1 Modern Technologies for Tracking the Baseball Alan Nathan University of Illinois and Complete Game Consulting

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

3 Review of Baseball Aerodynamics Forces on a Spinning Baseball in Flight mg FDFD FMFM Drag slows ball down Magnus + mg deflects ball from straight line See Michael Richmond’s talk

4 Example: Bonds’ record home run

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

6 PITCHf/x and HITf/x Two video 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

7 PITCHf/x and HITf/x Used for TV broadcasts, MLB Gameday, analysis,… See

8 Camera Registration T(x,y,z)  screen coordinates (u,v) 7 parameters needed for T –Camera location (x C,y C,z C ) –Camera orientation (pan, tilt, roll) –Magnification (focal length of zoom lens)

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

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

11 Possible Parametrizations Constant acceleration –x(t) = x 0 +v x0 t + ½a x t 2 (etc. for y,z) –Solve simultaneous linear equations for 9P –This is scheme used in PITCHf/x Constant “jerk” –x(t) = x 0 +v x0 t + ½a x0 t 2 +1/6j x t 3 –Solve simultaneous linear equations for 12P “exact” –Non-linear least-squares fit to get 9P* x 0,y 0,z 0,v x0,v y0,v z0,C d,C l, 

12 9P vs. Exact Trajectory x(t) v y (t) Many studies like this show that 9P works extremely well

13 z vertically up All useful parameters derived from 9P Release point NOT measured x 0,z 0 are locations at y 0 =50 ft easily extrapolated to 55 ft Derived parameters v 0, v f = speed at y=50,HP p x, p z: = location at y=HP pfx x, pfx z = movement y=40-HP spin axis = related to direction of movement C d, C l related to v f /v 0, pfx Spin rpm is NOT measured but approximate value inferred from pfx values

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

15 Central values close to exact  9P works well 1 pixel rms  rms on following quantities: v 0 : 0.23 mph ; x 0, z 0 : 0.4” ; px, pz: 0.7” ; pfx_x, pfx_z: 1.6” v0v0 x0x0 px pfx_x exact-inferred

16 Some Comments on Registration In-game monitors –“blue-field” vs. actual field –LOP error

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

18 Drag Coefficient: Anaheim, 2009 Camera registrations changed between days 187, *

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

20 Phased Array Doppler Radar: TrackMan

21 Measurement principle I Doppler Frequency f D = Doppler Shift = F TX - F RX =  2F TX (V R /c) Example: F TX = 10.5 GHz; c=0.67 Gmph; V R =90 mph f D =  2.82 kHz

22 Doppler shiftRadial velocity Time  Pitched ball Batted ball Frequency/Velocity vs. Time Bat Bounce

23 Measurement principle II Phase Shift Phase shift = 2  DF TX sin(  )/c Measurement principle II Phase Shift

: Vertical angle 1-3: Horizontal angle Measurement principle II Phase Shift

25 Spin Measurement principle Doppler frequency modulated by rotation frequency  sidebands

26 Doppler radar measures radial velocity –V R  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

27 Additional Details Need location and orientation of TM device (just like PFX) Need R(0)

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

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

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

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!

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 ( ft)

33 Landing Point Comparison TrackMan high by about 2.5 ft.: Could be R 0 issue

34 Spin Comparison

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

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

37 Some Examples of Analysis Pitched ball analysis –Dan Brooks will do much more Batted ball analysis

38 Ex 1: “Late Break”: Truth or Myth Mariano Rivera’s Cut Fastball View from above: actual trajectory linear extrapolation

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 v f /v 0 Denver

40 Ex 2 Ubaldo Jimenez Pitching at High Altitude Denver v f /v 0 Denver San Diego Denver v f /v 0

41 Ex 3: Effect of batted ball speed and launch angle on fly balls: TrackMan from StL, 2009 R vs. v 0 R vs.  0 USEFUL BENCHMARK mph ~5 ft per mph 25 o -35 o

42 Ex 4: What Constitutes a Well-Hit Ball? Hitf/x from April 2009 w/o home runs HR BABIP V 0 >90 Basis for outcome- independent batting metrics

43 Combining HITf/x with Hittracker HITf/x  (v 0, ,  ) Hittracker  (x f,y f,z f,T) Together  full trajectory –HFX+HTT determine unique C d,  b,  s –Full trajectory numerically computed T   b horizontal distance and T  C d sideways deflection   s

44 How well does this work? Test experimentally (Safeco expt) My Safeco Experiment w/TrackMan It works amazingly well!

45 Some examples of HFX+HTT Analysis Windy Yankee Stadium? Quantifying the Coors Field effect Home runs and batted ball speed

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)

47 HITf/x + Hittracker Analysis: 4354 HR from 2009 Denver ClevelandYankee Stadium

48 Average Relative Air Density Denver Phoenix SF

49 The Coors Effect ~26 ft

50 Phoenix vs. SF Phoenix +5.5 ft SF -5.5 ft

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

52 Now that you (think you) understand everything… Slo-mo video here

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!