Analytic Methods in Sports

Using Mathematics and Statistics to Understand Data from Baseball, Football, Basketball, and Other Sports

Thomas A Severini

• Publisher: Chapman and Hall/CRC
• Year: 2020
• ISBN:
  9781000050943
• Edition: 2
• Topic: Mathématiques
• Subtopic: Mathématiques générales

One of the greatest changes in the sports world in the past 20 years has been the use of mathematical methods to analyze performances, recognize trends and patterns, and predict results. Analytic Methods in Sports: Using Mathematics and Statistics to Understand Data from Baseball, Football, Basketball, and Other Sports, Second Edition provides a concise yet thorough introduction to the analytic and statistical methods that are useful in studying sports.

The book gives you all the tools necessary to answer key questions in sports analysis. It explains how to apply the methods to sports data and interpret the results, demonstrating that the analysis of sports data is often different from standard statistical analyses. The book integrates a large number of motivating sports examples throughout and offers guidance on computation and suggestions for further reading in each chapter.

Features

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• Covers numerous statistical procedures for analyzing data based on sports results

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• Presents fundamental methods for describing and summarizing data

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• Describes aspects of probability theory and basic statistical concepts that are necessary to understand and deal with the randomness inherent in sports data

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• Explains the statistical reasoning underlying the methods

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• Illustrates the methods using real data drawn from a wide variety of sports

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• Offers many of the datasets on the author's website, enabling you to replicate the analyses or conduct related analyses

New to the Second Edition

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• R code included for all calculations

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• A new chapter discussing several more advanced methods, such as binary response models, random effects, multilevel models, spline methods, and principal components analysis, and more

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• Exercises added to the end of each chapter, to enable use for courses and self-study

• Full solutions manual available to course instructors.
  
  

1

Introduction

1.1 Analytic Methods

Analytic methods use data to draw conclusions and make decisions. The challenge in using these methods is that the messages of the data are not always clear, and it is often necessary to filter out the noise to see the underlying relationships. Therefore, one distinguishing feature of analytic methods is that they recognize the inherent randomness of data and they are designed to extract useful information in the presence of this randomness.

This is particularly important when analyzing sports data because we all know that the results of a game or other sporting event depend not only on the skill of the participants but also on “luck” and randomness, and separating the contribution of skill from that of luck is not always easy. A second difficulty in analyzing sports data is that a sporting event is a type of “observational study,” a study in which important aspects are not under the control of the analyst; that is, we simply observe the data as they are generated, and in contrast to a controlled experiment, we cannot choose which players or teams participate in a particular event or in a given situation.

Given the emphasis on data analysis, it is not surprising that statistical concepts are central to methods presented in this book. Although statistical methodology is a vast topic, fortunately, there are a few central concepts and basic methods that can greatly improve our understanding of data and the processes that generated them. Knowledge in this area will be beneficial to all serious sports fans, whether they simply want to better understand the “new statistics” that have been proposed or whether they want to conduct their own statistical analyses.

There are at least two important roles of statistics in analytic methods. One is the use of statistical methodology designed to efficiently extract relevant information about measurements and their relationships. Statistical models are essential in this process. The models used to analyze sports data are generally empirical rather than based on some underlying theory. That is, the models used describe general features of relationships between variables; such models have been found useful in many fields and form the core of statistical methodology. What distinguishes statistical models from other types of models is the use of the concept of probability in describing relationships; such models are often described as “stochastic,” as opposed to a “deterministic” model, in which probability does not play a role. However, statistical methods do more than recognize randomness; they filter it out, exposing the meaningful relationships in data.

When using statistical models of any type, it is important to keep in mind that they involve some idealization and simplification of complicated physical relationships. However, this does not diminish their usefulness; in fact, it is an essential part of it. Appropriate simplification is a crucial step in stripping away the randomness that often clouds our perception of the salient factors driving sports results.

A second role of statistical concepts in analytic methods is to give a framework for using probability to describe uncertainty. Given the random nature of the results of sporting events, any conclusions we draw from analyzing sports data will naturally have some uncertainty associated with them. Statistical methodology is designed to assess this uncertainty and express it in a useful and meaningful way. Explicit recognition of the random nature of sports is one of the primary contributions of analytic methods, such as those used in sabermetrics, to the analysis of sports data.

1.2 Organization of the Book

Although a central theme of the book is the use of statistical models in understanding and interpreting sports data, before presenting the details of these methods, it is important to understand the basic properties of data. These properties are the subject of Chapter 2, which covers the fundamental methods of describing and summarizing data.

As noted in the previous section, the use of probability theory and statistical methodology to describe relationships and express conclusions is a crucial part of analytic methods. Chapter 3 covers those aspects of probability theory that are necessary to understand the randomness inherent in sports data. These concepts are applied to a number of scenarios in sports in which consideration of the underlying probabilities leads to useful insights. As noted previously, appreciating and understanding randomness is one of the main contributions of analytic methods.

Chapter 4 has several goals. One is to describe the statistical reasoning that underlies the analytic methods described in this book. Another is to present some basic statistical concepts, such as the margin of error and statistical significance, that play a central role in dealing with the randomness of sports data. Finally, Chapter 4 covers some basic statistical methods that are essential in studying sports data.

Chapters 5 through 7 develop the core statistical procedures for analyzing data based on sports results. Chapter 5 is concerned with detecting the presence of a relationship between variables and measuring the strength of such relationships. Several different methods are presented, designed to deal with different types of data and different goals for the analysis.

Chapter 6 takes the basic theme of Chapter 5—the relationship between variables—and goes a step further, covering methods for summarizing the relationship between two variables in a concise and useful way. These methods, known collectively as linear regression, use statistical methodology to find a function relating the two variables. The simplest method of this type yields a linear function for the variables; Chapter 6 also covers more sophisticated methods that are used when the relationship is nonlinear.

In Chapter 7, these methods are extended to the case of several variables when we wish to describe one of the variables, known as the response variable, in terms of the others, known as predictors. These methods, also known as linear regression, are perhaps the most commonly used statistical procedures, with applications in a wide range of scientific fields. Chapter 7 contains a detailed discussion of the basic methodology, along with more advanced topics such as the use of categorical variables as predictors, methods for finding the most important predictor, and interaction, which occurs when the effect of one of the predictors depends on the values of other predictors. In addition to the descriptions of the relevant statistical methodology, Chapters 6 and 7 include important information on the strengths and limitations of these methods as well as on the implementation of the methodology and the interpretation of the results.

Chapter 8 discusses some more advanced methods that build on the topics covered in Chapters 5 through 7. Many of these methods are extensions of the regression methodology covered in Chapters 6 and 7, such as logistic regression for modeling the relationship between a binary response variable and predictor variables, and spline models for modeling highly nonlinear relationships. Other methods, such as using pooling to estimate team- and player-specific parameters, principal components analysis for summarizing data, and the use of random effects to analyze variability, introduce new concepts.

The topics covered in this book are similar to those that would be covered in courses on statistical methodology. However, they have been chosen specifically because of their importance and usefulness in analyzing sports data. Therefore, statistical methods that are not useful in analyzing sports data are not covered. Furthermore, many of the topics that are discussed are fairly advanced in the sense that they would not typically be covered in an introductory statistics course.

1.3 Data

The analytic methods described in this book have as their ultimate goal the analysis of data. Therefore, throughout the book, the methodology presented is illustrated on genuine data drawn from a wide variety of sports. Readers are encouraged to replicate these analyses, as well as to conduct related analyses using their own data.

There is no shortage of data available on the internet. Some sites that have been found useful include sites operated by sports leagues or organizations (e.g., MLB.com, NFL.com, PGA.com, etc.); the sites operated by news organizations (e.g., ESPN.com, SI.com, yahoo.sports.com, etc.); the sports reference sites (e.g., Baseball-Reference.com, Pro-Football-Reference.com); and independent sites such as FanGraphs.com. The “Reference.com” sites (e.g., Baseball-Reference.com and Pro-Football-Reference.com) are particularly noteworthy for the detailed data available and for their search engines, which are invaluable for finding data relevant to a specific question. Although some of these features require a modest subscription fee, for serious study of sports, the cost is minor.

For many of the examples given in this book, there are several possible sources for the data, and a specific source is not given. This is generally the case when the data analyzed are based directly on game results. Although all sites for a given sport contain the same basic data, different sites often contain different specialized data, such as “splits,” data for specific situations, or “advanced statistics” that have ...