Wheelchair basketball, regulated by the International Wheelchair Basketball Federation, is a sport designed for individuals with physical disabilities. This paper presents a data-driven tool that effectively determines optimal team line-ups based on past performance data and metrics for player effectiveness. Our proposed methodology involves combining a Bayesian longitudinal model with an integer linear problem to optimise the line-up of a wheelchair basketball team. To illustrate our approach, we use real data from a team competing in the Rollstuhlbasketball Bundesliga, namely the Doneck Dolphins Trier. We consider three distinct performance metrics for each player and incorporate uncertainty from the posterior predictive distribution of the longitudinal model into the optimisation process. The results demonstrate the tool's ability to select the most suitable team compositions and calculate posterior probabilities of compatibility or incompatibility among players on the court.
Maddox, et al. (2022) establish a new win probability estimation for college basketball and compared the results with previous methods of Stern (1994), Desphande and Jensen (2016) and Benz (2019). This paper proposes modifications to the approach of Maddox, et al. (2022) for the NBA game and investigates the performance of the model. Enhancements to the model are developed, and the resulting adjusted model is compared with existing methods and to the ESPN counterpart. To illustrate utility, all methods are applied to the November 23, 2019 game between the Chicago Bulls and Charlotte Hornets.
Every shot in basketball has an opportunity cost; one player's shot eliminates all potential opportunities from their teammates for that play. For this reason, player-shot efficiency should ultimately be considered relative to the lineup. This aspect of efficiency---the optimal way to allocate shots within a lineup---is the focus of our paper. Allocative efficiency should be considered in a spatial context since the distribution of shot attempts within a lineup is highly dependent on court location. We propose a new metric for spatial allocative efficiency by comparing a player's field goal pe…
Two new Bayesian methods for estimating and predicting in-game home team win probabilities are proposed. The first method has a prior that adjusts as a function of lead differential and time elapsed. The second is an adjusted version of the first, where the adjustment is a linear combination of the Bayesian estimator with a time-weighted pre-game win probability. The proposed methods are compared to existing methods, showing the new methods perform better for both estimation and prediction. The utility is illustrated via an application to the 2016 NCAA Division 1 Championship game.
In this paper we model basketball plays as episodes from team-specific non-stationary Markov decision processes (MDPs) with shot clock dependent transition probabilities. Bayesian hierarchical models are employed in the modeling and parametrization of the transition probabilities to borrow strength across players and through time. To enable computational feasibility, we combine lineup-specific MDPs into team-average MDPs using a novel transition weighting scheme. Specifically, we derive the dynamics of the team-average process such that the expected transition count for an arbitrary state-pair…
In recent years, analytics has started to revolutionize the game of basketball: quantitative analyses of the game inform team strategy, management of player health and fitness, and how teams draft, sign, and trade players. In this review, we focus on methods for quantifying and characterizing basketball gameplay. At the team level, we discuss methods for characterizing team strategy and performance, while at the player level, we take a deep look into a myriad of tools for player evaluation. This includes metrics for overall player value, defensive ability, and shot modeling, and methods for un…
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 na…
What Influences the Field Goal Attempts of Professional Players? Analysis of Basketball Shot Charts via Log Gaussian Cox Processes with Spatially Varying Coefficients
In sports betting it is easier to predict the winner of a game match than the team that covers the bet. Since, a winner team might not cover a bet. This study focuses on the relation of the variable win to the betting variable cover the point spread. The study is performed with data from professional basketball (betting lines and scores) and tries to answer the question: Does the winning team always covers the point spread?. In order to answer this question, a regression analysis is performed taking into account the most and less winning teams, together with their betting variables since the 1…
In the domain of Sport Analytics, Global Positioning Systems devices are intensively used as they permit to retrieve players' movements. Team sports' managers and coaches are interested on the relation between players' patterns of movements and team performance, in order to better manage their team. In this paper we propose a Cluster Analysis and Multidimensional Scaling approach to find and describe separate patterns of players movements. Using real data of multiple professional basketball teams, we find, consistently over different case studies, that in the defensive clusters players are clo…
Basketball players' performance measurement is of critical importance for a broad spectrum of decisions related to training and game strategy. Despite this recognized central role, the main part of the studies on this topic focus on performance level measurement, neglecting other important characteristics, such as variability. In this paper, shooting performance variability is modeled with a Markov Switching dynamic, assuming the existence of two alternating performance regimes. Then, the relationships between each player's variability and the lineup composition is modeled as an ARIMA process …
For professional basketball, finding valuable and suitable players is the key to building a winning team. To deal with such challenges, basketball managers, scouts and coaches are increasingly turning to analytics. Objective evaluation of players and teams has always been the top goal of basketball analytics. Typical statistical analytics mainly focuses on the box score and has developed various metrics. In spite of the more and more advanced methods, metrics built upon box score statistics provide limited information about how players interact with each other. Two players with similar box sco…
The main objective of this paper is to investigate the extent to which the margin of victory can be predicted solely by the rankings of the opposing teams in NCAA Division I men's basketball games. Several past studies have modeled this relationship for the games played during the March Madness tournament, and this work aims at verifying if the models advocated in these papers still perform well for regular season games. Indeed, most previous articles have shown that a simple quadratic regression model provides fairly accurate predictions of the margin of victory when team rankings only range …
Statistical applications in sports have long centered on how to best separate signal (e.g. team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript, we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the…
Box score statistics are the baseline measures of performance for National Collegiate Athletic Association (NCAA) basketball. Between the 2011-2012 and 2015-2016 seasons, NCAA teams performed better at home compared to on the road in nearly all box score statistics across both genders and all three divisions. Using box score data from over 100,000 games spanning the three divisions for both women and men, we examine the factors underlying this discrepancy. The prevalence of neutral location games in the NCAA provides an additional angle through which to examine the gaps in box score statistic …
Maddox, et al. [9, 10] establish Bayesian methods for estimating home-team in-game win probability for college and NBA basketball. This paper introduces a Bayesian approach for estimating in-game home-team win probability for Division-I FBS college (American) football that uses expected number of remaining possessions and expected score as two predictors. Models for estimating these are presented and compared. These, along with other predictors are introduced into two Bayesian approaches for the final estimate of in-game home-team win probability. To illustrate utility, methods are applied to …
Experience is an important asset in almost any professional activity. In basketball, there is believed to be a positive association between coaching experience and effective use of team timeouts. Here, we analyze both the extent to which a team's change in scoring margin per possession after timeouts deviate from the team's average scoring margin per possession---what we called timeout factor, and the extent to which this performance measure is associated with coaching experience across all teams in the National Basketball Association over the 2009-2012 seasons. We find that timeout factor pla…
A new approach in team sports analysis consists in studying positioning and movements of players during the game in relation to team performance. State of the art tracking systems produce spatio-temporal traces of players that have facilitated a variety of research aimed to extract insights from trajectories. Several methods borrowed from machine learning, network and complex systems, geographic information system, computer vision and statistics have been proposed. After having reviewed the state of the art in those niches of literature aiming to extract useful information to analysts and expe…
Many popular sports involve matches between two teams or players where each team have the possibility of scoring points throughout the match. While the overall match winner and result is interesting, it conveys little information about the underlying scoring trends throughout the match. Modeling approaches that accommodate a finer granularity of the score difference throughout the match is needed to evaluate in-game strategies, discuss scoring streaks, teams strengths, and other aspects of the game. We propose a latent Gaussian process to model the score difference between two teams and introd…
It is common to be interested in rankings or order relationships among entities. In complex settings where one does not directly measure a univariate statistic upon which to base ranks, such inferences typically rely on statistical models having entity-specific parameters. These can be treated as random effects in hierarchical models characterizing variation among the entities. In this paper, we are particularly interested in the problem of ranking basketball players in terms of their contribution to team performance. Using data from the United States National Basketball Association (NBA), we …
This paper develops metrics from a social network perspective that are directly translatable to the outcome of a basketball game. We extend a state-of-the-art multi-resolution stochastic process approach to modeling basketball by modeling passes between teammates as directed dynamic relational links on a network and introduce multiplicative latent factors to study higher-order patterns in players' interactions that distinguish a successful game from a loss. Parameters are estimated using a Markov chain Monte Carlo sampler. Results in simulation experiments suggest that the sampling scheme is e…
Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of skill. This indicates the relative presence of luck and skill. We collected and analyzed all games from 198 sports leagues comprising 1503 seasons from 84 countries of 4 different sports: basketball, soccer, volleyball and handball. We measured the competitiveness by countries and sports. We also identify in each season which teams, if removed from its leag…
I address the difficult challenge of measuring the relative influence of competing basketball game strategies, and I apply my analysis to plays resulting in three-point shots. I use a glut of SportVU player tracking data from over 600 NBA games to derive custom position-based features that capture tangible game strategies from game-play data, such as teamwork, player matchups, and on-ball defender distances. Then, I demonstrate statistical methods for measuring the relative importance of any given basketball strategy. In doing so, I highlight the high importance of teamwork based strategies in…
Basketball games evolve continuously in space and time as players constantly interact with their teammates, the opposing team, and the ball. However, current analyses of basketball outcomes rely on discretized summaries of the game that reduce such interactions to tallies of points, assists, and similar events. In this paper, we propose a framework for using optical player tracking data to estimate, in real time, the expected number of points obtained by the end of a possession. This quantity, called \textit{expected possession value} (EPV), derives from a stochastic process model for the evol…
In this paper, we describe an approach to rank sport players based on their efficiency. Although is extremely useful to analyze the performance of team games there is no unanimity on the use of a single index to perform such a ranking. We propose a method to summarize the huge amount of information collected at different aspects of a sport team which is almost daily publicly available. The tool will allow agents involved in a player's negotiation to show the strengths (and weaknesses) of the player with respect to other players. The approach is based on applying a multicriteria outranking meth…
Big Data Analytics help team sports' managers in their decisions by processing a number of different kind of data. With the advent of Information Technologies, collecting, processing and storing big amounts of sport data in different form became possible. A problem that often arises when using sport data regards the need for automatic data cleaning procedures. In this paper we develop a data cleaning procedure for basketball which is based on players' trajectories. Starting from a data matrix that tracks the movements of the players on the court at different moments in the game, we propose an …
Although basketball is a dynamic process sport, with 5 plus 5 players competing on both offense and defense simultaneously, learning some static information is predominant for professional players, coaches and team mangers. 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 recovers the large proportion of the court with zero field goal attempts,…
Motivated by the goal of evaluating real-time forecasts of home team win probabilities in the National Basketball Association, we develop new tools for measuring the quality of continuously updated probabilistic forecasts. This includes introducing calibration surface plots, and simple graphical summaries of them, to evaluate at a glance whether a given continuously updated probability forecasting method is well-calibrated, as well as developing statistical tests and graphical tools to evaluate the skill, or relative performance, of two competing continuously updated forecasting methods. These…
In the sports of soccer, hockey and basketball the most commonly used statistics for player performance assessment are divided into two categories: offensive statistics and defensive statistics. However, qualitative assessments of playmaking (for example making "smart" passes) are difficult to quantify. It would be advantageous to have available a single statistic that can emphasize the flow of a game, rewarding those players who initiate and contribute to successful plays more. In this paper we will examine a model based on Google's PageRank. Other papers have explored ranking teams, coaches,…
We consider a study of players employed by teams who are members of the National Basketball Association where units of observation are functional curves that are realizations of production measurements taken through the course of one's career. The observed functional output displays large amounts of between player heterogeneity in the sense that some individuals produce curves that are fairly smooth while others are (much) more erratic. We argue that this variability in curve shape is a feature that can be exploited to guide decision making, learn about processes under study and improve predic…
Data analytics in sports is crucial to evaluate the performance of single players and the whole team. The literature proposes a number of tools for both offence and defence scenarios. Data coming from tracking location of players, in this respect, may be used to enrich the amount of useful information. In basketball, however, actions are interleaved with inactive periods. This paper describes a methodological approach to automatically identify active periods during a game and to classify them as offensive or defensive. The method is based on the application of thresholds to players kinematic p…
How much is an on-ball screen worth? How much is a backdoor cut away from the ball worth? Basketball is one of a number of sports which, within the past decade, have seen an explosion in quantitative metrics and methods for evaluating players and teams. However, it is still challenging to evaluate individual off-ball events in terms of how they contribute to the success of a possession. In this study, we develop an end-to-end deep learning architecture DeepHoops to process a unique dataset composed of spatio-temporal tracking data from NBA games in order to generate a running stream of predict…
To analyze the movements and to study the trajectories of players is a crucial need for a team when it looks to improve its chances of winning a match or to understand its performances. State of the art tracking systems now produce spatio-temporal traces of player trajectories with high definition and frequency that has facilitated a variety of research efforts to extract insight from the trajectories. Despite many methods borrowed from different disciplines (machine learning, network and complex systems, GIS, computer vision, statistics) has been proposed to answer to the needs of teams, a fr…
Soccer is undeniably the most popular sport world-wide and everyone from general managers and coaching staff to fans and media are interested in evaluating players' performance. Metrics applied successfully in other sports, such as the (adjusted) +/- that allows for division of credit among a basketball team's players, exhibit several challenges when applied to soccer due to severe co-linearities. Recently, a number of player evaluation metrics have been developed utilizing optical tracking data, but they are based on proprietary data. In this work, our objective is to develop an open framewor…
The release of NBA player tracking data greatly enhances the granularity and dimensionality of basketball statistics used to evaluate and compare player performance. However, the high dimensionality of this new data source can be troublesome as it demands more computational resources and reduces the ability to easily interpret findings. Therefore, we must find a way to reduce the dimensionality of the data while retaining the ability to differentiate and compare player performance. In this paper, Principal Component Analysis (PCA) is used to identify four principal components that account for …
The North Carolina School of Science and Mathematics（北卡罗来纳科学与数学学院）
Our objective is to find the five best college sports coaches of past century for three different sports. We decided to look at men's basketball, football, and baseball. We wanted to use an approach that could definitively determine team skill from the games played, and then use a machine-learning algorithm to calculate the correct coach skills for each team in a given year. We created a networks-based model to calculate team skill from historical game data. A digraph was created for each year in each sport. Nodes represented teams, and edges represented a game played between two teams. The ar…
