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.
Introduction Analytic methods Organization of the book Data Computation Describing and Summarizing Sports Data Introduction 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? Computation Probability Introduction 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" Computation Statistical Methods Introduction 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 Computation Using Correlation to Detect Statistical Relationships Introduction 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? Computation Modeling Relationships Using Linear Regression Introduction 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 Computation Regression Models with Several Predictor Variables Introduction 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 Computation Descriptions of Available Datasets References Suggestions for further reading appear at the end of each chapter.
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