Math in Sports

Paul Moore

Handout

Outline

  1. Math in Basketball
  2. Basics
  3. Dimensions, score keeping
  4. Math and Physics behind Foul Shots
  5. Math in Baseball
  6. Batting
  7. Sweet spot, bat vibration frequencies
  8. Pitching
  9. Curveball
  10. Magnus Force
  11. Home Run Hitting
  12. Angles in Soccer
  13. Defensive Angles
  14. Offensive Angles
  15. Math Education

Useful Equations

·  Baseball Stats

·  Kinematic Equations

[Displacement] s = s0 + v0t + ½at2

[Useful height equation without time]

[Solved for v0]


Exercises

1. Can you give vx and vy in terms of v and θ?

2. At a particular ball park, the wall behind outfield is 500 feet away from the batter, and 20 feet off the ground. Assume you hit the ball 3 feet off the ground at a 35 degree angle. What is the required velocity for the ball to reach the top of the outfield wall?

3. Using Brian McCann’s stats below, fill in the empty career AVG square below.

2010 Season Stats
SPLITS / G / AB / R / H / 2B / 3B / HR / RBI / BB / SO / SB / CS / AVG / OBP / SLG / OPS
Season / 8 / 23 / 8 / 8 / 2 / 0 / 2 / 5 / 8 / 2 / 1 / 0 / .348 / .516 / .696 / 1.212
Career / 619 / 2146 / 271 / 631 / 158 / 2 / 93 / 394 / 208 / 303 / 13 / 3 / .358 / .500 / .858
Last 7 days / 6 / 18 / 4 / 6 / 2 / 0 / 1 / 4 / 4 / 2 / 0 / 0 / .333 / .455 / .611 / 1.066
Projected / 162 / 466 / 162 / 162 / 41 / 0 / 41 / 101 / 162 / 41 / 20 / 0 / .348 / .516 / .696 / 1.212