1. 1 Combining HITf/x with Landing Point Alan Nathan, Univ. of Illinois Introduction What can be learned directly from the data? Fancier analysis methods The Big Question: –How well can HITf/x predict landing point? hang time? full trajectory?

2. 2 Why do we care? HITf/x data come for “free” If HITf/x can determine full trajectory, then we have a handle on –Hang time –Fielder range and reaction time –Outcome-independent hitting metrics –Accurate spray charts –…..

3. 3 My approach to studying the problem A.Get initial trajectory from HITf/x B.Get landing point and flight time from hittrackeronline.com –thanks to Greg Rybarczyk C. Determine how well A determines B

4. 4 The physics issues If we know the initial conditions (HITf/x) and we know all the forces, then we can predict the full trajectory. What are the forces and how well are they known?

5. 5 What are the Forces? Gravity Drag (“air resistance”) Magnus Force (due to spin) mg F drag F Magnus Drag and Magnus depend on air density, wind Drag depends on “drag coefficient” C d Magnus depends on spin backspin  b : upward force sidespin  s : sideways force

6. 6 What can be learned directly from the data? characteristics of home runs effect of sidespin effect of backspin effect of drag and spin on fly ball distance --does a ball “carry” better in some ball parks than in others? --is there a “Yankee Stadium” effect?

7. 7 SOB and Launch Angle

8. 8 How important is SOB? each additional mph of SOB increases range by ~4 ft

9. 9 What is optimum launch angle for home runs? approximately 30 0 normalized range = range/(k*v0)

10. 10 sideways break  sidespin (  s ) ff ii RF foul line 1B    i -  f measures sideways break

11. 11 Effect of Sidespin break to right break to left RF CF LF balls breaks towards foul pole amount of break increases with spray angle balls hit to CF seem to slice the slice results in asymmetry between RHH and LHH LHH RHH

12. 12 Hang Time: ratio to vacuum value backspin increase hang time drag decreases hang time ratio of hang time to vacuum value approaches 1 with larger launch angle

13. 13 R = actual distance/vacuum distance = D/D 0 = 379/532 = 0.71 Effect of Drag and Lift on Range D0D0 D

14. 14 R = D/D 0 vs. initial vertical velocity

15. 15 Larger normalized R means better “carry”

16. 16 best carry: Houston, Denver worst carry: Cleveland, Detroit, Oakland best-worst: 10% or about 40 ft

17. 17 Does the ball carry better in Yankee Stadium? No evidence for better carry in the present data. Coors YS

18. 18 Home Run Spray Chart RF LF CF

19. 19 Fancier Analysis Methods There are things we don’t know well –the spin on the batted ball (  b and  s ) –the drag coefficient C d Therefore, we will use the actual data as a way to constrain  b,  s, C d –develop relationships between these quantities and initial velocity vector –investigate how well these relationships reproduce the landing point data.

20. 20 for given hitf/x initial conditions, adjust C d,  b,  s to reproduce landing point (x,y,z) at the measured flight time unique solution is always possible --flight time determines  b --horizontal distance and flight time determines C d --sideways deflection determines  s

21. 21 How Far Did That Ball Travel? How to extrapolate from D to R Compare angle of fall to launch angle tan(  fall )=H/(R-D) D R H R-D  fall H R-D  fall

22. 22  fall   fall /   R  fall /  = 1.4

23. 23 Sidespin LHH  s (rpm)  (deg)

24. 24 Backspin  b (rpm)  (deg)  b (rpm)

25. 25 Summary we have expressions for  b (  ) and  s (  ) there is lots of scatter of the data about these mean values –Is the scatter real? that means we still have a ways to go to meet our goal of predicting landing point and hang time from HITf/x data alone but we have learned some things along the way –Optimum launch angle for home run –Importance of SOB: 4 ft/mph –L-R asymmetry in  s –characterization of “carry” look forward to landing data from hit balls other than home runs

26. 26 Smaller means easier to hit home runs

27. 27 easiest parks to hit home run: Denver, Boston hardest parks to hit home run: Atlanta, Arizona