Further Reading: Game Simulation
Monte Carlo Methods
"Monte Carlo Methods" by Hammersley & Handscomb Classic textbook on Monte Carlo simulation theory.
"Simulation" by Sheldon Ross Comprehensive treatment of simulation methodology.
"Monte Carlo Statistical Methods" by Robert & Casella Advanced statistical perspective on Monte Carlo.
Sports Simulation
"The Book: Playing the Percentages in Baseball" by Tango et al. Pioneering work on sports simulation, applicable to NFL.
"Pro Football Prospectus" series Annual publications with simulation-based projections.
"Mathletics" by Wayne Winston Sports analytics fundamentals including simulation.
NFL-Specific Resources
nflfastR Expected Points Model Foundation for drive-by-drive simulation. https://www.nflfastr.com/articles/nflfastR.html
Pro-Football-Reference Play Index Historical data for validating simulations. https://www.pro-football-reference.com/
ESPN Win Probability Model Real-time win probability for comparison. https://www.espn.com/
Win Probability Models
"Win Probability Added" by Brian Burke Original work on NFL win probability.
"How FiveThirtyEight's NFL Predictions Work" Methodology behind Elo-based simulations. https://fivethirtyeight.com/methodology/how-our-nfl-predictions-work/
EdjSports Win Probability Commercial win probability model.
Drive-Level Analysis
"Expected Points and Expected Points Added" papers Academic treatment of drive-level metrics.
"Drive Outcome Probability" research Studies on what determines drive success.
Football Outsiders DVOA Efficiency-based drive analysis.
Statistical Foundations
"Probability Theory" by Jaynes Deep dive into probability foundations.
"Statistical Inference" by Casella & Berger Rigorous statistical theory.
"Bayesian Data Analysis" by Gelman et al. Bayesian approaches to simulation.
Python Simulation Libraries
NumPy Random Module Foundation for random number generation. https://numpy.org/doc/stable/reference/random/
SciPy Statistical Distributions Distribution functions for simulation. https://docs.scipy.org/doc/scipy/reference/stats.html
SimPy Discrete event simulation library. https://simpy.readthedocs.io/
Validation and Testing
"Testing Random Number Generators" Ensuring simulation quality.
"Goodness of Fit Tests" documentation KS test and other distribution comparison methods.
"Calibration in Probabilistic Forecasting" Validating probability predictions.
Fantasy Sports Applications
"Projection Systems in Fantasy Sports" How fantasy platforms use simulation.
RotoWire / FantasyPros methodologies Commercial projection approaches.
Daily Fantasy Optimization Simulation for lineup construction.
Betting Market Applications
"Simulation-Based Betting Strategies" Using simulation for betting analysis.
"Risk Management in Sports Betting" Understanding variance through simulation.
Pinnacle Betting Resources Educational content on sports betting probability.
Real-Time Applications
"Live Win Probability" implementations Technical approaches to real-time calculation.
Streaming data processing Handling live game data for simulation.
ESPN/NFL app win probability Commercial implementations for reference.
Academic Papers
"Predicting the Outcome of NFL Games" Academic research on game prediction.
"Monte Carlo Simulation in Sports" Survey of simulation applications in sports.
"Modeling Football Outcomes" Statistical models for football prediction.
Video Resources
StatQuest: Monte Carlo Simulation Clear explanation of Monte Carlo basics. https://www.youtube.com/c/joshstarmer
3Blue1Brown: Probability Visual explanations of probability concepts.
Tools and Software
Python + NumPy Primary simulation environment.
R + Tidyverse Alternative statistical environment.
Julia High-performance computing for large simulations.
Excel/Google Sheets Simple simulations with built-in functions.
Blogs and Online Resources
Advanced Football Analytics (archived) Brian Burke's pioneering NFL analytics.
The Athletic Analytics Coverage Regular NFL analytics including simulation.
FiveThirtyEight Sports Simulation-based predictions and analysis.
Key Papers to Read
- Expected Points papers - Foundation for scoring probability
- Win Probability Added - Burke's original methodology
- Monte Carlo methods textbook - Statistical foundations
- Distribution comparison tests - Validation methodology
- NFL outcome prediction - Academic benchmarks
These resources provide depth for building sophisticated NFL simulation systems.