Modern Technologies for Tracking the Baseball

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Modern Technologies forTracking the Baseball
Alan Nathan University of Illinois and Complete
Game Consulting
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Heres what Ill 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

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Review of Baseball Aerodynamics Forces on a
Spinning Baseball in Flight
FM

• Drag slows ball down
• Magnus mg deflects ball from straight line

FD
mg
See Michael Richmonds talk
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Example Bonds record home run
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Familiar (and not so familiar) Effects

• Drag
• Fly balls dont 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 _at_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

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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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Sportvisions 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

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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
vy(t)
x(t)
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 y050 ft
• easily extrapolated to 55 ft
• Derived parameters
• v0, vf speed at y50,HP
• px, pz location at yHP
• pfxx, pfxz movement y40-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

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PITCHf/x PrecisonA 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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exact-inferred

• 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
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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

fD Doppler Shift FTX - FRX ? 2FTX(VR/c)
Example FTX 10.5 GHz c0.67 Gmph VR90
mph fD ?2.82 kHz
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Frequency/Velocity vs. Time
Doppler shift
Radial velocity
Time ?
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Measurement principle II
Measurement principle II

• Phase Shift

Phase Shift
Phase shift 2?DFTXsin(?)/c
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Measurement principle II
Phase Shift
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Spin Measurement principle
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 high-speed
  video camera
• Measure landing point with a very long tape
  measure (200-300 ft)

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Landing Point Comparison
TrackMan high by about 2.5 ft. Could be R0 issue
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Spin Comparison
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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 1 Late Break Truth or MythMariano
Riveras Cut Fastball
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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
Denver
Denver
Denver
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Ex 2 Ubaldo Jimenez Pitching at High Altitude
vf/v0
Denver
Denver
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
R vs. ?0
USEFUL BENCHMARK 400 ft _at_ 103 mph 5 ft per mph
peaks _at_ 25o-35o
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Ex 4 What Constitutes a Well-Hit Ball? Hitf/x
from April 2009
w/o home runs
Basis for outcome-independent batting metrics
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Combining HITf/x with Hittracker

• HITf/x ? (v0,?,?)
• Hittracker ? (xf,yf,zf,T)
• Together ? full trajectory
• HFXHTT 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)

It works amazingly well!
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Some examples of HFXHTT 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

• 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 Analysis4354 HR from 2009
Denver
Cleveland
Yankee Stadium
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Average Relative Air Density
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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!