Analysis of Knuckleball TrajectoriesAlan M. Nathan

University of Illinois at Urbana-Champaign

Recently retired knuckleball pitcher Tim Wakefield

Issues to be Addressed

• The “movement” of knuckleball pitches• The “smoothness” of knuckleball trajectories

Knuckleball thrown with very little spin no Magnus force

• But still lots of erratic “movement”• Origin of movement revealed in wind

tunnel experiments

Wind Tunnel Data, 4S OrientationMike Morrissey (MS Thesis) and John Borg (Marquette)

Agrees with Watts & Sawyer, AJP (1975)

Studying Knuckleball Trajectories Using the PITCHf/x Tracking System

Two video cameras @60 fps• approximately orthogonal axes

– full 3D reconstruction• tracks every pitch in every MLB ballpark

– all data publicly available

Image, courtesy of Sportvision

Studies of Knuckleball Movement

• Movement = deviation of trajectory from straight line, with gravity removed

• Easily measured with PITCHf/x

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50distance from home plate (ft)

View from above

5” movement

Direction of movement vs. release speed(Jon Lester)

707580859095

100

0

30

6090

120

210

240270

300

330

“Normal” pitches have predictable movement

Catcher’s View

55

60

65

70

75

0

30

6090

120

210

240270

300

330

Direction of movement vs. release speed(Tim Wakefield)

707580859095

100

0

30

6090

120

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240270

300

330

Knuckleballs do not have predictable movement

But is the trajectory “smooth”?

9 Free Parameters:x0, y0, z0, vx0, vy0, vz0, CD, CL,

• Fit to smooth function• Examine RMS deviation of data from fit

Normal(201)

Knuckleball (77)

• Normal and knuckleball pitches follow similar distributions• Knuckleballs only slightly (few tenths of inch) less smooth

278 pitches from August 29, 2011

Two Examples:Which one is the knuckleball?

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

5.0

5.2

5.4

5.6

5.8

6.0

6.2

6.4

0.00 0.10 0.20 0.30

t (sec)

z

x

-0.90

-0.80

-0.70

-0.60

-0.50

4.4

4.6

4.8

5.0

5.2

5.4

5.6

0.0 0.1 0.2 0.3

t (sec)

zx

76 mph knuckleballrms=0.374”

75 mph curveballrms=0.373”

2011Aug29-161108

Summary of Conclusions• Movement of knuckleball trajectories varies

considerably from pitch to pitch– Magnitude and direction quasi-random

• Any given trajectory is as smooth as those of ordinary pitches– within limits of precision of tracking data (~0.3”-0.5”)

• Open questions/work in progress– Are erratic movement and smoothness conclusions

consistent with wind tunnel data?– How can perception and reality be reconciled?