THE BOOK--Playing The Percentages In Baseball

This is really exciting news.  Will the new HITf/x have hang time?  Will the HITf/x data be publicly available like the PITCHf/x data is?

HITf/x in its current incarnation is essentially initial position (which we know already from PITCHf/x) and initial velocity of the batted ball.  It is taken from the last several frames of the PITCHf/x video, which covers the area between the pitcher’s mound and home plate.

You can make fairly good estimates of hang time from this data, good enough for a Dudek-like evaluation, certainly.  However, you can also figure out some clever ways to constrain the situation in order to get more accurate estimates of the full trajectory.

Mike and Dave - Any initial position information for Hit f/x will be an estimate extrapolated from the later frames after the ball is hit.  The initial vertical and horizontal angles will also probably be part of the information provided for most hit balls.  For a small percentage of hit balls (mostly those that hit the ground near home plate) there will not be enough frames to calculate Hit f/x information.

The problem with computing hang time and landing location from the frames of hit ball information currently being captured is that the spin of the hit ball cannot be determined.  As Mike says above, hang time and landing location can both be estimated by estimating the spin on the hit ball, but not very well.  Wind is another factor that affects landing location and that is not measured precisely enough to allow for a good estimate.

The Hit f/x information is expected to be publically available for research purposes.

From Dudek’s work, hang time measurements with error on the order of a half second seem to be quite valuable.  I think we can get there just from the Hfx velocity vector data, ignoring lift from spin altogether and estimating the drag from the more slowly changing environmental variables (i.e., accounting for air density but not for wind).

If we want to get a little more accurate, we can probably guess at the spin based on the vertical launch angle.  I am working on ways of doing even better than that, calculating the spin more directly from the ball-bat collision.  We can also constrain the trajectory by using the fielding location from Gameday, although of course that introduces another set of problems (fielding location may not equal landing location, etc.).

The Dudek article should certainly serve as inspiration. 

Basically, every additional second the ball is in the air, there is an extra 0.25 outs that results.

If I’d try to guess how accurate I’d want the data to be, I’d say I’d like to know the hang time within 0.2 seconds.

Just to be clear, Greg R. and I are recording the hang time of some, but not nearly all, air balls, and no ground balls, for a project we are working on. We are only doing that for the past 2 or 3 seasons and have no immediate plans to do it for 2009. Unfortunately, it is not going to be for public consumption.

I have no idea what BIS and Dewan are doing.  According to the article in the Seattle Times, BIS and/or Dewan are going to be recording hang time starting this season.  Since they already are apparently watching video of every game, it is easy for them to do.

Timing hang time with a stop watch, BTW, is pretty accurate. I suppose it could be done with computer video software.  Whether that would be more or less accurate, I have no idea.

I have checked some of the times recorded by the observers, and they have generally agreed with my timings within 0.05 seconds.  No worries on the accuracy of the data as long as the observer is being diligent, and is willing to repeat a measurement if they botch it the first time…

Regular television video is shot at 30 fps, or 0.033 seconds per frame.  If the frame-counting method is faster/easier, then of course Dewan ought to do it, but it’s hard to say it will be significantly more accurate than a stopwatch wielded by a diligent observer.  When I assessed my own accuracy on a “test” of frame counted homers (thanks to one of my assistants who is a TV producer), my numbers were “inside” the frame counts, i.e. indistinguishable from the times generated from the video analysis.

In other words, I expect the BIS hang time data to be very accurate, plenty enough for what everyone wants to do with it…

MGL, I remember you told Dewan when YEARS ago to do hang time, and he liked the idea.  Any idea why it took this long for him to implement?

By the way guys, should I ask Dewan if he wants to do a live chat?

Tango, I don’t remember ever having any contact with Dewan.  I probably mentioned it to the STATS guys a long time ago.  Don’t forget that the main consumers of the data from STATS, BIS, and other companies are the teams.  Prior to recently, no teams had any interest in hang times.  That is one reason it never got done.  The main reason it never got done and probably would not have (for a while) if not for Dewan is that these companies collect traditional data generally, and not data that hard core researchers want or need - especially since those researchers don’t like to pay for that data.  Let’s face it - no one clamored for “hang time” other than us guys, and they really don’t and shouldn’t care what we want…

I am somewhat skeptical of Mike’s claim (#4) that the initial velocity (speed and angle) from hitf/x can be used to predict hang time within a 1/2 sec. by totally neglecting the lift due to spin.  Show me some data to persuade me.  I am more confident of the claim that the hang time can be determined that well by using a model for the spin of the batted ball based on the batted ball speed, vertical launch angle, and perhaps other things.  Of course, it depends on how good the model is.  Combining hitf/x data with direct measurements of hang time should be helpful in developing a model.

Alan, what I claimed was an error on the order of a half second.  This was my memory from the data I had looked at earlier.  I took a quick look back tonight and compared to video.  The video I have is pretty rough, so my hang time measurements from the video are only to the nearest quarter second.

Here is the data for six batted balls, comparing the hang time calculation that only incorporates the HITf/x initial velocity and and a drag calculation (and gravity, of course) to the actual hang time from video.

Hfx calc - Actual
4.3 sec - 4.75 sec
3.3 - 3.75
5.3 - 6
3.1 - 3.5
5.2 - 6
1.4 - 1.75

These were all balls in the air, five fly balls and one line drive.  You can see that the Hfx no-spin calculation consistently underestimates the hang time because it is neglecting the effect of backspin, but the error is on average 0.6 seconds. 

The error is also related to the hang time; the bigger the hang time, the bigger the error. So that is an effect that is easy to correct for to get the error down under half a second without even knowing anything more about the spin.

Mike, what’s your source for these Hit F/X numbers, and what were those hits (i.e. who, when?)

Mike...Thanks for posting your data, which goes in the direction I would expect (underestimate), for exactly the reason you stated.  The one test case I ran last night was a fly ball with a long hang time (100 mph, 30 deg initial conditions), so that the difference was more like 1 sec. between 0 and 2000 rpm backspin.  So, we are not in disagreement.

Re mgl #6:  It’s unfortunate your work on hang times won’t be for public consumption.  That’s part of the problem of being a consultant!  Sportvision is running through all the 2008 video to analyze the batted ball with the pitchf/x cameras.  Combining that information with the hang time will provide a wealth of information for people trying to develop a collision model to determine the spin on the batted ball.

Alan, are we agreed that calculating hang time using “elapsed frames” (one frame = .0333 seconds) is sufficient?

Tango:  When you ask whether 1/30 sec is sufficient, do you mean sufficient to determine the backspin?  If so, that is a good question.  Certainly it can determine the backspin to some level of precision.  So, let me sharpen up the question a bit.  If the flight time is determined to 1/30 sec, what is the uncertainty in the inferred backspin?  I won’t try to answer it off the top of my head and instead will do some simulations and get back to you later today (hopefully).

Isn’t flight time only certain within 2/30 second, since there is uncertainty at both ends of the trajectory?

Back to Tango’s question (#15) as to whether an accuracy of 1 standard video frame, 1/30 sec, is good enough to nail down the spin.  I spend some time today looking at this and come to the conclusion that it is probably good enough, especially in view of other uncertainties that are less well under control.  I think that Greg’s spotters use standard video to get the flight time for his home run analysis (Greg, correct me if I am wrong).

One of my current research projects is to figure out the minimum amount of information needed to constrain the full trajectory.  I have already formed some general impressions, but I don’t have any definite answers yet.  I spend a good chunk of my time working on this problem.

I’ve gotten about as far as Mike had a few months ago, apparently:

http://www.hardballtimes.com/main/blog_article/hang-time/

Estimates of hang time from Hit F/X calculated without the effects of spin. I have it calculated to the tenth of the second, but I rounded to half seconds both as a presentational issue and because I don’t think the accuracy is there to support tenths of seconds. (Although owing to the method of computation, I should probably switch to hundredth or thousanths of seconds, which should increase the accuracy of my distance estimates.)

Colin:  I am not sure exactly how you did your calculation, but I am pretty sure that neglecting the spin is not a very good approximation.  I just did a quickee calculation of a typical home run trajectory (100 mph, 29 deg).  Without spin, the hang time is 3.9 sec.  With 2000 rpm backspin, it is 5.4 sec.  One thing I have done is used at hitf/x data combined with Greg R’s hittracker data for home runs.  What I can do is compare the measured hang time (by Greg) with the hang time expected in the absence of any aerodynamic effects of lift and drag.  What I find is that the actual hang time is longer (as you would expect) by an average of 20% (sometimes as much as 40%, sometimes as low as 0%). 

For a line drive type of hit, the hang time is even more senstive to the spin (at least, percentage-wise).  E.g., a line drive hit 3 ft off the ground at 0-deg has a hang time of 0.44 and 0.74 with 0 and 2000 rpm of backspin, respectively.

Getting the spin is important to getting the trajectory (and therefore the hang time).  Hitf/x does not get us the spin.  Unfortunate, but true.

Professor Nathan - All the formulas I used were derived from the spreadsheet at your site (linked to in the article). I used the cd estimates based upon current velocity, rather than the cd constant.

I reran the calculations including the spin, using 2000 rpm of backspin as a constant. Both values (along with distance) are provided here:

http://www.editgrid.com/user/cwyers/HitFX_Hang_Time_Estimates_v2

First column is the id as per the provided table from Sportsvision, next two columns are without spin, two columns that follow are with spin.

On average, hang time estimates are 80% smaller without spin included, which coincides with what you said.

What I don’t know is if 2000 rpm backspin is typical of hits on balls in play. If I’m understanding the physics correctly (and I’ll conceed that it’s very possible I am not), home runs are more likely to have significant backspin than the general population.

What I cannot answer - at least without more data - is whether even these crude estimates (without spin or with spin as a constant) are better than our current FB/LD/IFFB buckets; I suspect they are, but with only one month of data I cannot actually prove it.

Colin:  Generally I would expect the amount of backspin to increase with increasing launch angle, implying more backspin on a fly ball than on a line drive (and even more yet on a popup).  Hittracker data gives us a pretty good handle on hang time for home runs.  Those data show that hang time increases more or less linearly with the initial vertical component of the velocity, going from about 4 sec at 50 ft/s (34 mph) to 6 sec at 90 ft/s (60 mph).  One of my current projects is to use the combination of hitf/x and hittracker data, along with an aerodynamics model for lift and drag, to determine the spin on the batted ball.  This is still a work in progress.

Colin’s got another article that whets the appetite of HITf/x:

http://www.hardballtimes.com/main/article/evaluating-defense-using-hit-f-x/