Penn Sports Analytics Reading Group - Spring 2021

6. Arcsine Laws

• Safe Leads and Lead Changes in Competitive Team Sports, 2015

• Ryan’s Notes - Proofs of Arcsine Laws

5. Shannon Entropy as a Measure of the Uncertainty of a Distribution (Shannon, 1948)

• Shannon, 1948 - A Mathematical Theory of Communication (Pages 10-13 + Appendix 2)

4. AI & Soccer

• 2020 - What AI can do for Football, and What Football can do for AI

3. Kelly Criterion & Log-Optimal Betting

• Kelly, 1956 - A New Interpretation of Information Rate

• Ryan’s Notes - Kelly Criterion Derivation (Case: No Rake)

• Ryan’s Notes - Kelly Criterion Derivation (Case: Rake)

• Ryan’s Notes - Applying Kelly Criteron to the 2021 March Madness Elite 8

• Example of a Kelly-Optimal and Negative EV Bet

• Wyner and Rising, 2012 - Partial Kelly Portfolios and Shrinkage Estimators

2. In-Season Prediction of Batting Averages (Brown, 2008)

• Brown, 2008 - In-Season Prediction of Batting Averages: A Field Test of Empirical Bayes and Bayes Methodologies

• Ryan’s Notes - Brown 2008 Setup

• Ryan’s Notes - James Stein Estimator Derivation

• Ryan’s Notes - Parametric Empirical Bayes Estimator (MLE) Derivation

• Ryan’s Notes - Nonparametric Empirical Bayes Estimator Derivation

• Rahul’s Code - Implementing the Estimators from Brown 2008

1. Bradley Terry & ELO

• Stanford Stat 200 - Intro to Bradley-Terry Model

• Szczecinski and Djebbi - Understanding and Pushing the Limits of the Elo Rating Algorithm

• Aldous - Elo Ratings and the Sports Model: a Neglected Topic in Applied Probability?

• Aldous - Mathematical Probability Foundations of Dynamic Sports Ratings

• Ryan’s Notes - Bradley-Terry Model & Logistic Regression

• Hunter - MM Algorithms for Generalized Bradley-Terry Models