Statistics via Sports

• Recommended prerequisites: calculus, probability, R coding; matrix algebra helps
• Taught as part of the Wharton Sports Analytics Summer Research Lab

Lectures:

Intro

• Linear algebra primer
  • planned lecture
  • live lecture
• Probability primer
  • planned lecture
  • live lecture
• Example of the research process
  • Rethinking WAR for starting pitchers
  • planned lecture
  • live lecture
• Statistical models vs. mathematical models
  • Rethinking WAR for starting pitchers
  • planned lecture
  • live lecture
  • code
  • data
  • XGBoost pre-trained hyperparameters
    

Regression

• Simple linear regression
  • predict batting average across seasons, pythagorean win percentage
  • planned lecture
  • live lecture
  • code
• Multivariable linear regression
  • NCAA basketball power ratings, NFL expected points
  • planned lecture
  • live lecture
  • code
  • NCAA mbb schedule data, NCAA mbb team data, and NFL expected points data
  • HW: Value of a draft position
• Logistic regression
  • putt success probability, Bradley-Terry power ratings
  • planned lecture
  • live lecture
  • code
  • NCAA mbb schedule data, NCAA mbb team data
  • HW: Power score comparison
    

Shrinkage & Bayesianism

• Regularization and the bias-variance tradeoff
  • MLB park effects
  • planned lecture
  • live lecture
  • code
  • MLB half-inning data
  • HW: Adjusted plus-minus and RAPM
• The power of fake data (priors)
  • predict end-of-season win percentage from mid-season win percentage
  • planned lecture
  • live lecture
  • HW: Priors for in-season prediction of win percentage
• Empirical Bayes
  • predict end-of-season batting average from mid-season batting average
  • planned lecture
  • live lecture
  • code
  • 2019 batting average data
  • HW: Empirical Bayes player quality
  • paper – In-season prediction of batting averages: a field test of empirical Bayes and Bayes methodologies
• Examples: Bayesian modeling in sports
  • A high-level overview of Bayesian statistics
  • Bayesball: A Bayesian hierarchical model for evaluating fielding in Major League Baseball
    • Shane’s slides
    • paper
  • How often does the best team win? A unified approach to understanding randomness in North American sport.
    • planned lecture
    • live lecture
    • paper
  • More Bayesian sports papers:
    • A Hierarchical Bayesian model of pitch framing
    • Evaluating plate discipline in Major League Baseball with Bayesian Additive Regression Trees
    • A Bayesian analysis of the time through the order penalty in baseball
      
      

Tree machine learning

• Our example: in-game NFL win probabilities
  • This unit’s HW
  • Get my cleaned NFL WP play-by-play dataset data7b.csv
• Decision trees
  • planned lecture
  • live lecture
• Random forests
  • planned lecture
  • live lecture
  • paper: Arcing Classifiers (explores the bias-variance tradeoff for classifiers)
  • paper: Making sense of random forest probabilities
• XGBoost
  • planned lecture
  • live lecture
  • paper: XGBoost
  • XGBoost win probability & fourth down code (instructions in README.md)
• Nonparametric bootstrapped uncertainty quantification on simulated data
  • planned lecture
  • live lecture
  • codefiles 1, 2, 3, 4
• Uncertainty quantification in fourth down decision making
  • planned lecture
  • live lecture
  • stay tuned for our paper coming soon!
  • XGBoost win probability & fourth down code (instructions in README.md)
    

Future Lesson Ideas:

Clustering

• K-means clustering
  • NBA player clustering
• Eigenvalues, diagonalization, SVD
• PCA, factor analysis

Other Fun Stuff

• Kelly betting
• NFL Draft chart
• Spatio-temporal modeling (Bornn, Cervone, etc.)
• Selection Bias
• Data visualization tutorial