I am a mathematician and a baseball fan. For several years, I thought about how to put these two interests together, by searching for ways to use math to better understand baseball. This blog is about a baseball simulation game that I invented, called AccuBaseball. It combines a new mathematical model of baseball with easy-to-follow rules, and plays historical or fictitious games with statistical fidelity.
Theory
Construction
Playing the board game
Playing the Computer Game
TABLE OF CONTENTS (planned)
Prologue
- the matchup problem
- early experiments with matchup prediction
- probability in Strat-O-MaticTM
- the log5 solution
- pitcher vs batter matchups
- rediscovery of naive bayes
- concept of playable simulation
- credits
Theory
- naive Bayesian theory
- calculating odds ratios for pitchers and batters
- using odds ratios to predict match-ups
- odds ratios for arbitrary factors
- bin-conditional probabilities
- possible extensions to multi-dimensional binning
- steal estimation and counter-factual
- observations on the evolution of play: dead ball vs modern bb
Construction
- the retrosheet project
- computing odds ratios for batters and pitchers
- computing odds ratios for outs, bases, park
- converting an odds ratio to a grade
- determining rookie pitcher/batter grades
- scoring and binning a season for batting table
- computing base running probabilities
- mapping probability to dice rolls
- grading stealers and holders
- determining plausible rosters
- deriving the management book, stealing, pinch hitting, relieving
Playing the board game
- the rule book
- the AB scoring method
- selecting a roster and lineup
- scoring a matchup
- rookies in play
- adjusting for outs, bases, park, streak
- adjusting for incomplete fielding
- rolling on a batting table
- bunting
- intentional walk
- the pitcher at the plate
- rolling on a running table
- running after bunt
- starting the runners
- implicit errors, e.g. G1
- rolling on a steal table
- double steal
- example play(s)
- management by the book, stealing, pinch hitting, relieving
- playing solitaire
- guidance for fielding new teams or playing teams out of season
Playing the Computer Game
