Transcript Juiced Baseballs, Corked Bats, and other Myths of Baseball

Modern Technologies for
Tracking the Baseball
Alan Nathan
University of Illinois and Complete Game Consulting
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Here’s what I’ll talk about:
• Brief review of baseball aerodynamics
• The new technologies
– Camera-based systems:
• PITCHf/x and HITf/x:
– Doppler radar-based systems:
• TrackMan
• Using these technologies for analysis
– Lots of examples
2
Review of Baseball Aerodynamics
Forces on a Spinning Baseball in Flight
v
FM
• Drag slows ball down
1
2
FD = - CDρAv vˆ
2
• Magnus + mg deflects
ball from straight line
1
ˆ  v)
ˆ
FM = CLρAv 2 (ω
2
ω
FD
mg
See Michael Richmond’s talk
3
Example: Bonds’ record home run
4
Familiar (and not so familiar) Effects:
• Drag
– Fly balls don’t travel as far (factor of ~2!)
– Pitched balls lose ~10%
• Magnus
– Movement on pitches (many examples later)
– Batted balls
• Backspin  longer fly balls; tricky popups
• Topspin  nosedive on line drives; tricky
grounders
• Sidespin  balls curve toward foul pole
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PITCHf/x and HITf/x
Marv White, Physics,
UIUC, 1969
Two video cameras @60 fps
• “high home” and “high first”
• tracks every pitch in every MLB ballpark
– data publicly available
• tracks initial trajectory of batted ball
– data not publicly available
Image, courtesy of Sportvision
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PITCHf/x and HITf/x
• Used for TV broadcasts, MLB Gameday, analysis,…
• See http://www.sportvision.com/baseball.html
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Camera Registration
• T(x,y,z)  screen coordinates (u,v)
• 7 parameters needed for T
– Camera location (xC,yC,zC)
– Camera orientation (pan, tilt, roll)
– Magnification (focal length of zoom lens)
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Details of Tracking Process
• Each camera image determines LOP
• If cameras were synchronized
– LOP intersection  (x,y,z)
• Cameras not synchronized
– Need a clever idea
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Sportvision’s Clever Idea
• Physics  trajectory is smooth
• Parametrize smooth trajectory mathematically
– e.g., constant acceleration (9 parameters)
• Adjust parameters to fit pixel data
– We then have full trajectory
x
 
u
 
 y
k  v   T 
z
1
 
 
1
 
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Possible Parametrizations
• Constant acceleration
– x(t) = x0 +vx0t + ½axt2 (etc. for y,z)
– Solve simultaneous linear equations for 9P
– This is scheme used in PITCHf/x
• Constant “jerk”
– x(t) = x0 +vx0t + ½ax0t2 +1/6jxt3
– Solve simultaneous linear equations for 12P
• “exact”
– Non-linear least-squares fit to get 9P*
x0,y0,z0,vx0,vy0,vz0,Cd,Cl,
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9P vs. Exact Trajectory
3.0
0.15
x(t)
2.5
1.5
0
1.0
-0.05
0.10
0.15
0.20
t
vy(t)
-120
0.05
0.05
0.4
0.1
2.0
0.5
0.00
-115
0.25
0.30
0.35
-0.1
0.40
0.2
vy (ft/s)
v
-125
0
-130
-0.2
-135
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
-0.4
0.40
t (sec)
Many studies like this show that 9P works extremely well
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All useful parameters derived from 9P
• Release point NOT measured
• x0,z0 are locations at y0=50 ft
• easily extrapolated to 55 ft
z vertically up
• Derived parameters
• v0, vf = speed at y=50,HP
• px, pz: = location at y=HP
• pfxx, pfxz = movement y=40-HP
• spin axis = related to direction of movement
• Cd, Cl related to vf/v0 , pfx
• Spin rpm is NOT measured
• but approximate value inferred from pfx values13
PITCHf/x Precison:
A Monte Carlo Simulation
•
•
•
•
•
Start with exact trajectories
Use cameras to get pixels
Add random “noise” (1 pixel rms)
Get 9P and derived quantities
Compare with the exact quantities
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v0
pfx_x
exact-inferred
x0
px
• Central values close to exact  9P works well
• 1 pixel rms  rms on following quantities:
v0 : 0.23 mph ; x0, z0 : 0.4” ; px, pz: 0.7” ; pfx_x, pfx_z: 1.6”
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Some Comments on Registration
• In-game monitors
– “blue-field” vs. actual field
– LOP error
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Registration Studies in Progress
• Could accuracy be improved with additional
“pole” calibrations?
• Can the data themselves be used to
recalibrate the cameras?
– An example follows
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Drag Coefficient: Anaheim, 2009
Camera registrations changed between days 187,188
188
187
187
188*
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Some Remarks on Hitf/x
• Pixel data fit to constant velocity (6P)
– Not enough of trajectory to do any better
• Impact location inferred from intersection of
pitched and batted ball trajectories
• BBS and VLA are systematically low due to drag
and gravity
– Not a big effect
– One could correct for it fairly easily
• Balls hitting ground in field of view are somewhat
problematic
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Phased Array Doppler Radar:
TrackMan
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Measurement principle I
Doppler Frequency
TRANSMITTER
FTX
V
FTX
fd
RECEIVER
VR
FRX
f = F -F = 2*V *F /c
fD = Doppler Shift
= FTX - FRX =  2FTX(VR/c)
d
TX
RX
R
TX
Example: FTX = 10.5 GHz; c=0.67 Gmph; VR=90 mph
fD = 2.82 kHz
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Frequency/Velocity vs. Time
Doppler shift
Radial velocity
Batted ball
Bat
Bounce
Pitched ball
Time 
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Measurement principle II
Phase Shift
TRANSMITTER
FTX
FTX
fd1
RECEIVER 1
FRX1

FTX
fd2
RECEIVER 2
D
FRX2
) - (f
) = 2**sin()*D*F
/c
Phase(f
shift
= 2DF
TXsin()/c
d1
d2
TX
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Measurement principle II
Phase Shift
2
1-2: Vertical angle
1
1-3: Horizontal angle
3
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Spin Measurement principle
Weaker reflection
Radar
w*r
r
Vtot = Vrad - w*r
w
Strong reflection
Vrad
Vtot = Vrad
Weaker reflection
w*r
Vtot = Vrad + w*r
Conclusion:
A Doppler radar does not only see one velocity, but a
velocity spectrum.
The velocity spectrum turns out to have discrete
frequency components spaced with the spin frequency w.
Doppler frequency modulated by rotation frequency  sidebands
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Summary of Technique
• Doppler radar measures radial velocity
– VR  R(t) = distance of ball from radar
– …provided initial R is known
• 3-detector array to measure phase
– two angles (t), (t)  location on sphere
• R(t), (t), (t) gives full 3D trajectory
• Spin modulates to give sidebands
– spin frequency 
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Additional Details
•
Need location and orientation of TM
device (just like PFX)
•
Need R(0)
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TrackMan Capabilities I
• Full pitched ball trajectory
– Everything PITCHf/x gives plus….
• Actual release point  perceived velocity
• Total spin (including “gyro” component)
• Many more points on the trajectory
But given smooth trajectory, additional points are
not necessarily useful
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Comment about Spin
• Tracking (either TM or PFX) only determines
component of spin in the x-z plane
– No deflection due to y (gyro) component
• Many pitches have a gyro component
– Especially slider
• Combining TrackMan total spin with the indirect
determination of x-z component gives 3D spin
axis
– …a potentially useful analysis tool
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TrackMan Capabilities II
• Full batted ball trajectory, including…
• Batted ball speed, launch & spray angles
– Equivalent to HITf/x
– Landing point coordinates at ground level and
hang time
• Equivalent to Hittracker
– Initial spin
– and more, if you want it
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TrackMan Data Quality I
• Comparisons with Pitchf/x
– Pitch-by-pitch comparisons from May 2010 in
StL and Bos look excellent
– Comparable in precision and accuracy to PFX
– Our Red Sox friends could tell us more, if we
ask them really nicely! 
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TrackMan Data Quality II
• My Safeco Field experiment, October
2008
– Project fly balls with pitching machine
– Track with TrackMan
– Measure initial velocity and spin with highspeed video camera
– Measure landing point with a very long tape
measure (200-300 ft)
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Landing Point Comparison
TrackMan distance (ft)
Landing: TrackMan vs. Actual
340
320
300
280
260
240
220
200
200
220
240
260
280
300
320
340
actual distance (ft)
TrackMan high by about 2.5 ft.: Could be R0 issue
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Spin Comparison
TrackMan spin (rpm)
spin: TrackMan vs. video
4000
3500
3000
2500
2000
1500
1000
500
0
0
1000
2000
3000
4000
video spin (rpm)
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Summary of Safeco Results
• Initial velocity vector excellent
• Initial spin mostly excellent
– But sometimes off by an integer factor (?)
• Landing point correlates well
– But systematic difference ~2.5 ft
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One final point about batted balls
• We need a convenient way to tabulate
batted ball trajectories
• Current TM scheme:
– Initial velocity vector
– Landing point and hang time, both
extrapolated to field level
• Constant jerk (12P) might work
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Some Examples of Analysis
• Pitched ball analysis
– Dan Brooks will do much more
• Batted ball analysis
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Ex 2 Ubaldo Jimenez
Pitching at High Altitude
vf/v0
"Every time that I come here to San Diego, it's
always good. Everything moves different. The
breaking ball is really nasty, and my fastball
moves a lot. So I love it here."
Denver
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Ex 2 Ubaldo Jimenez
Pitching at High Altitude
Denver
vf/vv0f/v0
San Diego
San Diego
Denver
Denver
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Ex 3: Effect of batted ball speed and launch
angle on fly balls: TrackMan from StL, 2009
R vs. v0
USEFUL BENCHMARK
400 ft @ 103 mph
~5 ft per mph
R vs. 0
peaks @ 25o-35o
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Ex 4: What Constitutes a Well-Hit Ball?
Hitf/x from April 2009
BABIP
w/o home runs
V0>90
Basis
HR
for
outcomeindependent
batting metrics 42
Combining HITf/x with Hittracker
• HITf/x  (v0,,)
• Hittracker  (xf,yf,zf,T)
• Together  full trajectory
– HFX+HTT determine unique Cd, b, s
– Full trajectory numerically computed
• T  b
• horizontal distance and T  Cd
• sideways deflection  s
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How well does this work?
Test experimentally (Safeco expt)
My Safeco Experiment w/TrackMan
70
60
50
40
30
20
10
0
0
50
100
150 200 250
distance (ft)
300
350
It works amazingly well!
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Some examples of HFX+HTT
Analysis
• Windy Yankee Stadium?
• Quantifying the Coors Field effect
• Home runs and batted ball speed
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HITf/x + hittracker Analysis:
The “carry” of a fly ball
(379,20,5.2)
• Motivation: does the ball carry especially well in
the new Yankee Stadium?
• “carry” ≡ (actual distance)/(vacuum distance)
for same initial conditions
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HITf/x + Hittracker Analysis:
4354 HR from 2009
Denver
Cleveland
Yankee Stadium
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Average Relative Air Density
SF
Phoenix
Denver
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The Coors Effect
~26 ft
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Phoenix vs. SF
Phoenix +5.5 ft
SF -5.5 ft
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Home Runs and BBS
• 4% reduction in BBS
– 20 ft reduction in fly ball distance (~5%)
– 50% reduction in home runs
– NOTE: typical of NCAA reduction with new bats
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Now that you (think you)
understand everything…
Slo-mo video here
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My Final Slide
• Lots of new information from tracking data
• We have only just begun to harvest it
• These new data will keep us all very busy!
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