Paired comparison models applied to the design of the Major League baseball play-offs

This paper presents an analysis of the eff ect of various baseball play-off configurations on the probability of advancing to the World Series. Play-off games are assumed to be independent. Several paired comparisons models are considered for modeling the probability of a home team winning a single game as a function of the winning percentages of the contestants over the course of the season. The uniform and logistic regression models are both adequate, whereas the Bradley-Terry model (modified for within-pair order eff ects, i.e. the home field advantage) is not. The single-game probabilities are then used to compute the probability of winning the play-off s under various structures. The extra round of play-off s, instituted in 1994, significantly lowers the probability of the team with the best record advancing to the World Series, whereas home field advantage and the diff erent possible play-offdraws have a minimal eff ect.     

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.     

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     

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.     

An Evaluation of Major League Baseball Offensive Performance Models

Numerous statistics have been proposed to evaluate offensive performance in baseball. Each statistic or estimator can be related to an explicit run production model. An evaluation of ten run production models is presented based on major league team run production in the period 1969–1976. The results are applied to evaluating individual players in both the American and National baseball leagues.     

A Starting Point for Navigating the World of Daily Fantasy Basketball

Fantasy sports, particularly the daily variety in which new lineups are selected each day, are a rapidly growing industry. The two largest companies in the daily fantasy business, DraftKings and Fanduel, have been valued as high as $2 billion. This research focuses on the development of a complete system for daily fantasy basketball, including both the prediction of player performance and the construction of a team. First, a Bayesian random effects model is used to predict an aggregate measure of daily NBA player performance. The predictions are then used to construct teams under the constraints of the game, typically related to a fictional salary cap and player positions. Permutation based and K-nearest neighbors approaches are compared in terms of the identification of “successful” teams—those who would be competitive more often than not based on historical data. We demonstrate the efficacy of our system by comparing our predictions to those from a well-known analytics website, and by simulating daily competitions over the course of the 2015–2016 season. Our results show an expected profit of approximately $9,000 on an initial $500 investment using the K-nearest neighbors approach, a 36% increase relative to using the permutation-based approach alone. Supplementary materials for this article are available online.     

Bayesian binary segmentation procedure for detecting streakiness in sports

Summary.  When an individual player or team enjoys periods of good form, and when these occur, is a widely observed phenomenon typically called 'streakiness'. It is interesting to assess which team is a streaky team, or who is a streaky player in sports. Such competitors might have a large number of successes during some periods and few or no successes during other periods. Thus, their success rate is not constant over time. We provide a Bayesian binary segmentation procedure for locating changepoints and the associated success rates simultaneously for these competitors. The procedure is based on a series of nested hypothesis tests each using the Bayes factor or the Bayesian information criterion. At each stage, we only need to compare a model with one changepoint with a model based on a constant success rate. Thus, the method circumvents the computational complexity that we would normally face in problems with an unknown number of changepoints. We apply the procedure to data corresponding to sports teams and players from basketball, golf and baseball.     

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.     

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。     

Zero-inflated Poisson model with clustered regression coefficients: Application to heterogeneity learning of field goal attempts of professional basketball players

Although basketball is a dynamic process sport, played between two sides of five players each, learning some static information is essential for professional players, coaches, and team managers. In order to have a deep understanding of field goal attempts among different players, we propose a zero-inflated Poisson model with clustered regression coefficients to learn the shooting habits of different players over the court and the heterogeneity among them. Specifically, the zero-inflated model captures a large portion of the court with zero field goal attempts, and the mixture of finite mixtures model captures the heterogeneity among different players based on clustered regression coefficients and inflated probabilities. Both theoretical and empirical justification through simulation studies validate our proposed method. We apply our proposed model to data from the National Basketball Association (NBA), for learning players' shooting habits and heterogeneity among different players over the 2017–2018 regular season. This illustrates our model as a way of providing insights from different aspects.     

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.     

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.     

Measuring the Experience-Productivity Relationship: The Case of Major League Baseball

This article develops and estimates a model of the typical major league baseball player's lifetime batting average profile. The batting average profile can be thought of as an experience-productivity relationship. The estimation techniques are those suggested by MaCurdy (1981 a, b) for estimating model parameters when using panel data, including the parameters of the error structure. The method could be used to estimate the relationship between experience and productivity in any situation where a measure of individual output is available. The results include estimates of the peak of a baseball player's career and the rate at which batting averages change with age.     

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.     

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.     

Studying improved performance in golf

The topic of improved performances by athletes in both team and individual sports has shown that each sport has its own unique set of characteristics and these have to be analysed accordingly. This paper presents an extensive analysis of the nature and extent of improvement in golf by analysing the performances of the top players in the Masters tournament throughout the entire history of the event. The results indicate that golfers are obtaining lower scores over time and that the variation of the scores has declined. Further, the distributions of scores are symmetric and display a monotonic reduction of peakedness (kurtosis). These findings are indicative of rapid and improved performance and increased competition.     

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.     

Best-Ball Events in Golf: An Application of the Multinomial Distribution

Probability models are developed for two-man teams in best-ball events in golf. The multinomial distribution is used to develop the theoretical probabilities for possible team scores. Here each individual player is assigned a set of probabilities for making a certain score on each hole of an 18-hole round of golf. The two-man team results are compared with the 1980-1982 Bing Crosby Pro-Ams held in Monterey, California.     

Measuring sport performances under pressure by classification trees with application to basketball shooting

Measuring players'' performance in team sports is fundamental since managers need to evaluate players with respect to the ability to score during crucial moments of the game. Using Classification and Regression Trees (CART) and play-by-play basketball data, we estimate the probabilities to score the shot with respect to a selection of game covariates related to game pressure. We use scoring probabilities to develop a player-specific shooting performance index that takes into account for the difficulty associated to score different types of shots. By applying this procedure to a large sample of 2016–2017 Basketball Champions League (BCL) and 2017–2018 National Basketball Association (NBA) games, we compare the factors affecting shooting performance in Europe and in the United States and we evaluate a selection of players in terms of the proposed shooting performance index with the final aim of providing useful guidelines for the team strategy.     

Discovering associations between players' performance indicators and matches' results in the European Soccer Leagues

The application of data mining techniques and statistical analysis to the sports field has received increasing attention in the last decade. One of the most famous sports in the world is soccer, and the present work deals with it, using data from the 2009/2010 season to the 2015/2016 season from nine European leagues extracted from the Kaggle European Soccer database. Overall performance indicators of the four roles in a soccer team (forward, midfielder, defender and goalkeeper) for home and away teams are used to investigate the relationships between them and the results of matches, and to predict the wins of the home team. The model used to answer both these demands is the Bayesian Network. This study shows that this model can be very useful for mining the relations between players'' performance indicators and for improving knowledge of the game strategies applied by coaches in different leagues. Moreover, it is shown that the ability to predict match results of the proposed Bayesian Network is roughly the same as that of the Naive Bayes model.