Analytic Methods in Sports: Using Mathematics and Statistics to Understand Data from Baseball, Football, Basketball, and Other Sports, 1st Edition (Hardback) book cover

Analytic Methods in Sports

Using Mathematics and Statistics to Understand Data from Baseball, Football, Basketball, and Other Sports, 1st Edition

By Thomas A. Severini

Chapman and Hall/CRC

254 pages | 66 B/W Illus.

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Hardback: 9781482237016
pub: 2014-08-05
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The Most Useful Techniques for Analyzing Sports Data

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 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 analysis. Requiring familiarity with mathematics but no previous background in statistics, the book integrates a large number of motivating sports examples throughout and offers guidance on computation and suggestions for further reading in each chapter.


"Professor Severini’s stated aim for this book is ‘to provide a concise but thorough introduction to the analytic and statistical methods that are useful in studying sport’. Overall, the book scores many points in this regard. …

There is much to like throughout this book. It is not long (approximately 250 pages) and assumes almost no background in mathematics apart from some basics of algebra. However, it is dense with quality examples of the use of statistical methods. Those considering adopting this book as a text for an introductory statistics course will be encouraged by the fact that the selection and order of topics coincides with those from many introductory statistics texts. The book is also rich in data with over 40 different datasets the vast majority of which are multivariate and all of which are publicly available at the author’s website: Each chapter finishes with a set of example calculations and a list of further readings on the topics covered in that chapter. …

In summary, Severini’s book on statistical and analytic methods for sports is a winning addition to the literature on the analysis of sport data. It scores well on its goal of being an introduction to statistical methods for such data. The content will suit the intended audience and with some augmentation the book would be quite appropriate to use in teaching a first course on statistical methods that takes sport as focus or motivation."

—Micheal E. Schuckers, St. Lawrence University, in the Australian & New Zealand Journal of Statistics, September 2017

"… this book is ideally suited to someone who has a keen interest in various sports and mathematics and would like to take their interest to a deeper, more quantitative level. I could also imagine using this book as a supplementary resource in an introductory statistics courses given its trove of interesting examples. … the book is extremely well written and includes a multitude of tools for someone interested in quantitative methods in sports. I would highly recommend the book for the audiences described above and, in particular, someone teaching introductory statistics who needs motivating examples for his/her course(s)."

The American Statistician, August 2015

"There is much to like here. The book provides an overview of statistical methods and gives applications of these methods for a wide variety of sports. … the book is a nice complement to other introductory statistics sports texts and could be used in teaching a lively introduction to statistics using sports."

Significance, April 2015

"Students and interested sports fans will find Analytic Methods in Sports very useful for learning the probability and statistics they need to begin analyzing sports data. The author provides the intuition behind the analytic methods discussed, avoiding overly technical explanations, and presents many interesting and thought-provoking examples that help to illuminate the material."

—David Rosenthal, Associate Professor of Mathematics, St. John’s University, and co-author of A Readable Introduction to Real Mathematics

"A comprehensive and up-to-date look at the primary tools and techniques in sports analytics, covering every major sport, Analytic Methods in Sports condenses what took me five years to learn into 200 pages. It’s both easy to read and complete with mathematic rigor. If you’re serious about getting into analytics in any sport at any level, this needs to be on your bookshelf."

—Brian Burke, Founder of Advanced Football Analytics and NFL Team Consultant

"Many people enter the rapidly growing sports analytics industry without the adequate tools to perform analysis. In his book, Severini details the fundamental statistical skill set needed to succeed with examples from every major sport. It will appeal to readers just introduced to the field of statistics as well as the more experienced looking to further develop their ability to manage and interpret data. A worthy addition to any analyst’s library."

—Keith Goldner, Chief Analyst, numberFire

Table of Contents


Analytic methods

Organization of the book



Describing and Summarizing Sports Data


Types of data encountered in sports

Frequency distributions

Summarizing results by a single number: mean and median

Measuring the variation in sports data

Sources of variation: comparing between-team and within-team variation

Measuring the variation in a qualitative variable such as pitch type

Using transformations to improve measures of team and player performance

Home runs per at-bat or at-bats per home run?




Applying the rules of probability to sports

Modeling the results of sporting events as random variables

Summarizing the distribution of a random variable

Point distributions and expected points

Relationship between probability distributions and sports data

Tailoring probability calculations to specific scenarios: conditional probability

Relating unconditional and conditional probabilities: the law of total probability

The importance of scoring first in soccer

Win probabilities

Using the law of total probability to adjust sports statistics

Comparing NFL field goal kickers

Two important distributions for modeling sports data: the binomial and normal distributions

Using Z-scores to compare top NFL season receiving performances

Applying probability theory to streaks in sports

Using probability theory to evaluate "statistical oddities"


Statistical Methods


Using the margin of error to quantify the variation in sports statistics

Calculating the margin of error of averages and related statistics

Using simulation to measure the variation in more complicated statistics

The margin of error of the NFL passer rating

Comparison of teams and players

Could this result be due to chance? Understanding statistical significance

Comparing the American and National Leagues

Margin of error and adjusted statistics

Important considerations when applying statistical methods to sports


Using Correlation to Detect Statistical Relationships


Linear relationships: the correlation coefficient

Can the "Pythagorean theorem" be used to predict a team’s second-half performance?

Using rank correlation for certain types of nonlinear relationships

The importance of a top running back in the NFL

Recognizing and removing the effect of a lurking variable

The relationship between ERA and LOBA for MLB pitchers

Using autocorrelation to detect patterns in sports data

Quantifying the effect of the NFL salary cap

Measures of association for categorical variables

Measuring the effect of pass rush on Brady’s performance

What does Nadal do better on clay?

A caution on using team-level data

Are batters more successful if they see more pitches?


Modeling Relationships Using Linear Regression


Modeling the relationship between two variables using simple linear regression

The uncertainty in regression coefficients: margin of error and statistical significance

The relationship between WAR and team wins

Regression to the mean: why the best tend to get worse and the worst tend to get better

Trying to detect clutch hitting

Do NFL coaches expire? A case of missing data

Using polynomial regression to model nonlinear relationships

The relationship between passing and scoring in the EPL

Models for variables with a multiplicative effect on performance using log transformations

An issue to be aware of when using multi-year data


Regression Models with Several Predictor Variables


Multiple regression analysis

Interpreting the coefficients in a multiple regression model

Modeling strikeout rate in terms of pitch velocity and movement

Another look at the relationship between passing and scoring in the EPL

Multiple correlation and regression

Measuring the offensive contribution of players in La Liga

Models for variables with a synergistic or antagonistic effect on performance using interaction

A model for 40-yard dash times in terms of weight and strength

Interaction in the model for strikeout rate in terms of pitch velocity and movement

Using categorical variables, such as league or position, as predictors

The relationship between rebounding and scoring in the NBA

Identifying the factors that have the greatest effect on performance: the relative importance of predictors

Factors affecting the scores of PGA golfers

Choosing the predictor variables: finding a model for team scoring in the NFL

Using regression models for adjustment

Adjusted goals-against average for NHL goalies


Descriptions of Available Datasets


Suggestions for further reading appear at the end of each chapter.

About the Author

Thomas A. Severini is a professor of statistics at Northwestern University. He is a fellow of the American Statistical Association and the author of Likelihood Methods in Statistics and Elements of Distribution Theory. He received his PhD in statistics from the University of Chicago. His research areas include likelihood inference, nonparametric and semiparametric methods, and applications to econometrics.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General