The Science of Baseball

Batting, Bats, Bat-Ball Collisions, and the Flight of the Ball

  • A. Terry Bahill

Table of contents

  1. Front Matter
    Pages i-xxxix
  2. A. Terry Bahill
    Pages 1-11
  3. A. Terry Bahill
    Pages 13-22
  4. A. Terry Bahill
    Pages 23-47
  5. A. Terry Bahill
    Pages 49-108
  6. A. Terry Bahill
    Pages 109-149
  7. A. Terry Bahill
    Pages 151-155
  8. A. Terry Bahill
    Pages 157-207
  9. A. Terry Bahill
    Pages 209-229
  10. A. Terry Bahill
    Pages 231-252
  11. A. Terry Bahill
    Pages 279-291
  12. A. Terry Bahill
    Pages 293-306
  13. Back Matter
    Pages 307-309

About this book


This augmented, new edition adds discussion of the bat’s vertical sweetness gradient, eye-hand cross-dominance, models for the swing of a bat, and accuracy of simulations. The book retains its description of dynamic collisions between baseballs, softballs, and bats, and the intricate modeling of these interactions, using only basic math and physical principles. Veteran baseball science author Terry Bahill explains models for the speed and spin of balls and bats and calculations for bat-ball collisions at a level accessible to most students of the science of baseball. Demystifying the most important factors for understanding bat performance—bat weight, moment of inertia, the coefficient of restitution, and characteristics of humans swinging the bats—Dr. Bahill also explains physical aspects of the optimal bat and the sweet spot.

Praise for the First Edition

 “Dr. Bahill’s book is the perfect tool for teaching how to solve some of baseball’s basic science problems. Using only simple Newtonian principles and the conservation laws, Dr. Bahill explains how to model bat-ball collisions. Also, he derives equations governing the flight of the ball, and proceeds to show what factors affect air density and how this density affects the ball’s flight. And as a unique addition to his fine book, he provides advice for selecting the optimal bat—a surprising bonus!”

Dave Baldwin, PhD

Major League pitcher, 1966-1973, lifetime Major League ERA, 3.08

 “If I were the General Manger of a baseball team, I would tell my people to write a ten-page paper describing what this book contains that could improve our performance. I think the book provides the foundation for change.”

Bruce Gissing

Executive VP-Operations (retired)
Boeing Commercial Airplanes

“[I] had a chance to read your research, and I fully agree with your findings.”

Baseball Legend Ted Williams, in a 1984 letter to the author



Science of Baseball Baseball Ball velocity after a collision Batted-ball speed Center of Percussion Coefficient of Restitution Collision at center of mass Collision at sweet spot Conservation of Angular Momentum Conservation of Linear Momentum Conservation of Momentum Equations for Bat-ball Collisions Models for swinging a bat Optimal bat Physics of baseball Pitch speed Sensitivity analysis Sensitivity functions Softball Spin of ball Sweet spot

Authors and affiliations

  • A. Terry Bahill
    • 1
  1. 1.Systems and Industrial EngineeringUniversity of ArizonaTucsonUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-03031-5
  • Online ISBN 978-3-030-03032-2
  • Buy this book on publisher's site