A discrete-time and finite-state Markov Chain model for association football matches

A birth process model proposed by Dixon and Robinson has been widely used in football spread betting market. However, multiple goals in a minute are permitted in the model, which does not conform to historical record. Moreover, it is difficult to calculate the outcome probability of the process accurately. The article presents a discrete-time and finite-state Markov chain model for real-time forecast of football matches and a recursive algorithm is derived to calculate the outcome probability accurately. The empirical study shows that the proposed model outperforms the models of Dixon and Robinson and Dixon and Coles.     

Power Ratings for NCAA Division II Football

ABSTRACT

There is an abundance of entities that disseminate power ratings for NCAA Division I-A and I-AA football teams. This is not true for the NCAA Division II level. Statistical data on all NCAA Divisions II football games for two years were examined to develop a rating system. Several statistical techniques were performed on the data. Ultimately, the ratings were based on won-lost percentage, margin of victory, strength of schedule, and quality wins. Results are given for the 2001 and 2002 seasons. Ratings for the 2002 season for Divisions I-A and I-AA are also given using the techniques developed.     

Construction of a semi-Markov model for the performance of a football team in the presence of missing data

Using play-by-play data from the very beginning of the professional football league in Turkey, a semi-Markov model is presented for describing the performance of football teams. The official match results of the selected teams during 55 football seasons are used and winning, drawing and losing are considered as Markov states. The semi-Markov model is constructed with transition rates inferred from the official match results. The duration between the last match of a season and the very first match of the following season is much longer than any other duration during the season. Therefore these values are considered as missing values and estimated by using expectation–maximization algorithm. The effect of the sojourn time in a state to the performance of a team is discussed as well as mean sojourn times after losing/winning are estimated. The limiting probabilities of winning, drawing and losing are calculated. Some insights about the performance of the selected teams are presented.     

Side betting and playing the National Lottery: an exercise in policy design

This paper demonstrates a methodology for estimating the frequencies by which numbers are selected by National Lottery players by utilizing a twofold approach of a Multi-Response Non-Linear Regression model in conjunction with a suggested approximation function for number selections, which leads to an explanation of number choice in terms of the spatial effects of form design. It shows that in a marketplace, side betting is complementary with the main online draw product, and market forces produce close substitutes if side betting on the National Lottery is prohibited.     

Analysis of the importance of on-field covariates in the German Bundesliga

In modern football, various variables as, for example, the distance a team runs or its percentage of ball possession, are collected throughout a match. However, there is a lack of methods to make use of these on-field variables simultaneously and to connect them with the final result of the match. This paper considers data from the German Bundesliga season 2015/2016. The objective is to identify the on-field variables that are connected to the sportive success or failure of the single teams. An extended Bradley–Terry model for football matches is proposed that is able to take into account on-field covariates. Penalty terms are used to reduce the complexity of the model and to find clusters of teams with equal covariate effects. The model identifies the running distance to be the on-field covariate that is most strongly connected to the match outcome.     

Financial spread betting

Traditional betting has two outcomes: you win or you lose. Spread betting has many more possibilities: you can win a lot or a little; you can lose or lose much, much more than you imagined. Spread betting, say its fans, brings a whole new level of uncertainty—and excitement. It has been described as the crack cocaine of gambling. Spread bets can be laid on almost any sporting or other result, but in the field of finance it is making particular inroads. David Buik , of the City spread betting company Cantor Index Ltd, explains.     

Non-random shuffling strategies in blackjack

Numerous playing and betting strategies for the game of twenty-one have been computed assuming the deck or decks are randomly shuffled. In practice, dealers do not spend the time necessary (it takes too long) to completely randomly shuffle the decks used. Hence, there is information not only from the current round of play, but potentially from the previous round of play. We present a model for a non-random shuffle and assert ways in which this information can be used. Rules are derived using a normal approximation which updates the current strategies utilizing information from a non-random shuffle.     

Estimating Probability Distributions by Observing Betting Practices

A bookmaker takes bets on a two-horse race, attempting to minimize expected loss over all possible outcomes of the race. Profits are controlled by manipulation of customer' betting behavior; in order to do this, we need some information about the probability distribution which describes how the customers will bet. We examine what information initial customer' betting behavior provides about this probability distribution, and consider how to use this to estimate the probability distribution for remaining customers.     

Bayesian hierarchical model for the prediction of football results

The problem of modelling football data has become increasingly popular in the last few years and many different models have been proposed with the aim of estimating the characteristics that bring a team to lose or win a game, or to predict the score of a particular match. We propose a Bayesian hierarchical model to fulfil both these aims and test its predictive strength based on data about the Italian Serie A 1991–1992 championship. To overcome the issue of overshrinkage produced by the Bayesian hierarchical model, we specify a more complex mixture model that results in a better fit to the observed data. We test its performance using an example of the Italian Serie A 2007–2008 championship.     

Betting the future online

The Internet has brought, among other things, the online betting exchange. From desks in the City or from laptops on sunny beaches, those in the know or out of it can place bets with each other on anything under the sun, whether likely—Australia beating England at cricket—or the reverse. If you have a hunch that a genetically engineered Tyrannosaur will wander down Oxford Street next year, and if you want to put money on it, Internet betting exchanges will find someone to accommodate you. Leighton Vaughan Williams explains how a simple change in tax regime has brought something other than just a more efficient gambling system. It has created a strangely accurate way of foretelling the future.     

Stakes and chips

Gambling has provided centuries of inspiration to probabilists and statisticians. The process continues. There also exist fundamental links between betting and a newer subject, Information Theory, which began with Claude Shannon and his ground-breaking 1948 paper A Mathematical Theory of Communication.
It is a result which arises very naturally. A successful gambler and a successful data compression algorithm must both accurately estimate probability distributions. There are practical results as well as theoretical: Shannon and colleagues, including the legendary gambler and mathematician Edward Thorp, actually attempted to apply results from information theory in Las Vegas casinos and stock market transactions. Oliver Johnson examines the connections.     

A new continuous distribution on the unit interval applied to modelling the points ratio of football teams

We introduce a new flexible distribution to deal with variables on the unit interval based on a transformation of the sinh–arcsinh distribution, which accommodates different degrees of skewness and kurtosis and becomes an interesting alternative to model this type of data. We also include this new distribution into the generalised additive models for location, scale and shape (GAMLSS) framework in order to develop and fit its regression model. For different parameter settings, some simulations are performed to investigate the behaviour of the estimators. The potentiality of the new regression model is illustrated by means of a real dataset related to the points rate of football teams at the end of a championship from the four most important leagues in the world: Barclays Premier League (England), Bundesliga (Germany), Serie A (Italy) and BBVA league (Spain) during three seasons (2011–2012, 2012–2013 and 2013–2014).     

Bayesian hierarchical models for the prediction of volleyball results

Statistical modelling of sports data has become more and more popular in the recent years and different types of models have been proposed to achieve a variety of objectives: from identifying the key characteristics which lead a team to win or lose to predicting the outcome of a game or the team rankings in national leagues. Although not as popular as football or basketball, volleyball is a team sport with both national and international level competitions in almost every country. However, there is almost no study investigating the prediction of volleyball game outcomes and team rankings in national leagues. We propose a Bayesian hierarchical model for the prediction of the rankings of volleyball national teams, which also allows to estimate the results of each match in the league. We consider two alternative model specifications of different complexity which are validated using data from the women''s volleyball Italian Serie A1 2017–2018 season.     

Fitting probability forecasting models by scoring rules and maximum likelihood

Probability forecasting models can be estimated using weighted score functions that (by definition) capture the performance of the estimated probabilities relative to arbitrary “baseline” probability assessments, such as those produced by another model, by a bookmaker or betting market, or by a human probability assessor. Maximum likelihood estimation (MLE) is interpretable as just one such method of optimum score estimation. We find that when MLE-based probabilities are themselves treated as the baseline, forecasting models estimated by optimizing any of the proven families of power and pseudospherical economic score functions yield the very same probabilities as MLE. The finding that probabilities estimated by optimum score estimation respond to MLE-baseline probabilities by mimicking them supports reliance on MLE as the default form of optimum score estimation.     

Elite players’ perceptions of football playing surfaces: a mixed effects ordinal logistic regression model of players’ perceptions

The aim of this study was to determine potential explanatory factors that may be associated with different attitudes amongst the global population of elite footballers to the use of different surfaces for football. A questionnaire was used to capture elite football players’ perceptions of playing surfaces and a mixed effects ordinal logistic regression model was used to explore potential explanatory factors of players’ perceptions. In total, responses from 1129 players from 44 different countries were analysed. The majority of players expressed a strong preference for the use of Natural Turf pitches over alternatives such as Artificial Turf. The regression model, with a players’ country as a random effect, indicated that players were less favourable towards either Natural Turf or Artificial Turf where there was perceived to be greater variability in surface qualities or the surface was perceived to have less desirable properties. Player’s surface experience was also linked to their overall attitudes, with a suggestion that the quality of the Natural Turf surface players experienced dictated players’ support for Artificial Turf.     

How to improve a team's position in the FIFA ranking? A simulation study

In this paper, we study the efficacy of the official ranking for international football teams compiled by FIFA, the body governing football competition around the globe. We present strategies for improving a team's position in the ranking. By combining several statistical techniques, we derive an objective function in a decision problem of optimal scheduling of future matches. The presented results display how a team's position can be improved. Along the way, we compare the official procedure to the famous Elo rating system. Although it originates from chess, it has been successfully tailored to ranking football teams as well.     

Time Series Models for Count or Qualitative Observations

Time series sometimes consist of count data in which the number of events occurring in a given time interval is recorded. Such data are necessarily nonnegative integers, and an assumption of a Poisson or negative binomial distribution is often appropriate. This article sets ups a model in which the level of the process generating the observations changes over time. A recursion analogous to the Kalman filter is used to construct the likelihood function and to make predictions of future observations. Qualitative variables, based on a binomial or multinomial distribution, may be handled in a similar way. The model for count data may be extended to include explanatory variables. This enables nonstochastic slope and seasonal components to be included in the model, as well as permitting intervention analysis. The techniques are illustrated with a number of applications, and an attempt is made to develop a model-selection strategy along the lines of that used for Gaussian structural time series models. The applications include an analysis of the results of international football matches played between England and Scotland and an assessment of the effect of the British seat-belt law on the drivers of light-goods vehicles.     

Testing homogeneity in clustered (longitudinal) count data regression model with over-dispersion

Clustered (longitudinal) count data arise in many bio-statistical practices in which a number of repeated count responses are observed on a number of individuals. The repeated observations may also represent counts over time from a number of individuals. One important problem that arises in practice is to test homogeneity within clusters (individuals) and between clusters (individuals). As data within clusters are observations of repeated responses, the count data may be correlated and/or over-dispersed. For over-dispersed count data with unknown over-dispersion parameter we derive two score tests by assuming a random intercept model within the framework of (i) the negative binomial mixed effects model and (ii) the double extended quasi-likelihood mixed effects model (Lee and Nelder, 2001). These two statistics are much simpler than a statistic derived by Jacqmin-Gadda and Commenges (1995) under the framework of the over-dispersed generalized linear model. The first statistic takes the over-dispersion more directly into the model and therefore is expected to do well when the model assumptions are satisfied and the other statistic is expected to be robust. Simulations show superior level property of the statistics derived under the negative binomial and double extended quasi-likelihood model assumptions. A data set is analyzed and a discussion is given.     

Anomalies in the Gambling Market

Apparent irregularities between the win and the place betting markets in Australian horseracing are examined. Win odds are used to predict win probabilities from which place probabilities are estimated and compared with the place odds on offer. It is concluded that anomalies do in fact exist and are capable, in theory at least, of profitable exploitation.     

A Two-Stage Estimator of the Dependence Parameter for the Clayton-Oakes Model

This paper describes the properties of a two-stage estimator of the dependence parameter in the Clayton-Oakes multivariate failure time model. The parameter is estimated from a likelihood function in which the marginal hazard functions are replaced by estimates. The method extends the approach of Shih and Louis (1995) and Genest, Ghoudi and Rivest (1995) to allow the marginal hazard for failure times to follow a stratified Cox (1972) model. The method is computationally simple and under mild regularity conditions produces a consistent, asymptotically normal estimator.