1 modern technologies for tracking the baseball alan nathan university of illinois and complete game...
TRANSCRIPT
![Page 1: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/1.jpg)
1
Modern Technologies forTracking the Baseball
Alan NathanUniversity of Illinois and Complete Game Consulting
![Page 2: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/2.jpg)
2
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
![Page 3: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/3.jpg)
3
Review of Baseball Aerodynamics Forces on a Spinning Baseball in Flight
D2
D C1
ˆF = - ρAv v2
2LM
1ˆ ˆF = ρAv (ωC v)
2
v
ω
mgFD
FM
• Drag slows ball down
• Magnus + mg deflects ball from straight line
See Michael Richmond’s talk
![Page 4: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/4.jpg)
4
Example: Bonds’ record home run
![Page 5: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/5.jpg)
5
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
![Page 6: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/6.jpg)
6
PITCHf/x and HITf/xTwo 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
Marv White, Physics,UIUC, 1969
![Page 7: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/7.jpg)
7
PITCHf/x and HITf/x• Used for TV broadcasts, MLB Gameday, analysis,…• See http://www.sportvision.com/baseball.html
![Page 8: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/8.jpg)
8
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)
![Page 9: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/9.jpg)
9
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
![Page 10: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/10.jpg)
10
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
1
z
y
x
T
1
v
u
k
![Page 11: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/11.jpg)
11
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,
![Page 12: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/12.jpg)
12
9P vs. Exact Trajectory
0.5
1.0
1.5
2.0
2.5
3.0
-0.1
-0.05
0
0.05
0.1
0.15
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
t
-135
-130
-125
-120
-115
-0.4
-0.2
0
0.2
0.4
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
vy (ft/s) v
t (sec)
x(t) vy(t)
Many studies like this show that 9P works extremely well
![Page 13: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/13.jpg)
13
z vertically up
All useful parameters derived from 9P• Release point NOT measured
• x0,z0 are locations at y0=50 ft• easily extrapolated to 55 ft
• 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 values
![Page 14: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/14.jpg)
14
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
![Page 15: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/15.jpg)
15
• 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”
v0
x0px
pfx_xexact-inferred
![Page 16: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/16.jpg)
16
Some Comments on Registration • In-game monitors
– “blue-field” vs. actual field– LOP error
![Page 17: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/17.jpg)
17
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
![Page 18: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/18.jpg)
18
Drag Coefficient: Anaheim, 2009
Camera registrations changed between days 187,188
188187
187188*
![Page 19: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/19.jpg)
19
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
![Page 20: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/20.jpg)
20
Phased Array Doppler Radar: TrackMan
![Page 21: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/21.jpg)
21
TRANSMITTER
RECEIVER
FTX
FTX
FRX
V
VR
fd
fd = FTX-FRX = 2*VR*FTX/c
Measurement principle IDoppler Frequency
fD = Doppler Shift = FTX - FRX = 2FTX(VR/c)
Example: FTX = 10.5 GHz; c=0.67 Gmph; VR=90 mphfD = 2.82 kHz
![Page 22: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/22.jpg)
22
Doppler shift Radial velocity
Time
Pitched ball
Batted ball
Frequency/Velocity vs. Time
Bat
Bounce
![Page 23: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/23.jpg)
23
Measurement principle IIPhase Shift
TRANSMITTER
RECEIVER 1
FTX
FTX
FRX1fd1
(fd1 ) - (fd2) = 2**sin()*D*FTX/cRECEIVER 2FRX2
fd2
FTX
D
Phase shift = 2DFTXsin()/c
Measurement principle IIPhase Shift
![Page 24: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/24.jpg)
24
1
2
3
1-2: Vertical angle
1-3: Horizontal angle
Measurement principle IIPhase Shift
![Page 25: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/25.jpg)
25
Spin Measurement principle
w*r
w*r
VradRadar
Strong reflection
Weaker reflection
Weaker reflection
rw
Vtot = Vrad - w*r
Vtot = Vrad + w*r
Vtot = Vrad
Conclusion:A Doppler radar does not only see one velocity, but avelocity spectrum.
The velocity spectrum turns out to have discretefrequency components spaced with the spin frequency w.
Doppler frequency modulated by rotation frequency sidebands
![Page 26: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/26.jpg)
26
• 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
Summary of Technique
![Page 27: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/27.jpg)
27
Additional Details
• Need location and orientation of TM device (just like PFX)
• Need R(0)
![Page 28: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/28.jpg)
28
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
![Page 29: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/29.jpg)
29
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
![Page 30: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/30.jpg)
30
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
![Page 31: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/31.jpg)
31
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!
![Page 32: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/32.jpg)
32
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 high-
speed video camera– Measure landing point with a very long tape
measure (200-300 ft)
![Page 33: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/33.jpg)
33
Landing: TrackMan vs. Actual
200
220
240
260
280
300
320
340
200 220 240 260 280 300 320 340
actual distance (ft)
Tra
ckM
an
dis
tan
ce (
ft)
Landing Point Comparison
TrackMan high by about 2.5 ft.: Could be R0 issue
![Page 34: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/34.jpg)
34
spin: TrackMan vs. video
0
500
1000
1500
2000
2500
3000
3500
4000
0 1000 2000 3000 4000
video spin (rpm)
Tra
ckM
an s
pin
(rpm
)Spin Comparison
![Page 35: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/35.jpg)
35
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
![Page 36: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/36.jpg)
36
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
![Page 37: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/37.jpg)
37
Some Examples of Analysis
• Pitched ball analysis– Dan Brooks will do much more
• Batted ball analysis
![Page 38: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/38.jpg)
39
"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."
Ex 2 Ubaldo Jimenez Pitching at High Altitude
Denver
vf/v0
DenverDenverDenver
![Page 39: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/39.jpg)
40
Ex 2 Ubaldo Jimenez Pitching at High Altitude
Denver
vf/v0
DenverDenverDenver
San Diego
San Diego
Denver
Denver
vf/v0
![Page 40: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/40.jpg)
41
Ex 3: Effect of batted ball speed and launch angle on fly balls: TrackMan from StL, 2009
R vs. v0 R vs. 0
USEFUL BENCHMARK400 ft @ 103 mph
~5 ft per mph
peaks @ 25o-35o
![Page 41: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/41.jpg)
42
Ex 4: What Constitutes a Well-Hit Ball? Hitf/x from April 2009
w/o home runs
HR
BABIP V0>90 Basis for outcome-independent batting metrics
![Page 42: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/42.jpg)
43
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
![Page 43: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/43.jpg)
44
How well does this work?Test experimentally (Safeco expt)
010203040506070
0 50 100 150 200 250 300 350distance (ft)
My Safeco Experiment w/TrackMan
It works amazingly well!
![Page 44: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/44.jpg)
45
Some examples of HFX+HTT Analysis
• Windy Yankee Stadium?
• Quantifying the Coors Field effect
• Home runs and batted ball speed
![Page 45: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/45.jpg)
46
HITf/x + hittracker Analysis: The “carry” of a fly ball
• Motivation: does the ball carry especially well in the new Yankee Stadium? • “carry” ≡ (actual distance)/(vacuum distance)
for same initial conditions
(379,20,5.2)
![Page 46: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/46.jpg)
47
HITf/x + Hittracker Analysis:4354 HR from 2009
Denver
Cleveland Yankee Stadium
![Page 47: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/47.jpg)
48
Average Relative Air Density
Denver
Phoenix
SF
![Page 48: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/48.jpg)
49
The Coors Effect
~26 ft
![Page 49: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/49.jpg)
50
Phoenix vs. SF
Phoenix +5.5 ft
SF -5.5 ft
![Page 50: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/50.jpg)
51
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
![Page 51: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/51.jpg)
52
Now that you (think you) understand everything…
Slo-mo video here
![Page 52: 1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting](https://reader035.vdocuments.us/reader035/viewer/2022062408/56649ed55503460f94be5992/html5/thumbnails/52.jpg)
53
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!