ArticlePDF Available
American Journal of Sports Science
2017; 5(6): 45-49
http://www.sciencepublishinggroup.com/j/ajss
doi: 10.11648/j.ajss.20170506.12
ISSN: 2330-8559 (Print); ISSN: 2330-8540 (Online)
Adjusting Bookmaker’s Odds to Allow for Overround
Stephen Clarke1, *, Stephanie Kovalchik2, 3, Martin Ingram4
1Department of Mathematics, Swinburne University of Technology, Melbourne, Australia
2Tennis Australia, Melbourne Park, Melbourne, Australia
3Institute of Sport Exercise and Active Living, Victoria University, Footscray, Australia
4Division of Machine Learning, Silverpond, Melbourne, Australia
Email address:
sandkclarke@hotmail.com (S. Clarke)
*Corresponding author
To cite this article:
Stephen Clarke, Stephanie Kovalchik, Martin Ingram. Adjusting Bookmaker’s Odds to Allow for Overround. American Journal of Sports
Science. Vol. 5, No. 6, 2017, pp. 45-49. doi: 10.11648/j.ajss.20170506.12
Received: September 9, 2017; Accepted: October 12, 2017; Published: December 25, 2017
Abstract: Several methods have been proposed to adjust bookmakers’ implied probabilities, including an additive model, a
normalization model, and an iterative method proposed by Shin. These approaches have one or more defects: the additive
model can give negative adjusted probabilities, normalization does not account for favorite long-shot bias, and both the
normalization and Shin approaches can produce bookmaker probabilities greater than 1 when applied in reverse. Moreover, it
is shown that the Shin and additive methods are equivalent for races with two competitors. Vovk and Zhadanov (2009) and
Clarke (2016) suggested a power method, where the implied probabilities are raised to a fixed power, which never produces
bookmaker or fair probabilities outside the 0-1 range and allows for the favorite long-shot bias. This paper describes and
applies the methods to three large bookmaker datasets, each in a different sport, and shows that the power method universally
outperforms the multiplicative method and outperforms or is comparable to the Shin method.
Keywords: Adjusting Forecasts, Betting, Sports Forecasting, Probability Forecasting
1. Introduction
Bookmaker odds have a useful role for sports performance
research and commercial applications. Bookmaker odds have
been repeatedly shown to provide improved expectations
about outcomes in sport [1-2], which can be used by
practitioners to set more realistic expectations before and
after competitive events. Efficiency in bookmaker odds is
fundamental to the success of sports betting firms, an
industry that continues to grow and have an influence on all
professional sports [3].
Sports researchers and professionals can get the most use
out of bookmaker odds if they have an accurate method to
convert odds into event probabilities [4]. The probabilities πi
implied by bookmakers odds, or prices, invariably sum to
more than 1. The total π of the implied probabilities is known
as the booksum, and the excess π-1 the overround. The
overround determines the expected return to punters, which
is 1/π in the long run. Due to the overround, the implied
probabilities from bookmaker odds require an adjustment to
obtain the actual probability expectations of bookmakers.
While the need to remove the overround to estimate fair or
true probabilities pi is the most common situation in sport
research, Clarke [5] gives an example of the reverse process.
This previous study considered the commercial application of
a major betting agency, in which a mathematical model
produced fair probabilities for the number of runs in the next
over of cricket. With only a small window while players
changed ends to set odds and take bets, a mathematical
formula was needed to convert the true probabilities to
bookmaker odds with the required overround. In a second
application the same process was used to set odds for the
point score in the next game of tennis. With the expansion of
sports betting, many bookmakers or exchanges now use
mathematical models plus an adjustment for overround to
determine initial prices. As the event nears, further
adjustments are then made due to the weight of money on
placed bets.
The present paper discusses and compares four methods
for removing (or incorporating) overround. For simplicity
American Journal of Sports Science 2017; 5(6): 45-49 46
racing terminology is used, but the analysis applies to any
experiment (race, match, contest, etc.) with n outcomes on
which betting takes place. Section 2 describes four
adjustment methods of distributing the overround: additive,
normalization, Shin and the power method. Section 3
compares the performance of each method on various data
sets, and is followed by the conclusion.
2. Adjustment Methods
Four methods of adjustment for overround have been used
in the literature. In the following subsections each method is
described and its distinguishing features summarized.
2.1. The Additive Method
Better described as the additive method, additive uses an
additive model where the overround is split evenly between
the n outcomes. Thus, the true probability for the ith
outcome, pi, is
 and  (1)
Although used by Viney et al. and others [4], the additive
method is rarely used in the literature, as the changes
between the implied and adjusted probabilities for outsiders
can be quite dramatic. Not infrequently, the additive method
can produce negative probabilities for rank outsiders. In fact,
this will occur whenever the ratio of the overround and
implied probability is greater than the number of competitors,
. The reverse process can also produce
bookmaker probabilities greater than 1 for hot favorites.
2.2. The Multiplicative Method
The multiplicative or normalization method allocates the
overround proportionally. So that,
 or . (2)
Because of its simplicity, this is the most commonly used
method. While seemingly appropriate for totalisator data, an
automated betting system that allocates the same proportion
of the pool for all horses, it fails to account for the favorite
longshot bias, where it is well known that long-shots tend to
be overbet while favorites are underbet. Thus a greater
proportion of overround needs to be removed/added to
longshots than favorites. It also suffers from sometimes
producing probabilities greater than 1 for favorites in the
conversion from fair to bookmaker’s probabilities.
2.3. The Shin Method
Shin [6-7] proposed a correction method based on an
assumed fraction z of knowledgeable punters. As given in
[8], this results in

 (4)
or


 (5)
where

!" 
 (6)
To create bookmakers odds from fair odds requires using
(4) and (6) and iterating on z to produce the required
overround. To adjust bookmaker’s odds to produce fair odds
requires using iteration on (5) and (6).
This method helps to protect against the favorite longshot
bias, and has been shown to produce better predictive true
probabilities than normalization [9-10]. However, it is shown
in the Appendix that in the case of two outcomes the Shin
method is equivalent to the simple additive method, and as
such can adjust outsiders too much. While (5) implies it can
never produce negative true probabilities, (4) can produce
bookmaker’s probabilities greater than 1 for hot favorites.
2.4. The Power Method
A natural extension of the additive method used in the
additive approach (where probabilities are adjusted by a
constant addition), and the multiplicative method used in
normalization (where probabilities are adjusted by a constant
multiplier), is to raise the probabilities to a constant power.
Clarke [11] gives details of this method, used in a
commercial application described in [5]. It was also
described in Vovk and Zhdanov [12] and attributed to Victor
Khutsishvili. The power approach proposed by these authors
can be written as, # or "$ (7)
The logic behind this method stems from the idea that
bookmaker probabilities derived from fair probabilities for
joint events should satisfy the usual multiplicative law for
independent events. In practical terms, this condition implies
that the return to a punter from investing his winnings on
subsequent events is the same as a single investment on the
joint event. When the n competitors are all equally likely, the
value for k is calculated as, %&'(
&'(
). However, in most
cases iteration on k is necessary to ensure , or the
required booksum.
A clear advantage of the power method is that it can never
produce probabilities outside the [0, 1] range. Similarly, it
can be applied directly to prices, as the fair and adjusted
prices follow the same power law with the same k as the true
and implied probabilities. The power method also ensures a
greater change to outsider probabilities than favorites.
However, when compared to Shin it adjusts favorites and
longshots more but middle-of-the-range priced horses less.
47 Stephen Clarke et al.: Adjusting Bookmaker’s Odds to Allow for Overround
3. Methods
The operational characteristics of each method are shown
with several illustrative examples. Analyses are then
presented on the actual predictive performance of each
method on large-scale sports datasets for 3 different sports.
Historical bookmaker odds were gathered for 3 different
sporting events: tennis, greyhound racing, and horse racing.
These datasets were chosen to represent a range of
competitor numbers and overround characteristics. The ATP
dataset included nearly 15,000 men’s singles matches from
2000 to the present. Bookmaker prices for this dataset were
the average betting odds reported by Oddsportal. The
greyhound data comprised tote data (from over 27,000 races)
at 2,206 meetings in New Zealand between 1/8/2011 and
18/8/2016. The final dataset was gallop data that consisted of
closing prices from the Victorian Tote on Australian
thoroughbred races in the first half of 2008. Together, these
datasets range from 2 to 12 competitor events and have
average overrounds ranging between 6% and 27% (Table 1).
Table 1. Description of Datasets used in Performance Evaluation.
Dataset Events
Average Number of
Competitors
Average Overround
(95% Interval)
ATP 14,925
2 6.1 (4.7 – 7.0)
Gallop 4,663 12 27.2 (9.0 – 78.2)
Greyhound
20,206
8 19.5 (11.1 – 22.2)
Three measures of performance were evaluated. The first
was the distribution in the adjusted win probability assigned
to the winning competitor. The higher the mean and the
lower the variance in this probability, the better the predictive
performance of the adjustment method. We also report the
logloss, which is a loss measure that is closely connected to
the Kelly betting criterion [13]. This measure is unique in
that it penalizes inaccurate predictions that are made with
higher confidence. For the non-binary events, a binary
classifier was created that assigned one category to the
winner and all other competitors to the losing category. Using
the same binary classifier, we also evaluated the root-mean
squared error, or Brier score, for each method. As with the
logloss, a lower square-error indicates a superior prediction
method.
4. Results
4.1. Operational Characteristics
Tables 2 and 3 show an example of transforming
probabilities in both directions using the four adjustment
methods. These tables clearly show the shortcomings of the
additive method, and the varying degree to which the Shin
and Power method adjust favorites and longshots. Later we
compare the efficacy of the predictive power of the
probabilities produced by these two methods.
Table 2. Comparison of 4 Methods of Adjusting 1.25 Booksum to Produce Fair Probabilities.
Prices and their Implied probs Calculated True Probabilities Calculated Fair Prices
Add. Mult. Shin Power Add. Mult. Shin Power
$1.15 0.870 0.828 0.696 0.769 0.825 $1.21 $1.44 $1.30 $1.21
$5.00 0.200 0.158 0.160 0.148 0.110 $6.31 $6.25 $6.78 $9.12
$10.00 0.100 0.058 0.080 0.059 0.042 $17.12 $12.50 $16.94 $23.63
$20.00 0.050 0.008 0.040 0.020 0.016 $118.97 $24.99 $49.84 $61.23
$50.00 0.020 -0.022 0.016 0.004 0.005 -$46.31 $62.48 $264.78 $215.54
$100.00 0.010 -0.032 0.008 0.001 0.002 -$31.65 $124.96 $1,026.96 $558.47
Total 1.250 1.000 1.000 1.000 1.000
Again Table 3 shows the possibility of both the multiplicative and Shin method producing probabilities greater than 1 for
short priced favorites. Since probabilities in [0, 1] remain in [0, 1] when raised to any positive power, the power method
always produces realistic transformations.
Table 3. Comparison of 4 Methods of Adjusting true Probabilities to Produce a 1.25 Booksum.
True Probs Fair Prices Adjusted Probabilities Boookmaker Prices
Add. Mult. Shin Power Add. Mult. Shin Power
0.01 $100.00 0.052 0.013 0.033 0.040 $19.35 $80.00 $30.74 $24.93
0.015 $66.67 0.057 0.019 0.041 0.053 $17.65 $53.33 $24.44 $18.78
0.02 $50.00 0.062 0.025 0.048 0.065 $16.22 $40.00 $20.64 $15.36
0.025 $40.00 0.067 0.031 0.055 0.076 $15.00 $32.00 $18.02 $13.15
0.03 $33.33 0.072 0.038 0.062 0.086 $13.95 $26.67 $16.08 $11.57
0.9 $1.11 0.942 1.125 1.010 0.929 $1.06 $0.89 $0.99 $1.08
1 1.250 1.250 1.250 1.250
The findings indicate that the power method has some
advantage over the other three methods in that it never
produces improper probabilities. The Appendix shows that the
additive and Shin method are equivalent for two-competitor
races. The following subsection explores the predictive power
of the probabilities produced by the various methods.
4.2. Predictive Performance
The results for the ATP data, with only two outcomes,
confirmed in the Appendix, in that the additive and Shin
methods always had the same result. In all three measures the
Clarke power method achieved the best or equal best result,
American Journal of Sports Science 2017; 5(6): 45-49 48
with the multiplicative method the worst (Table 4). For the
gallop data, the additive model was superior, followed by
Shin. The multiplicative model was the worst performing on
all measures. Results for the greyhound data were more
variable. The multiplicative model was again the worst
performer on two measures, but second on the log loss
measure, with Shin being the second worst on all measures.
The additive method proved the best on the probability
assigned to winner and RMSE, but only third on log loss.
The power method was either first or second on each
measure.
Table 4. Performance Comparison of Alternative Methods of Removing Overround.
Performance Measure ATP Gallop Greyhound
Prob. Assigned to Winner, Mean (95% Interval)
Power 62.8 (18.1 - 97.3) 19.2 (1.5 – 47.4) 24.8 (3.3 – 67.5)
Additive 62.4 (19.2 – 95.6) 20.4 (0.8 – 48.7) 25.6 (2.3 – 68.8)
Multiplicative 61.7 (21.1 – 93.4) 18.2 (2.4 – 44.6) 23.5 (4.0 – 59.4)
Shin 62.4 (19.2 – 95.6) 19.2 (1.6 – 46.7) 24.6 (3.1 – 64.4)
LogLoss
Power 0.548 1.971 1.686
Additive 0.548 1.968 1.696
Multiplicative 0.550 1.994 1.692
Shin 0.548 1.968 1.696
RMSE
Power 74.39 79.14 155.28
Additive 74.41 78.12 154.14
Multiplicative 74.50 79.75 156.90
Shin 74.41 79.03 155.42
Clearly the additive method has performed surprisingly
well, but as pointed out earlier it does have some problems in
producing probabilities outside the range [0, 1]. The
multiplicative generally does very poorly. The power method
outperforms the multiplicative method on all data sets on
each measure. Similarly it universally outperforms or equals
Shin, with the exception of the RMSE measure on the
Greyhound data.
5. Conclusions
This is the first paper to give a complete description of the
most popular methods for adjustment of bookmaker odds and
provide the most comprehensive comparison of their
performance with actual sporting data. While simple to
apply, the additive method can produce negative
probabilities, and the multiplicative or normalization method
performed badly on all predictive performance measures. On
the data sets analysed, the power method generally
performed better than the Shin approach. It also performed
better than all other methods on the ATP dataset, which is the
only dataset obtained from bookmakers.
Given the comparability in performance between the Shin
and power method, ease-of-implementation will be a critical
consideration for practitioners and industry. Both the Shin
and the power method require iteration. As with Shin, the
power method has an underlying logical basis for its
derivation. However, as a natural extension of the additive
and multiplicative transformation the power method is
conceptually simpler and generally easier to implement than
Shin.
Past commercial applications also indicate an industry
preference for the power method. Clarke [5] has used the
power method successfully in a commercial application to
incorporate overround into probabilities estimated from a
mathematical model. To the authors’ knowledge, at least two
Australian companies currently use the power method to
transform bookmakers’ prices as a means to obtain an
estimate of market knowledge about specific competitive
events (personal communication).
There are multiple adjustment methods available to sports
researchers and professionals for translating bookmaker odds
into true event expectations. Considerations of performance,
ease-of-implementation, and commercial record make the
power adjustment method a strong competitor among
approaches for correcting for overround.
Acknowledgements
We thank Anthony Bedford of Xtrade for supplying the
gallop and greyhound data.
Appendix: Equivalence of Shin and the
Additive Method for 2 Outcomes
Many events on which betting takes place have only two
outcomes, usually win or loss. Betting on the line (whether a
score will exceed or not exceed a given value), or laying
(betting on an event not occurring) can reduce events with
multiple outcomes to one with only two outcomes. Strumbelj
[8] notes that in this special case, equation (5) above has a
tractable solution. While this may be of interest in calculating
the proportion of knowledgeable punters, it is not necessary
to calculate z to find pi, as we show here that for n = 2 the
Shin probabilities are given by the additive method.
Specifically,

*and 
49 Stephen Clarke et al.: Adjusting Bookmaker’s Odds to Allow for Overround
Proof: For n = 2, we have π1 and π2 are bookmaker prices
that sum to π and pi are Shin adjusted prices that sum to 1.
To simplify let
+,-
(A1)
So from equation (6)
+.
(A2)
So +.
From (A2), -=/"/"
-//

So,
++.++
,
0,"
,
...}/,
0,"
),}/,
So, =0)(}/
Since and .
Then,
Solving using  gives .
1*
.
1
or alternatively that .
1*
.
1
as required
Alternatively, there is similar proof using (4)
Again for simplicity let 2
Then 222222
= 2- 2
= z(-)+(1-z) (-)
= (- )(z +1-z) since + =1
=(-)=(.-)=(-.)
But
Solving gives =+ .
1, =-.
1 as
required.
Note it is easily seen that this can result in π‘s greater than
1.
References
[1] C. Leitner, A. Zeileis, and K. Hornik, "Forecasting sports
tournaments by ratings of (prob) abilities: A comparison for
the EURO 2008." International Journal of Forecasting 26, no.
3, 2010, pp. 471-481.
[2] S. Kovalchik, "Searching for the GOAT of tennis win
prediction." Journal of Quantitative Analysis in Sports 12, no.
3, 2016, pp. 127-138.
[3] L. Robinson, "The business of sport" in Sport & Society: A
Student Introduction, Houlihan, B. Eds. London: SAGE, 2003,
pp. 165-183.
[4] M. Viney A. Bedford, and E. Kondo, “Incorporating over-
round into in-play Markov Chain models in tennis”. 15th
International Conference on Gambling & Risk-Taking, Las
Vegas, USA, 2013.
[5] S. R. Clarke, “Successful applications of statistical modeling
to betting markets”. In IMA Sport 2007: First International
conference on Mathematics in Sport. D. Percy, P Scarf & C
Robinson, Eds., The Institute of Mathematics and its
Applications: Salford, United Kingdom, 2007, pp. 35-43.
[6] H. S. Shin, “Prices of State Contingent Claims with Insider
traders, and the Favorite-Longshot Bias”. The Economic
Journal, 1992, 102, pp. 426-435.
[7] H. S. Shin, “Measuring the Incidence of Insider Trading in a
Market for State-Contingent Claims”. The Economic Journal,
1993, 103(420), pp. 1141-1153.
[8] E. J. Strumbelj, "On Determining Probability Forecasts from
Betting Odds." International Journal of Forecasting, 2014,
30(4), pp. 934-943.
[9] M. Cain, D. Law, and D. Peel, “The favorite-longshot bias,
bookmaker margins and insider trading in a variety of betting
markets”. Bulletin of Economic Research, 2003, 55, pp. 263–
273.
[10] M. A. Smith, D. Paton, and L. V. Williams, “Do bookmakers
possess superior skills to bettors in predicting outcomes?”
Journal of Economic Behavior & Organization, 2009, 71, 539
– 549.
[11] S. R. Clarke, “Adjusting true odds to allow for vigorish”. In
Proceedings of the 13th Australasian Conference on
Mathematics and Computers in Sport. R. Stefani and A.
Shembri, Eds., 2016: Melbourne, pp. 111-115.
[12] V. Vovk, and F. Zhdanov, “Prediction with Expert Advice for
the Brier Game”. Journal of Machine Learning Research,
2009, 10, pp. 2445-2471.
[13] L. H. Yuan, A. Liu, A., Yeh, A. et al. “A mixture-of-modelers
approach to forecasting NCAA tournament outcomes”.
Journal of Quantitative Analysis in Sports, 2015, 11(1), pp.
13-27.
... In his model, which is developed in the context of horse racing, he assumes that insiders know the identity of the winning horse before the race starts. His conversion of odds into implied winning probabilities is more complex than basic normalization, but it seems to provide better implied probabilities than the method of basic normalization (see for instance Clarke et al. 2017;Koning and Boot 2020). Štrumbelj (2014) is one of the very few papers that applies Shin's model to soccer matches, and he shows that implied probabilities derived from Shin's model are a better predictor of outcomes than implied probabilities derived from basic normalization. ...
... Most early studies that analyze the efficiency of the fixed odds betting sports market focused on horse racing, although more recent studies show that the favourite-longshot bias found in horse racing occurs within several other gambling sports markets, including tennis and soccer (Abinzano et al. 2016;Clarke et al. 2017;Koning and Boot 2020). Deschamps and Gergaud (2007) explore the favourite-longshot bias in English soccer data and show that this bias depends on the odds status. ...
... To obtain an effective betting strategy, the winning probabilities should account for the favourite-longshot bias. Clarke et al. (2017) compare the four most popular methods to transform betting odds for tennis, horse racing, and greyhound racing and conclude that the Shin (1993) model is a more accurate approach than basic normalization. Additionally, Štrumbelj (2014) also suggests that probabilities estimated using the Shin (1993) model are, on average, better than probabilities based on basic normalization. ...
Article
Full-text available
Implied winning probabilities are usually derived from betting odds by the normalization: inverse odds are divided by the booksum (sum of the inverse odds) to ensure that the implied probabilities add up to 1. Another, less frequently used method, is Shin’s model, which endogenously accounts for a possible favourite-longshot bias. In this paper, we compare these two methods in two betting markets on soccer games. The method we use for the comparison is new and has two advantages. Unlike the binning method that is used predominantly, it is based on match-level data. The method allows for residual favourite-longshot bias, and also allows for incorporation of match specific variables that may determine the relation between the actual probability of the outcome and the implied winning probabilities. The method can be applied to any probabilistic classification problem. In our application, we find that Shin’s model yields unbiased estimates for the actual probability of outcome in the English Premier League. In the Spanish La Liga, implied probabilities derived from the betting odds using either the method of normalization or Shin’s model suffer from favourite bias: favourites tend to win their matches more frequently than the implied probabilities suggest.
... Deschamps & Gergaud (2007) find a negative longshot-favourite bias on draw odds in the home-away-draw (HAD) market. Clarke et al. (2017) study the forecasting ability after adjusting bookmaker's odds to allow for overround. Forecasts from statistical model often contain the information that the betting market not taken into account (Pope & Peel, 1989;Goddard & Asimakopoulos, 2004;Dixon & Pope, 2004). ...
... Betting odds issued by bookmakers reflect implicit probabilities about sporting outcomes (Stekler et al., 2010;Leitner et al., 2010;Kovalchik, 2016;Clarke et al., 2017). Some empirical evidences show that the forecast provides moderate accuracy and outperforms tipsters prediction (Reade, 2014;Spann & Skiera, 2009;Stekler et al., 2010). ...
... The existence of favourite-longshot bias in the corner O/U, HAD and number of total goals scored O/U markets are examined by a negative mean logarithmic scoring rule (Gneiting & Raftery, 2007). The R package implied (Lindstrøm, 2021) offers a few margin removal methods to calculate implied probabilities of betting odds namely basic method, odd ratio method, power method and Shin method (Shin, 1993;Clarke et al., 2017). Except the basic method allocates margin equally, all other methods penalise longshot and apply less margin on favourite selections. ...
Preprint
Full-text available
This paper presents a novel compound Poisson regression model to forecast number of corner kicks taken in association football. Corner kick taken events are often decisive in the match outcome and embody serial correlation and clustered pattern. Providing parameter estimates with intuitive interpretation, a class of compound Poisson distribution including a Bayesian implementation of geometric-Poisson distribution is introduced. Apart from introducing a new statistical framework, the utilisation of cross-market data, target encoding techniques and treatment to the data-rich-data-poor problem to enhance the model predictability are also discussed.
... This way, the commission is spread equally between the home and away team's odds. This assumption is actually rather strong, as there is no evidence that the bookmakers symmetrically apply their margin to all the odds (Clarke et al., 2017). Nevertheless, using the normalized odds is interesting as we note that the favourite-longshot bias is more evident in this case. ...
Article
Full-text available
Several recent studies suggest that the home advantage, that is, the benefit competitors accrue from performing in familiar surroundings, was-at least temporarily-reduced in games played without spectators during the COVID-19 Pandemic. These games played without fans during the Pandemic have been dubbed 'ghost games'. However, the majority of the research to date focuses on soccer and no contributions have been provided for indoor sports, where the effect of the support of the fans might have a stronger impact than in outdoor arenas. In this paper, we fill this gap by investigating the effect of ghost games in basketball. In particular, we test (i) for the reduction of the home advantage in basketball, (ii) whether such reduction tends to disappear over time, (iii) if the bookmakers promptly adapt to such structural change or whether mispricing was created on the betting market. The results from a large data set covering all seasons since 2004 for the ten most popular basketball leagues in Europe show an overall significant reduction of the home advantage of around 5% and no evidence that suggests that this effect has been reduced at as teams became more accustomed to playing without fans. At the same time, bookmakers appear to have anticipated such an effect and priced home wins in basketball matches accordingly, thus avoiding any mispricing on betting markets.
Article
Under-representation of women persists in many industries and represents an important area of concern for society. We use a revealed preference approach to test for bias against females in an underexplored environment. Whilst much use has been made of the financial industry to examine how market prices reveal implicit views on the relative productivity of men and women, our setting offers advantages through both volume of data and unambiguity of outcome. Over a 20-year period, the effect of jockey gender on fixed price betting odds was examined in National Hunt racing. Employing censored regression to account for non-finishers we find female jockeys to be underestimated by the UK betting market. Results indicate an increasing trend for underestimation in recent years, despite growing representation and rising performance levels of female jockeys. We conclude that mistake-based discrimination and confirmation bias may be impacting efficiency in the betting market. The market might recognise some improvement in female performance but may be failing to adapt at the speed with which female jockeys are professionalising.
Conference Paper
Full-text available
The modern medicine widely uses an ionizing radiation for different purposes, including patients’ treatment by means of a radiation therapy. However, health hazards and risks of adverse biological effects associated with an ionizing radiation are high. These make it necessary to take measures of a radiation protection of radiation therapy patients and to carry out In-Vivo dosimetry. Leading medical facilities in Georgia prefer OSL technology system for In-Vivo dosimetry. In addition to a specialized dosimeter it provides for a delivered radiation dose reader and a computer software. An OSL dosimeter for In-Vivo dosimetry is a high performance, compact and convenient device and these features are, indeed, increasing the significance of In-Vivo dosimetry system in the radiation protection of the radiation therapy patients.
Article
This paper examines the performance of five different measures for forecasting men’s and women’s professional tennis matches. We use data derived from every match played at the 2018 and 2019 Wimbledon tennis championships, the 2019 French Open, the 2019 US Open, and the 2020 Australian Open. We look at the betting odds, the official tennis rankings, the standard Elo ratings, surface-specific Elo ratings, and weighted composites of these ratings, including and excluding the betting odds. The performance indicators used are prediction accuracy, calibration, model discrimination, Brier score, and expected return. We find that the betting odds perform relatively well across these tournaments, while standard Elo (especially for women’s tennis) and surface-adjusted Elo (especially for men’s tennis) also perform well on a range of indicators. For all but the hard-court surfaces, a forecasting model which incorporates the betting odds tends also to perform well on some indicators. We find that the official ranking system proved to be a relatively poor measure of likely performance compared to betting odds and Elo-related methods. Our results add weight to the case for a wider use of Elo-based approaches within sports forecasting, as well as arguably within the player rankings methodologies.
Article
This paper examines whether sports betting markets are semistrong-form efficient—i.e., whether new information is rapidly and completely incorporated into betting prices. We use the news of ghost matches in the top European football leagues due to the COVID-19 pandemic as the arrival of public information. Because spectators are absent in ghost games, the home field advantage is reduced, and we test whether this information is fully reflected in betting prices. Our results show that bookmakers systematically overestimate a home team’s winning probability during the first period of the ghost games, which suggests that betting markets are, at least temporally, not semistrong-form efficient. We exploit a betting strategy that yields a positive net payoff over more than one month.
Conference Paper
Full-text available
A mathematical model predicting sporting outcomes produces probabilities that sum to one, whereas the-round is the excess probability that supplies the bookies margin, and could typically range from 2% to over 20%. If the probabilities from a mathematical model are to be used for supplying real time odds they need to be adjusted need to be adjusted so that the implied probabilities sum to one. Schembri et al (2011) discusses two methods normalisation and equal distribution. However neither of these suitably allow for the fact that the margin on outsiders is usually greater than favourites. A true price of 1.05canbereducedto1.05 can be reduced to 1.03 for less than 2% margin, whereas a 100truepricecouldbesetat100 true price could be set at 50 for a $50% margin. This paper discusses an alternative approach using a power function to transform probabilities. This was successfully used when supplying real time odds to a leading bookmarker (Clarke, 2007).
Article
Sports forecasting models – beyond their interest to bettors – are important resources for sports analysts and coaches. Like the best athletes, the best forecasting models should be rigorously tested and judged by how well their performance holds up against top competitors. Although a number of models have been proposed for predicting match outcomes in professional tennis, their comparative performance is largely unknown. The present paper tests the predictive performance of 11 published forecasting models for predicting the outcomes of 2395 singles matches during the 2014 season of the Association of Tennis Professionals Tour. The evaluated models fall into three categories: regression-based, point-based, and paired comparison models. Bookmaker predictions were used as a performance benchmark. Using only 1 year of prior performance data, regression models based on player ranking and an Elo approach developed by FiveThirtyEight were the most accurate approaches. The FiveThirtyEight model predictions had an accuracy of 75% for matches of the most highly-ranked players, which was competitive with the bookmakers. The inclusion of career-to-date improved the FiveThirtyEight model predictions for lower-ranked players (from 59% to 64%) but did not change the performance for higher-ranked players. All models were 10–20 percentage points less accurate at predicting match outcomes among lower-ranked players than matches with the top players in the sport. The gap in performance according to player ranking and the simplicity of the information used in Elo ratings highlight directions for further model development that could improve the practical utility and generalizability of forecasting in tennis.
Article
Predicting the outcome of a single sporting event is difficult; predicting all of the outcomes for an entire tournament is a monumental challenge. Despite the difficulties, millions of people compete each year to forecast the outcome of the NCAA men’s basketball tournament, which spans 63 games over 3 weeks. Statistical prediction of game outcomes involves a multitude of possible covariates and information sources, large performance variations from game to game, and a scarcity of detailed historical data. In this paper, we present the results of a team of modelers working together to forecast the 2014 NCAA men’s basketball tournament. We present not only the methods and data used, but also several novel ideas for post-processing statistical forecasts and decontaminating data sources. In particular, we highlight the difficulties in using publicly available data and suggest techniques for improving their relevance.
Article
We show that the probabilities determined from betting odds using Shin’s model are more accurate forecasts than those determined using basic normalization or regression models. We also provide empirical evidence that some bookmakers are significantly different sources of probabilities in terms of forecasting accuracy, and that betting exchange odds are not always the best source, especially in smaller markets. The advantage of using Shin probabilities and the differences between bookmakers decrease with an increasing market size.
Article
In this paper we test the hypothesis that bookmakers display superior skills to bettors in predicting the outcome of sporting events by using matched data from traditional bookmaking and person-to-person exchanges. Employing a conditional logistic regression model on horse racing data from the UK we find that, in high liquidity betting markets, betting exchange odds have more predictive value than the corresponding bookmaker odds. To control for potential spillovers between the two markets, we repeat the analysis for cases where prices diverge significantly. Once again, exchange odds yield more valuable information concerning race outcomes than the bookmaker equivalents.
Article
Different methods for assessing the abilities of participants in a sports tournament, and their corresponding winning probabilities for the tournament, are embedded in a common framework and their predictive performances compared. First, ratings of abilities (such as the Elo rating) are complemented with a simulation approach which yields winning probabilities for the full tournament. Second, tournament winning probabilities are extracted from bookmakers' odds using a consensus model, and the underlying abilities of the competitors are then derived by an "inverse" application of the tournament simulation. Both techniques are employed for forecasting the results of the European football championship 2008 (UEFA EURO 2008), for which the consensus model based on bookmakers' odds outperforms methods based on both the Elo rating and the FIFA/Coca Cola World rating. Moreover, the bookmaker consensus model correctly predicts that the final will be played by the teams from Germany and Spain (with a probability of about 20.5%), while showing that both finalists profit from being drawn in groups with relatively weak competitors.
Article
This paper verifies the existence of the favourite-longshot bias in a variety of sports betting markets where odds are set by bookmakers, but the precise pattern of the bias is not identical. Evidence is found to support a central prediction of the Shin (1993) model, which asserts that bookmakers are impelled to create a bias in their odds because of the presence of insider traders: that margins increase with the number of competitors. Copyright Blackwell Publishers Ltd and the Board of Trustees of the Bulletin of Economic Research, 2003.
Article
Even in competitive financial markets, the presence of insider traders leads to a divergence between the selling and buying price, as intermediaries attempt to recoup their losses to the insiders by extracting a margin from other traders. The extent of this divergence is an indication of the severity of the market distortion due to insider trading. Conversely, the incidence of insider trading may be inferred from observed spreads given an appropriate model of trading. In this paper, the market for bets in a horse race in which bookmakers set prices serves as the vehicle for such an investigation. By solving for the equilibrium prices in a game in which bookmakers compete in prices, the market spread is obtained as a function of the incidence of insider trading and other parameters. this incidence is then estimated from U.K. data. Copyright 1993 by Royal Economic Society.
Article
This paper examines the pricing of state contingent claims in the presence of insider traders. The specific setting is the market for bets in a horse race in which bookmakers compete in prices in anticipation of betting from a group of bettors, some of whom have insider information. The author identifies a condition which is necessary and sufficient for the so called "favorite-bias" in which, the prices on the favorites understate the winning changes of these horses relatively less than the prices on the longshots. The robustness of this result is examined in a more general framework, and the bias is shown to survive in a generalized form. Copyright 1992 by Royal Economic Society.