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.     

Linear Conditional Expectation for Discretized Distributions

Many statistical methods for continuous distributions assume a linear conditional expectation. Components of multivariate distributions are often measured on a discrete ordinal scale based on a discretization of an underlying continuous latent variable. The results in this paper show that common examples of discretized bivariate and trivariate distributions will have a linear conditional expectation. Examples and simulations are provided to illustrate the results.     

Dynamic Bayesian forecasting of AFL match results using the Skellam distribution

The scoring and defensive abilities of Australian Rules Football teams change over time as a result of evolving player rosters, tactics and other management factors. We develop a dynamic model based on the Poisson difference (Skellam) distribution which simultaneously models the two different point scoring mechanisms in Australian Rules Football, the motivation for which comes from work on predicting outcomes in soccer matches. Our model is developed in a Bayesian framework and is fitted using the Stan modelling language. Model validation is performed on the 2015 Australian Football league (AFL) home and away season.     

Non-parametric procedure for knockout tournaments

In a seeded knockout tournament, where teams have some preassigned strength, do we have any assurances that the best team in fact has won? Is there some insight to be gained by considering which teams beat which other teams solely examining the seeds? We pose an answer to these questions by using the difference in the seeds of the two players as the basis for a test statistic. We offer several models for the underlying probability structure to examine the null distribution and power functions and determine these for small tournaments (less than five teams). One structure each for 8 teams and 16 teams is examined, and we conjecture an asymptotic normal distribution for the test statistic.     

Common singular spectrum analysis of several time series

Singular spectrum analysis (SSA) is a non-parametric time series modelling technique where an observed time series is unfolded into the column vectors of a Hankel structured matrix, known as a trajectory matrix. For noise-free signals the column vectors of the trajectory matrix lie on a single R-flat. Singular value decomposition (SVD) can be used to find the orthonormal base vectors of the linear subspace parallel to this R-flat. SSA can essentially handle functions that are governed by a linear recurrent formula (LRF) and include the broad class of functions that was proposed by Buchstaber [1994. Time series analysis and Grassmannians. Amer. Math. Soc. Transl. 162 (2), 1–17]. SSA is useful to model time series with complex cyclical patterns that increase over time.Various methods have been studied to extend SSA for application to several time series, see Golyandina et al. [2003. Variants of the Caterpillar SSA-method for analysis of multidimensional time series (in Russian) hhttp://www.gistatgroup.com/cat/i]. Prior to that Von Storch and Zwiers (1999) and Allen and Robertson (1996) (see Ghil et al. [2002. Advanced spectral methods for climatic time series. Rev. Geophys. 40 (1), 3.1–3.41]) used multi-channel SSA (M-SSA), to apply SSA to “grand” block matrices. Our approach is different from all of these by using the common principal components approaches introduced by Flury [1988. Common Principal Components and Related Multivariate Models. Wiley, New York]. In this paper SSA is extended to several time series which are similar in some respects, like cointegrated, i.e. sharing a common R-flat. By using the common principal component (CPC) approach of Flury [1988. Common Principal Components and Related Multivariate Models. Wiley, New York] the SSA method is extended to common singular spectrum analysis (CSSA) where common features of several time series can be studied. CSSA decomposes the different original time series into the sum of a common small number of components which are related to common trend and oscillatory components and noise. The determination of the most likely dimension of the supporting linear subspace is studied using a heuristic approach and a hierarchical selection procedure.     

Estimation of factor-augmented panel regressions with weakly influential factors

The use of factor-augmented panel regressions has become very popular in recent years. Existing methods for such regressions require that the common factors are strong, an assumption that is likely to be mistaken in practice. Motivated by this, the current article offers an analysis of the effect of weak, semi-weak, and semi-strong factors on two of the most popular estimators for factor-augmented regressions, namely, principal components (PC) and common correlated effects (CCE).     

Soccer matches as experiments: how often does the ‘best’ team win?

Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is superior and examine the probability that the outcome of the experiment (match) truly represents the relative abilities of the two teams. Given a final score, it is possible by using a Bayesian approach to quantify the probability that it was or was not the case that ‘the best team won’. For typical scores, the probability of a misleading result is significant. Modifying the rules of the game to increase the typical number of goals scored would improve the situation, but a level of confidence that would normally be regarded as satisfactory could not be obtained unless the character of the game was radically changed.     

Go,Team! Using Teams to Manage Electronic Resources

The increasing prevalence of ejournals in library collections has impacted many aspects of library operations. Libraries have had to rethink workflows, processes, staffing needs, and other factors to account for the differences between print and online journals. The management of ejournals can often cross departmental boundaries and bring into question current workflow. To address the changing landscape of journal management, the University at Albany Libraries developed two teams: one to implement batchloading ejournal records and a second to address ongoing management and related policies. As a result of using a team approach for these responsibilities, the University Libraries was able to streamline processes, reduce duplication of effort across departments, coordinate policies and procedures, improve communication, and develop best practices.     

Reliability Estimation Based on System Data with an Unknown Load Share Rule

We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) the system load is distributed evenly among the working components, and (2) we assume only the load for each working component increases when other components in the system fail. Tests for these special load-share models are investigated.     

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.     

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.     

创新导向团队薪酬及其契约设计的实验研究

团队合作是现代企业创新活动的主要工作方式,团队薪酬的模式选择与契约设计对于企业创新具有重要意义。本文设计了一项奶茶店团队经营实验,采用实验研究的方法检验不同模式下团队薪酬对创新绩效的影响,以及团队薪酬中探索性薪酬的授予范围和业绩考核强度对创新绩效的影响。结果表明:与固定薪酬和浮动薪酬相比,探索性薪酬模式下实验团队的创新投入水平更高、创新产出更多;对于授予范围来说,与不授予探索性薪酬、较小范围授予探索性薪酬及全部授予探索性薪酬模式相比,较大范围授予探索性薪酬时实验团队的创新投入水平更高、创新产出更多;对于业绩考核强度来说,与宽松型业绩考核强度和严格型业绩考核强度相比,适中型业绩考核强度下实验团队的创新投入水平更高、创新产出更多;团队的风险规避程度同样影响创新绩效,探索性薪酬模式下风险偏好的团队普遍有更好的创新投入表现。本文的研究丰富了团队薪酬及其契约设计与创新绩效的相关文献,为企业设计创新导向的团队薪酬契约提供了理论依据。     

Having a ball: evaluating scoring streaks and game excitement using in-match trend estimation

AStA Advances in Statistical Analysis - Many popular sports involve matches between two teams or players where each team have the possibility of scoring points throughout the match. While the...     

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.     

企业持续改进能力的组织与运作——贵州省企业与全球企业之比较分析

主要采用主成分分析方法,综合主成分分析方法和系统聚类方法等多元统计中的数据处理手段,对全球可持续创新网络(CInet)于2004年组织调查的全球近500家企业所得数据进行分析。通过贵州省企业与全球其他国家的比较,发现在企业持续改进能力的组织与运作方面,贵州省企业与全球其他国家之间存在较大差异。为寻找造成这些差异的原因,采用综合主成分分析方法和系统聚类方法,建立了在持续改进的组织与运作方面能力强的目标企业群。然后通过贵州省企业与目标企业之间在企业组织与运作构成因子的对比分析,指出了贵州省企业在持续改进的组织与运作中所存在的问题,进而对贵州省企业提出了相应改进的建议及其对策。其中,目标企业的选取及其创新能力检验、数据表缺省项的填充方法、在分析数据时所采用的因子对比分析方法等对其他大型调研数据分析均具有一定的借鉴意义。     

Missing data and forecasting in multivariate time series: An application of the common components dynamic linear model

Summary The paper deals with missing data and forecasting problems in multivariate time series making use of the Common Components Dynamic Linear Model (DLMCC), presented in Quintana (1985), and West and Harrison (1989). Some results are presented and discussed: exploiting the correlation between series, estimated by the DLMCC, the paper shows as it is possible to update state vector posterior distributions for the unobserved series. This is realized on the base of the updating of the observed series state vectors, for which the usual Kalman filter equations can be applied. An application concerning some Italian private consumption series provides an example of the model capabilities.     

Case study in data analysis: The genetic analysis of inflammatory bowel disease

Four teams of analysts try to determine the existence of an association between inflammatory bowel disease and certain genetic markers on human chromosome number 6. Their investigation involves data on several control populations and on 110 familles with two or more affected individuals. The problem is introduced by Mirea, Bull, Silverberg and Siminovitch; they and three other groups (Chen, Kalbfleisch and Romero‐Hidalgo; Darlington and Paterson; Roslin, Loredo‐Osti, Greenwood and Morgan) present analyses. Their approaches are discussed by Field and Smith.     

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     

Decompositions by sources and by subpopulations of the Pietra index: two applications to professional football teams in Italy

In this paper two innovative procedures for the decomposition of the Pietra index are proposed. The first one allows the decomposition by sources, while the second one provides the decomposition by subpopulations. As special case of the latter procedure, the “classical” decomposition in two components (within and between) can be easily obtained. A remarkable feature of both the proposed procedures is that they permit the assessment of the contribution to the Pietra index at the smallest possible level: each source for the first one and each subpopulation for the second one. To highlight the usefulness of these procedures, two applications are provided regarding Italian professional football (soccer) teams.

     

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.