Modern Technologies for Tracking the Baseball

1. Modern Technologies forTracking 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 FM • Drag slows ball down • Magnus + mg deflects ball from straight line FD mg 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. Marv White, Physics, UIUC, 1969 Image, courtesy of Sportvision PITCHf/x and HITf/x 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

7. PITCHf/x and HITf/x • Used for TV broadcasts, MLB Gameday, analysis,… • See http://www.sportvision.com/baseball.html

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)

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) = 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,

12. 9P vs. Exact Trajectory vy(t) x(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 • 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

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. v0 pfx_x px x0 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”

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. 188 187 188* 187 Drag Coefficient: Anaheim, 2009 Camera registrations changed between days 187,188

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 fD = Doppler Shift = FTX - FRX = 2FTX(VR/c) Example:FTX = 10.5 GHz; c=0.67 Gmph; VR=90 mph fD = 2.82 kHz

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

23. Measurement principle II Measurement principle II Phase Shift Phase Shift Phase shift = 2DFTXsin()/c

24. Measurement principle II 2 1-2: Vertical angle 1 1-3: Horizontal angle 3 Phase Shift

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

26. 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 

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 (200-300 ft)

33. Landing Point Comparison TrackMan high by about 2.5 ft.: Could be R0 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 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

39. Denver vf/v0 San Diego San Diego Denver Ex 2 Ubaldo Jimenez Pitching at High Altitude vf/v0 Denver Denver Denver Denver

40. 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 @ 103 mph ~5 ft per mph peaks @ 25o-35o

41. V0>90 BABIP HR Ex 4: What Constitutes a Well-Hit Ball? Hitf/x from April 2009 w/o home runs Basis for outcome-independent 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

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

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

45. (379,20,5.2) 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

46. HITf/x + Hittracker Analysis:4354 HR from 2009 Denver Cleveland Yankee Stadium

47. SF Denver Phoenix Average Relative Air Density

48. The Coors Effect ~26 ft

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

50. 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