Rating teams and analysing outcomes in one-day and test cricket

Summary.  Multiple linear regression techniques are applied to determine the relative batting and bowling strengths and a common home advantage for teams playing both innings of international one-day cricket and the first innings of a test-match. It is established that in both forms of the game Australia and South Africa were rated substantially above the other teams. It is also shown that home teams generally enjoyed a significant advantage. Using the relative batting and bowling strengths of teams, together with parameters that are associated with common home advantage, winning the toss and the establishment of a first-innings lead, multinomial logistic regression techniques are applied to explore further how these factors critically affect outcomes of test-matches. It is established that in test cricket a team's first-innings batting and bowling strength, first-innings lead, batting order and home advantage are strong predictors of a winning match outcome. Contrary to popular opinion, it is found that the team batting second in a test enjoys a significant advantage. Notably, the relative superiority of teams during the fourth innings of a test-match, but not the third innings, is a strong predictor of a winning outcome. There is no evidence to suggest that teams generally gained a winning advantage as a result of winning the toss.     

The effectiveness of coach turnover and the effect on home team advantage,team quality and team ranking

The effectiveness of coach turnover on team performance is widely discussed in the literature due to the indirect impact of a team's performance on a club's revenues. This study examines the effect of coach turnover within a competition season by focusing on the change in team quality and the change in home team advantage under the new coach. The change in team quality or home team advantage can vary according to the team (team specific) or might be an independent quantity (non-team specific). We estimated nine possible regression models, given no change, team-specific change and non-team-specific change in quality or home team advantage. The data are the match results of Belgian male soccer teams playing in the highest national division during seven seasons. Results point to a team-specific effect of a new coach on a team's quality. This article further contributes by evaluating the new coach's success with regard to whether his ability to improve team quality also results in a better position of the team in the final ranking. A new coach will be able to improve the ranking of the team if the improved team quality under the new coach renders a positive team quality.     

Predictions and home advantage for Australian rules football

In a previous paper, it was demonstrated that distinctly different prediction methods when applied to 2435 American college and professional football games resulted in essentially the same fraction of correct selections of the winning team and essentially the same average absolute error for predicting the margin of victory. These results are now extended to 1446 Australian rules football games. Two distinctly different prediction methods are applied. A least-squares method provides a set of ratings. The predicted margin of victory in the next contest is less than the rating difference, corrected for home-ground advantage, while a 0.75 power method shrinks the ratings compared with those found by the least-squares technique and then performs predictions based on the rating difference and home-ground advantage. Both methods operate upon past margins of victory corrected for home advantage to obtain the ratings. It is shown that both methods perform similarly, based on the fraction of correct selections of the winning team and the average absolute error for predicting the margin of victory. That is, differing predictors using the same information tend to converge to a limiting level of accuracy. The least-squares approach also provides estimates of the accuracy of each prediction. The home advantage is evaluated for all teams collectively and also for individual teams. The data permit comparisons with other sports in other countries. The home team appears to have an advantage (the visiting team has a disadvantage) due to three factors:the visiting team suffers from travel fatigue; crowd intimidation by the home team fans; lack of familiarity with the playing conditions     

Population,Food and Economic Adjustment

This article investigates the number of games of baseball that should be played (1) in a World Series competition, and (2) in a pennant race competition within each league, in order to have a reasonable level of confidence that the best team wins the competition. The current number of games played is found to be highly inadequate for the World Series and only barely sufficient for the pennant race.     

Predicting the outcomes of annual sporting contests

Summary.  Data from 20 sporting contests in which the same two teams compete regularly are studied. Strong and weak symmetry requirements for possible models are identified, and some simple models are proposed and fitted to the data. The need to compute the exact likelihood function and the presence of missing values make this non-trivial. Forecasting match outcomes by using the models can give a modest improvement over a naïve forecast. Significance tests for studying the effect of 'match covariates' such as playing at home or away or winning the toss are introduced, and the effect of these covariates is in general found to be quite large.     

Predicting probabilities for the 2010 FIFA World Cup games using a Poisson-Gamma model

In this paper, we provide probabilistic predictions for soccer games of the 2010 FIFA World Cup modelling the number of goals scored in a game by each team. We use a Poisson distribution for the number of goals for each team in a game, where the scoring rate is considered unknown. We use a Gamma distribution for the scoring rate and the Gamma parameters are chosen using historical data and difference among teams defined by a strength factor for each team. The strength factor is a measure of discrimination among the national teams obtained from their memberships to fuzzy clusters. The clusters are obtained with the use of the Fuzzy C-means algorithm applied to a vector of variables, most of them available on the official FIFA website. Static and dynamic models were used to predict the World Cup outcomes and the performance of our predictions was evaluated using two comparison methods.     

Semiparametric Bayesian hierarchical models for heterogeneous population in nonlinear mixed effect model: application to gastric emptying studies

Gastric emptying studies are frequently used in medical research, both human and animal, when evaluating the effectiveness and determining the unintended side-effects of new and existing medications, diets, and procedures or interventions. It is essential that gastric emptying data be appropriately summarized before making comparisons between study groups of interest and to allow study the comparisons. Since gastric emptying data have a nonlinear emptying curve and are longitudinal data, nonlinear mixed effect (NLME) models can accommodate both the variation among measurements within individuals and the individual-to-individual variation. However, the NLME model requires strong assumptions that are often not satisfied in real applications that involve a relatively small number of subjects, have heterogeneous measurement errors, or have large variation among subjects. Therefore, we propose three semiparametric Bayesian NLMEs constructed with Dirichlet process priors, which automatically cluster sub-populations and estimate heterogeneous measurement errors. To compare three semiparametric models with the parametric model we propose a penalized posterior Bayes factor. We compare the performance of our semiparametric hierarchical Bayesian approaches with that of the parametric Bayesian hierarchical approach. Simulation results suggest that our semiparametric approaches are more robust and flexible. Our gastric emptying studies from equine medicine are used to demonstrate the advantage of our approaches.     

Neutral umpires and leg before wicket decisions in test cricket

Summary.  The proportions of dismissals which were leg before wicket in test cricket matches during 1978–2004 are analysed by using generalized linear and mixed models to assess the effect of location, team and the presence or otherwise of neutral umpires. The location and the team batting are clearly significant. There is also clear evidence of an interaction showing that some teams' players are out leg before wicket less often at home but there is no further interaction with neutral umpires, suggesting that this is not caused simply by home umpires favouring the home team.     

Markov Poisson regression models for discrete time series. Part 1: Methodology

This paper proposes and investigates a class of Markov Poisson regression models in which Poisson rate functions of covariates are conditional on unobserved states which follow a finite-state Markov chain. Features of the proposed model, estimation, inference, bootstrap confidence intervals, model selection and other implementation issues are discussed. Monte Carlo studies suggest that the proposed estimation method is accurate and reliable for single- and multiple-subject time series data; the choice of starting probabilities for the Markov process has little eff ect on the parameter estimates; and penalized likelihood criteria are reliable for determining the number of states. Part 2 provides applications of the proposed model.     

利用概率模型估算广东篮球彩票的中奖概率

2006年足球单场竞猜异常火爆,而全国联网篮彩却一直惨淡经营,竞猜型广东篮球彩票也只试行四个月就夭折,主要问题是篮球玩法和奖金设置不够合理.如何挽救低迷中的篮彩.是一个值得研究的课题,为使广东篮彩成为未来篮彩市场的主流.本文建议提高广东篮彩一等奖的返奖率,并给予保本优惠,再增设二等奖,在此基础上利用美国全国篮球联赛2004-2005赛季的数据建立概率模型来估计中奖概率,为奖金合理设置提供有益的参考.     

Are football referees really biased and inconsistent?: evidence on the incidence of disciplinary sanction in the English Premier League

Summary.  The paper presents a statistical analysis of patterns in the incidence of disciplinary sanction (yellow and red cards) that were taken against players in the English Premier League over the period 1996–2003. Several questions concerning sources of inconsistency and bias in refereeing standards are examined. Evidence is found to support a time consistency hypothesis, that the average incidence of disciplinary sanction is predominantly stable over time. However, a refereeing consistency hypothesis, that the incidence of disciplinary sanction does not vary between referees, is rejected. The tendency for away teams to incur more disciplinary points than home teams cannot be attributed to the home advantage effect on match results and appears to be due to a refereeing bias favouring the home team.     

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.     

A LOTTO SYSTEMS PROBLEM

A Lotto Systems bet allows the player to nominate n numbers from which (s)he believes the winning six numbers will be drawn, and to bet on all combinations of six of these n numbers. Assume that the winning six numbers come from the nominated n. How many combinations must be entered to guarantee that one combination will include at least five of the winning six numbers? The problem is generalized in this paper, and the method of simulated annealing is used to find solutions for various situations. The case where two supplementary numbers are drawn after the initial six winning numbers is also considered.     

A comparison of two approaches for power and sample size calculations in logistic regression models

Whittemore (1981) proposed an approach for calculating the sample size needed to test hypotheses with specified significance and power against a given alternative for logistic regression with small response probability. Based on the distribution of covariate, which could be either discrete or continuous, this approach first provides a simple closed-form approximation to the asymptotic covariance matrix of the maximum likelihood estimates, and then uses it to calculate the sample size needed to test a hypothesis about the parameter. Self et al. (1992) described a general approach for power and sample size calculations within the framework of generalized linear models, which include logistic regression as a special case. Their approach is based on an approximation to the distribution of the likelihood ratio statistic. Unlike the Whittemore approach, their approach is not limited to situations of small response probability. However, it is restricted to models with a finite number of covariate configurations. This study compares these two approaches to see how accurate they would be for the calculations of power and sample size in logistic regression models with various response probabilities and covariate distributions. The results indicate that the Whittemore approach has a slight advantage in achieving the nominal power only for one case with small response probability. It is outperformed for all other cases with larger response probabilities. In general, the approach proposed in Self et al. (1992) is recommended for all values of the response probability. However, its extension for logistic regression models with an infinite number of covariate configurations involves an arbitrary decision for categorization and leads to a discrete approximation. As shown in this paper, the examined discrete approximations appear to be sufficiently accurate for practical purpose.     

Some statistical analysis issues at the World Fertility Survey

"The World Fertility Survey carried out cross-sectional probability surveys of fertility in more than 40 developing countries between 1972 and 1984. Statistical issues in regression analysis of the data are reviewed, including treatment of interactions, the selection of regressor variables, and appropriate linear models for rate variables. Similar issues arise in many other applications of regression to observational data."     

Who wins the football?

Portsmouth have dumped their manager—will it change their results? Chelsea are on a winning streak—does it mean anything? Media pundits and sports fans—and punters—devote time and energy to speculation about who will win Saturday's beautiful game. The discussions—in pubs, newspapers and dressing rooms—are usually based on subjective opinion, or evidence that is at best partial or impressionistic. Can statisticians do better? John Goddard offers a large-scale analysis of patterns in English league results from the past 35 football seasons—new managers, winning and losing streaks, home advantages and all.     

Patterns of NBA team performance from 1950 to 1998

This paper examines team performance in the NBA over the last five decades. It was motivated by two previous observational studies, one of which studied the winning percentages of professional baseball teams over time, while the other examined individual player performance in the NBA. These studies considered professional sports as evolving systems, a view proposed by evolutionary biologist Stephen Jay Gould, who wrote extensively on the disappearance of .400 hitters in baseball. Gould argued that the disappearance is actually a sign of improvement in the quality of play, reflected in the reduction of variability in hitting performance. The previous studies reached similar conclusions in terms of winning percentages of baseball teams, and performance of individual players in basketball. This paper uses multivariate measures of team performance in the NBA to see if similar characteristics of evolution can be observed. The conclusion does not appear to be clearly affirmative, as in previous studies, and possible reasons for this are discussed.     

Modelling the evolution of distributions: an application to Major League baseball

Summary.  We develop Bayesian techniques for modelling the evolution of entire distributions over time and apply them to the distribution of team performance in Major League baseball for the period 1901–2000. Such models offer insight into many key issues (e.g. competitive balance) in a way that regression-based models cannot. The models involve discretizing the distribution and then modelling the evolution of the bins over time through transition probability matrices. We allow for these matrices to vary over time and across teams. We find that, with one exception, the transition probability matrices (and, hence, competitive balance) have been remarkably constant across time and over teams. The one exception is the Yankees, who have outperformed all other teams.     

ESTIMATING WITHIN-HOUSEHOLD CONTACT NETWORKS FROM EGOCENTRIC DATA

Acute respiratory diseases are transmitted over networks of social contacts. Large-scale simulation models are used to predict epidemic dynamics and evaluate the impact of various interventions, but the contact behavior in these models is based on simplistic and strong assumptions which are not informed by survey data. These assumptions are also used for estimating transmission measures such as the basic reproductive number and secondary attack rates. Development of methodology to infer contact networks from survey data could improve these models and estimation methods. We contribute to this area by developing a model of within-household social contacts and using it to analyze the Belgian POLYMOD data set, which contains detailed diaries of social contacts in a 24-hour period. We model dependency in contact behavior through a latent variable indicating which household members are at home. We estimate age-specific probabilities of being at home and age-specific probabilities of contact conditional on two members being at home. Our results differ from the standard random mixing assumption. In addition, we find that the probability that all members contact each other on a given day is fairly low: 0.49 for households with two 0-5 year olds and two 19-35 year olds, and 0.36 for households with two 12-18 year olds and two 36+ year olds. We find higher contact rates in households with 2-3 members, helping explain the higher influenza secondary attack rates found in households of this size.     

Order statistics and the length of the best-n-of-(2n − 1) competition

The best-4-of-7 series is a popular playoff format to decide the champion in most North American professional sports. World Series (best-4-of-7) type competitions give rise to interesting probabilistic and statistical questions. We determine the expected length of this type of series by relating it to a problem involving order statistics. We also calculate the variance of the length and provide a simple formula for series of fair games. The method can be extended to derive higher order moments. This novel approach leads to new results that can be formulated in closed forms in terms of the distribution function of various binomial distributions. The emphasis is on establishing the connection to order statistics and obtaining closed forms. The relation to the negative binomial distribution as well as to the sooner waiting time problem in sequential testing is also discussed. We also consider the case when ties are allowed in the single games.