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Soccer spread betting is analysed using standard probabilistic methods assuming that goals are scored in a match according
to Poisson distributions with constant means. A number of different possible forms of ‘edge’ (betting advantage) is identified.
It is shown how the centre spreads of the more common bets in the ‘bet universe’ may be calculated. A more general question
is then addressed, namely, how a punter should invest if they take a view that the online bookmakers have fixed the goal means
incorrectly or some other edge is in their favour. It is shown that a Markowitz portfolio theory framework may be set up in
such cases. This leads to the definitions of an ‘efficient betting frontier’ and an ‘optimal bet portfolio’. Examples are
used throughout to illustrate the theory that is developed.
Portfolio theory problem for three bets for Wigan versus Manchester United premiership match of 14 October 2006.
Content may be subject to copyright.
Content may be subject to copyright.
IMA Journal of Management Mathematics Page 1 of 18
Markowitz portfolio theory f or soccer spread betting
School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK
[Received on 16 August 2007; accepted on 30 July 2008]
Soccer spread betting is analysed using standard probabilistic methods assuming that goals are scored in
a match according to Poisson distributions with constant means. A number of different possible forms of
‘edge’ (betting advantage) is identified. It is shown how the centre spreads of the more common bets in
the ‘bet universe’ may be calculated. A more general question is then addressed, namely, how a punter
should invest if they take a vie w that the online bookmakers have fixed the goal means incorrectly or
some other edge is in their favour . It is shown that a Markowitz portfolio theory frame work may be set up
in such cases. This leads to the definitions of an ‘efficient betting frontier’ and an ‘optimal bet portfolio’.
Examples are used throughout to illustrate the theory that is developed.
Keywor ds : spread betting; portfolio theory; soccer betting; arbitrage; sports betting.
Sports spread betting has gained a huge following in the UK over the past 5–10 years. This popularity
has been mirrored in other parts of the world, with the exception of the USA (which has essentially
outlawed such betting for rather obscure ‘moral’ reasons and regularly arrests and imprisons those who
run online betting sites) and countries where religious beliefs deem that gambling is not permitted.
Soccer has proved particularly attractive to spread betters. Financially , a spread bet replicates a forward
or a future contract and, in line with such contracts, is traded via an ‘exchange’ which is normally run
by an online bookmaker (OB). A punter wishing to bet deposits a sum of money with their chosen OB,
thereby opening an account and allowing them to bet using the internet. All further transactions are then
carried out online. In all the examples given belo w, the OB used was one of the most popular internet
spread betting companies (though for obvious reasons we shall not identify exactly which one).
1.1 The mechanics of spread betting
The mechanics of spread betting are simple: for each match, bets are placed on the outcome of a range
of ‘indices’ offered by the OB. The index may consist of a simple quantity , such as the total number
of goals scored in a match, or be much more involved and depend on esoteric combinations of goal
times, corners and player bookings, etc. For each index, howe ver, the betting mechanics are identical:
the OB quotes a ‘spread’ [ B , T ] and the punter has a choice (at a unit stake, say) of either ‘buying the
spread at T ’ or ‘selling the spread at B ’. At the conclusion of the match, the final value S of the index is
tallied, and the punter then receives an amount S − T if they bought the spread and B − S if they sold
the spread. Receiving a negativ e amount (possible if the punter took an incorrect view) corresponds, of
course, to paying a sum to the OB, thereby explaining why spread betting is normally only conducted via
The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
IMA Journal of Management Mathematics Advance Access published November 5, 2008
... Fractional Kelly The result of the Kelly optimization problem is, for each opportunity, the ideal fraction ω → f * one is ought to invest to achieve the maximal long-term profits. The fraction f * thus dictates an upper-bound on the possible profit, meaning that increasing the invested fraction further will actually decrease the long-term profit 18 . This is commonly known as "overbetting". ...
... Portfolio optimization The approach of splitting the trader's workflow into the two steps of predictive modeling and investment optimization has a long tradition, and has been exploited in absolute majority of works [49,30,56,51,71, 18] , with some notable exceptions [24,38]. Extracting the parameter estimation out of the portfolio optimization problem then enabled the respective economic research to thrive in an isolated mathematical environment, giving rise to the frameworks of Markowitz [47] and Kelly [32], and their many successors [10,76,71,36,51]. ...
It is a common misconception that in order to make consistent profits as a trader, one needs to posses some extra information leading to an asset value estimation more accurate than that reflected by the current market price. While the idea makes intuitive sense and is also well substantiated by the widely popular Kelly criterion, we prove that it is generally possible to make systematic profits with a completely inferior price-predicting model. The key idea is to alter the training objective of the predictive models to explicitly decorrelate them from the market, enabling to exploit inconspicuous biases in market maker's pricing, and profit on the inherent advantage of the market taker. We introduce the problem setting throughout the diverse domains of stock trading and sports betting to provide insights into the common underlying properties of profitable predictive models, their connections to standard portfolio optimization strategies, and the, commonly overlooked, advantage of the market taker. Consequently, we prove desirability of the decorrelation objective across common market distributions, translate the concept into a practical machine learning setting, and demonstrate its viability with real world market data.
... Chapman [6] evaluated the use of the Kelly criterion for spread betting, that is, distributing bets over a range of outcomes for a continuous random variable. This topic was also considered by Fitt [8] for the time of arrival of events in soccer matches, albeit using the approach suggested by Markowitz [21] rather than the Kelly criterion. ...
... examine the hypothesis that sentimental bettors act like noise traders and can affect the path of prices in football betting markets. Futhermore, Fitt (2009) applies the efficient portfolio theory to analyzes the mis-pricing of cross-sectional odds. Online 1 See "Football Betting -the Global Gambling Industry worth Billions." ...
We develop a probabilistic model to track and forecast real-time odds for English Premier League (EPL) football games. We show how a difference in Poisson processes (a.k.a. Skellam process) provides a dynamic probabilistic model for the evolution of scores. Ex ante, we show how to calibrate expected goal scoring rates using market-based information on win, lose, draw odds. As the game evolves, we use the current score and our Skellam process to calculate the matrix of final score odds. This enables us to identify real time online betting opportunities relative to our model's predictions. We illustrate our methodology the EPL game between Everton and West Ham and Sunderland and Leicester City. Both games illustrate the flexibility of our model and how odds can change quickly as the score progresses. Finally, we conclude with directions for future research.
... If the right-hand side of the above inequality is strictly less than one, then the matrix A T 2 Γ d A T 2 is stable. Using (33)- (34) , this condition is satisfied by the following quadratic inequalities on µ k : ...
We consider solving multi-objective optimization problems in a distributed
manner by a network of cooperating and learning agents. The problem is
equivalent to optimizing a global cost that is the sum of individual
components. The optimizers of the individual components do not necessarily
coincide and the network therefore needs to seek Pareto optimal solutions. We
develop a distributed solution that relies on a general class of adaptive
diffusion strategies. We show how the diffusion process can be represented as
the cascade composition of three operators: two combination operators and a
gradient descent operator. Using the Banach fixed-point theorem, we establish
the existence of a unique fixed point for the composite cascade. We then study
how close each agent converges towards this fixed point, and also examine how
close the Pareto solution is to the fixed point. We perform a detailed
mean-square error analysis and establish that all agents are able to converge
to the same Pareto optimal solution within a sufficiently small
mean-square-error (MSE) bound even for constant step-sizes. We illustrate one
application of the theory to collaborative decision making in finance by a
network of agents.
In this study, it was researched that how the rate of repayment of loans will be increased and how the credit risk will be minimized in banking sector, by using Markowitz Portfolio Theory. Construction, textile and wholesale and retail sectors were examined under the central bank data. Portfolio groups were selected and risks(variances of Portfolio groups) were evaluated according to Markowitz portfolio theory. Markowitz portfolio theory is effective than the other portfolio selection instruments. Although Classical risk measurement tools measure risks, but they do not be able to answer how the risks can be reduced. On the other hand, Markowitz portfolio model, which is used in this study, show how the risks can be reduced.
The second edition of this popular book presents a detailed economic analysis of professional football at club level, with new material included to reflect the development of the economics of professional football over the past ten years. Using a combination of economic reasoning and statistical and econometric analysis, the authors build upon the successes and strengths of the first edition to guide readers through the economic complexities and peculiarities of English club football. It uses a wide range of international comparisons to help emphasize both the broader relevance as well as the unique characteristics of the English experience. Topics covered include some of the most hotly debated issues currently surrounding professional football, including player salaries, the effects of management on team performance, betting on football, racial discrimination and the performance of football referees. This edition also features new chapters on the economics of international football, including the World Cup.
April 2000 · Foundations of Physics Letters
Relativistic causality, namely, the impossibility of signaling at superluminal speeds, restricts the kinds of correlations which can occur between different parts of a composite physical system. Here we establish the basic restrictions which relativistic causality imposes on the joint probabilities involved in an experiment of the Einstein-Podolsky-Rosen-Bohm type. Quantum mechanics, on the other ... [Show full abstract] hand, places further restrictions beyond those required by general considerations like causality and consistency. We illustrate this fact by considering the sum of correlations involved in the CHSH inequality. Within the general framework of the CHSH inequality, we also consider the nonlocality theorem derived by Hardy, and discuss the constraints that relativistic causality, on the one hand, and quantum mechanics, on the other hand, impose on it. Finally, we derive a simple inequality which can be used to test quantum mechanics against general probabilistic theories.
In this paper, we focus on a critical subtask in event-level sentiment analysis, namely opinion target understanding, with the goal to determine which opinion target a comment talks about in an event description. Unlike traditional aspect-level sentiment analysis, opinion target understanding needs to not only recognize the opinion target in a comment, but also align the target to the ... [Show full abstract] corresponding opinion target in an event description. To address this problem, we propose a neural 2-sequences-to-1-sequence framework to jointly leverage both texts in an event description and an comment, and apply a word-by-word attention mechanism to capture the alignment between the two texts. Experimental results prove the effectiveness of the proposed approach to opinion target understanding in event-level sentiment analysis.
September 2006 · Management Decision
Purpose – The purpose of this research is twofold: to evaluate the performance of Spanish First-Division soccer teams, comparing the sports results that they actually obtain with those that they should have obtained on the basis of their potential, and to propose a future course of action. Design/methodology/approach – In order to assess the potential of each team in the Spanish professional ... [Show full abstract] soccer league between the years 1998 and 2005 an output-oriented version of Data Envelopment Analysis is used. In this way it is possible to calculate the number of points a team could have achieved with an efficient use of its actual resources and, consequently, its potential position in the league classification. Findings – The main conclusion is that a team's final league position depends more on its efficient use of resources than on its potential. Practical implications – From the practical perspective, the results seem to stress that measures directed at improving soccer teams' results should focus on improving their efficient use of available resources. Consequently, this work provides a preliminary result, obtained using economics tools, that suggests where soccer team managers might direct their efforts to improve their sports results. Originality/value – The present work is based on the same concept of potential in sports teams as Zak et al. (1979) and Hofler and Payne (1997), but with a number of differences compared with the earlier studies. First, the potential of the teams and their actual results are compared not by assessing their efficiency in the use of resources, but by observing their final league table positions. Second, the technique which is used to estimate the frontier is in this case Data Envelopment Analysis (DEA), or the deterministic non-parametric frontier method, which has not often been used in order to measure efficiency in soccer. Finally, the object of study is the Spanish First Division soccer teams in the seasons 1998/1999, 1999/2000, 2000/2001, 2001/2002, 2002/2003, 2003/2004 and 2004/2005.
January 1986 · The Annals of Probability
We prove general invariance principles for integral functions of the empirical process. As corollaries we derive probabilistic proofs of the sufficiency criteria for a distribution to belong to the domain of attraction of the normal and stable laws with index $0 < \alpha < 2$. In the process we obtain equivalent statements of these criteria in terms of the tail behaviour of the underlying ... [Show full abstract] quantile function. We also give a representation of any stable random variable with index $0 < \alpha < 2$ in terms of a linear combination of two independent and identically distributed Poisson integrals. The role of a fixed number of extreme terms is exactly determined.
January 2008 · Applied and Computational Mathematics
This paper addresses a tournament scoring problem that can lead to a score-based form of scheduling. Unlike classical combinatorial problems with some initial state and constraints, the problem is concerned with the construction of valid initial states according to some given final state and constraints and so it is named as reverse scheduling. Given a football tournament, this involves ... [Show full abstract] determining possible scores of all matches between teams, using the final state of the tournament table. For a feasible solution, the subject of multi-parameter partition is examined, the notion of black&white graphs is introduced, and a rules-based method is proposed. Also, using some particular table data, experimental results are presented along with the number of different scores and their computation time for one team.
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