence in
the market of arbitrageurs. In the absence of transactions costs, risk-neutral professional betters
would be able to punish bookmakers whose odds were biased and render efficiency an essential
feature of a sustainable market.
28

Here and in other papers, biases have been identified which (at least until 1999) created
some favourable betting opportunities. But the gains here and in other earlier analyses have
mostly been modest in the sense of showing a positive sign only if one assumed singles betting
and no tax. Restrictions on singles and the presence of a tax have, however, been institutional
features of the British market and the implied extra transactions costs have facilitated biased
odds as possibly sustainable and equilibrium features of soccer betting.
For illustration, we have argued that where a particular team attracts a large following,
those who support it in the betting market may be offered a better price (less unfair odds) than
usual. We found one betting strategy based on this idea was capable of yielding in excess of a
9% profit, a figure not untypical of the range of wagering gains cited by those who have sought
to identify strategies for profitable trading. On the face of it, it appears unlikely that a
bookmaker would be so eager to attract bets from fans of heavily supported teams that he would
award them an expected profit of 9%. But, given the bar on singles, he would not in fact be
doing so. The fan bettor would have two choices. The first would be to bet on the one game,
employing the device of a series of half-time/full-time doubles; but the shading of the odds on
this type of complex bet would be sufficient to convert the expected return from + 9 to – 9%, a
respectable profit for the bookmaker. Alternatively, the bettor could combine the bet on the
match in which he had a special interest with bets on two or more other games. The fan bettor is
likely to be less well informed regarding matches not involving his own team, so the bookmaker
might expect to earn a ‘normal’ commission on the other legs of the combination bet to again
realize an expected profit for himself (and loss for the bettor). Vis a vis this group of customers,
29

the favourable odds offered on their own team’s results is unlikely to expose the bookmaker to
loss.
But what of the risk-neutral professional bettor who could destroy the ability of the
bookmaker to offer ‘biased’ odds? This potential arbitrageur could acquire sufficient expertise
to identify three ‘favourable’ bets and combine them in a treble : the variance of returns would
be high but the expected gain still positive. That is true but the level of tax expected in the past
is equivalent to extra bookmaker commission and, in the case of the 9% prospective gain
hypothesised here, the tax would be just sufficient to deter the arbitrageur from entering the
market.
It has, then, been customary for bookmakers to price discriminate in terms of different
bets offering different degrees of value; but the restrictions on singles betting made any
prospective gains unrealisable by the leisure bettors while tax deterred the professional
arbitrageurs from entering the market. “Inefficient” odds were, in these circumstances,
sustainable and indeed to be expected. The degree of price discrimination was of course
constrained by the extent of the cushion offered by the tax on gaming (and this constraint may or
may not have been binding).
The world has, however, changed. The rapid growth of internet betting made it feasible
and desirable for British bookmakers to move offshore by 1999 to cater to a wider, international
market where the interest in betting on English soccer (particularly the Premier League) is very
high but where competition from bookmakers in other countries was now intense. British
30

ookmakers would have been poorly positioned to exploit the growing international market for
their product if tax had had to be levied, as it would have been if they had remained based at
home. Since British households could also use offshore branches of familiar bookmakers the
abolition of betting duty became inevitable and this occurred in 2001.
The reduction in transactions costs inherent in the removal of tax (essentially optional
since the establishment of offshore operations in 1999) severely limits the ability of bookmakers
henceforth to offer biased odds. The importance of transactions costs is, of course, central to
whether a market will display efficiency. If there were no transactions costs in the form of
bookmaker over-round or tax, then any bias in the odds would be non-sustainable because it
would create an opportunity for positive gain which arbitrageurs would be expected to eliminate.
The removal of tax (and greater flexibility in taking singles bets at least on Premier League
games) has greatly reduced the extent to which transactions costs impede the arbitrage process in
soccer betting. It is unsurprising therefore that, while our study confirms ‘traditional’ biases in
the betting market up to 1999, there is a rapid move to ‘efficiency’ by 2001.
It is perhaps anomalous that the ‘DIFFATTEND’ bias was still present in D2/D3 at the
end of our period and evidently still capable of generating opportunities for positive returns.
Thus far, betting on lower divisions has still been primarily a domestic market. Information is
much less readily available on lower-tiers of English soccer, so transactions costs are effectively
still high for potential arbitrageurs. Bookmakers have, evidently, still felt able to ‘bias’ the odds
for the presence in (or dominance of ) the market by fan-bettors. Equally, bookmakers still
rigorously protect themselves by restrictions against singles betting for these less high-profile
31

games (where inside information and match fixing are larger risks). But we would not
necessarily expect this lower-tier market to escape the attention of arbitrage indefinitely if tax-
free gains are prospectively to be made. Globalisation, by forcing the dismantling of betting tax,
appears to have triggered a strong move to market efficiency in this particular wagering market.
In other jurisdictions, offshore betting is likewise a threat to any ‘inefficiency’ protected up to
now by tax or indeed by legal or regulatory restrictions. With a globalised gaming environment,
we might in future expect fewer articles which can point to biases and ‘favorable trading
strategies’ in wagering markets.
32

FOOTNOTES
1 A large and convenient collection of such articles is provided by Hausch et al (1994).
2 In the season studied in this paper, 1997/8, the English FA Premiership comprised 20
clubs while Divisions 1 to 3 of the Football League comprised 24 teams each. Each team
meets a division rival twice, once home and once away. Movement between divisions is
achieved by promotion and relegation.
3 Although the bulk of fixtures are played on Saturday, the number of Saturday games will
occasionally be reduced because either the date is earmarked for knockout cup
competition or because of international fixtures. A few games each week are moved to
different days in order to be televised and betting is still possible in these cases.
4
Pools entries were (and are) made by mail or through a door-to-door collector.
5 An exception is a televised match. Perhaps the exemption is linked to the high-profile
nature of the contest chosen for television coverage. Inside information or match fixing
are unlikely to present a serious problem if the teams are well-known and the betting
volume high.
6
7
8
This involves staking £0.222 on the first bet, £0.182 on the second and £0.043 on the
third.
The over-round on bets is typically 11.7, i.e. one would spend £111.70 to bet on all three
outcomes at a level to earn £100 in pay back from the bookmaker. With a fully balanced
book , the bookmaker would return £11.70 of each £111.70 staked to earn a commission
of 10.5%.
A similar model is used by Lee (1997) in examining the final ranking of teams in the
1995/6 English FA Premiership season.
9 Home advantage in soccer is very important (Clarke and Norman (1995) and Courneya
and Cannon (1992)) to such an extent that, in the UK professional game, approximately
twice as many wins are recorded by home teams compared with away teams.
10 Actual bookmaker return would vary from 10.5% if the book was not fully balanced, i.e.
if liabilities to bettors differed accordingly to which outcome occurred.
11 Positive favourite-longshot bias, noted in home racing markets, is sometimes
(tautologically) attributed to risk-loving bettor utility functions. This is not necessarily in
contradiction with the analysis here. Team sports are organised so that games seldom
have a genuine outsider in the horse racing sense. Unit bets on team sports are therefore
very unlikely, relative to the horse racing case, to generate opportunities to lift the bettor
to a different range of his utility of wealth function.
33

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37

Table 1A
Regression results – all matches
Linear probability model estimated by weighted least squares with 20 trials.
1997-8 1998-9 1999-2000 2000-1
Constant 0.038 0.104 0.020 -0.024
(0) (6) (0) (0)
Bookmaker-probability 0.684 0.585 0.797 0.899
[2] [11] [2] [1]
(Home)(Bookmaker-probability) -0.047 0.162 -0.017 0.025
(0) (2) (0) (0)
Home 0.169 0.002 0.038 -0.003
(5) (0) (0) (0)
Diffattend 0.0055 0.0054 0.0027 -0.0007
(20) (20) (7) (0)
Sample size 1393 1491 1585 1389
Table shows mean coefficient estimates across twenty trials
[ ] number of cases where coefficient estimate is significantly different from one
( ) number of cases where coefficient estimate is significantly different from zero
38

Table 1B
Regression results – Premier League and Division One
Linear probability model estimated by weighted least squares with 20 trials.
1997-8 1998-9 1999-2000 2000-1
Constant -0.111 0.065 0.055 -0.060
(2) (0) (0) (0)
Bookmaker-probability 0.520 0.645 0.789 1.008
[5] [1] [0] [0]
(Home)(Bookmaker-probability) 0.381 0.388 -0.051 0.122
(4) (2) (1) (1)
Home -0.020 -0.078 0.099 -0.047
(1) (0) (1) (1)
Diffattend 0.0043 0.0045 0.0030 -0.0023
(9) (13) (3) (0)
Sample size 613 707 720 653
Table shows mean coefficient estimate across twenty trials
[ ] number of cases where coefficient estimate is significantly different from one
( ) number of cases where coefficient estimate is significantly different from zero
39

Table 1C
Regression results – Division Two and Three
Linear probability model estimated by weighted least squares with 20 trials.
1997-8 1998-9 1999-2000 2000-1
Constant -0.024 0.113 0.039 0.017
(0) (4) (0) (0)
Bookmaker-probability 0.790 0.614 0.814 0.751
[1] [4] [0] [1]
(Home)(Bookmaker-probability) -0.414 -0.071 -0.004 -0.014
(1) (1) (0) (0)
Home 0.328 0.082 0.001 0.076
(13) (2) (0) (1)
Diffattend 0.0112 0.0056 0.0102 0.0176
(7) (6) (7) (13)
Sample size 780 784 865 736
Table shows mean coefficient estimate across twenty trials
[ ] number of cases where co-efficient estimate is significantly different from one
( ) number of cases where co-efficient estimate is significantly different from zero
40

Table 2
Results of wagering on all available ‘to win’ bets where
Number of bets, total return
Probability of success implied by model
Bookmaker probability
41
>1.2
Model Model
Used: Applied to: All Matches PL/D1 D2/D3
Season Season
1997-8 1998-9 294, + 12.69% 113, - 4.51% 192, + 22.14%
1998-9 1999-2000 399, - 20.9% 22, + 40.91% 197, + 1.02%
1999-2000 2000-01 0 0 0
Calculations assume posted odds (no restriction against single bets) and ignore tax.

1 A large and convenient collection of such articles is provided by Hausch et al (1994).
2 In the season studied in this paper, 1997/8, the English FA Premiership comprised 20
clubs while Divisions 1 to 3 of the Football League comprised 24 teams each. Each team
meets a division rival twice, once home and once away. Movement between divisions is
achieved by promotion and relegation.
3 Although the bulk of fixtures are played on Saturday, the number of Saturday games will
occasionally be reduced because either the date is earmarked for knockout cup
competition or because of international fixtures. A few games each week are moved to
different days in order to be televised and betting is still possible in these cases.
4 Pools entries were (and are) made by mail or through a door-to-door collector.
5 An exception is a televised match. Perhaps the exemption is linked to the high-profile
nature of the contest chosen for television coverage. Inside information or match fixing
are unlikely to present a serious problem if the teams are well-known and the betting
volume high.
6
This involves staking £0.222 on the first bet, £0.182 on the second and £0.043 on the
third.
7 The over-round on bets is typically 11.7, i.e. one would spend £111.70 to bet on all three
outcomes at a level to earn £100 in pay back from the bookmaker. With a fully balanced
book , the bookmaker would return £11.70 of each £111.70 staked to earn a commission
of 10.5%.
8 A similar model is used by Lee (1997) in examining the final ranking of teams in the
1995/6 English FA Premiership season.
9 Home advantage in soccer is very important (Clarke and Norman (1995) and Courneya
and Cannon (1992)) to such an extent that, in the UK professional game, approximately
twice as many wins are recorded by home teams compared with away teams.
10 Actual bookmaker return would vary from 10.5% if the book was not fully balanced, i.e.
if liabilities to bettors differed accordingly to which outcome occurred.
11 Positive favourite-longshot bias, noted in home racing markets, is sometimes
(tautologically) attributed to risk-loving bettor utility functions. This is not necessarily in
contradiction with the analysis here. Team sports are organised so that games seldom
have a genuine outsider in the horse racing sense. Unit bets on team sports are therefore
very unlikely, relative to the horse racing case, to generate opportunities to lift the bettor
to a different range of his utility of wealth function.
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