THE BOOK--Playing The Percentages In Baseball

Is there a pitch f/x expert (or physicist) who could shed some light on how useful initial batted ball data would be?

Seems to me that if we know the temperature and humidity and have a rough estimate of wind… and pitch f/x tells the initial velocity, angle off the bat, and spin of the ball… couldn’t the ball’s path be modeled pretty accurately?  What would the standard error or such a model be, in terms of location, on a 300 foot fly ball?  10 feet?  3 feet?

The initial batted ball data would be incredibly useful for evaluating pitching and hitting.  It would be less useful for evaluating fielding, although Greg Rybarczyk had a great example of how it could be used in the Hardball Times Annual 2008.

Between errors in the initial parameters off the bat and the fact that HITf/x can’t measure the spin of the batted ball, the typical error on the final location of a fly ball might be 30 feet or more.  Not knowing the spin is a huge impediment to knowing the trajectory.

There are some ways to estimate the batted ball spin, however, that might improve the final location error substantially.  I’m working on an improved model of the ball-bat collision that could hopefully be used toward that end.

I’m still waiting for them to solve the original problem of finding a batter’s true zone so location data can actually be used.  You would think after a season and one-half they could control that by now.

Jimbo, most of MLBAM and Sportvision’s improvements to the measurement of the batter’s zone go into the private product that is used for umpire evaluation.  There is post processing done to improve the quality of that information, but MLB does not seem to be to eager to have their umpires evaluated publicly.  You can argue whether that is a good idea or a bad idea, but I think that is what is behind the lack of the better batter zone information being made public with the rest of the Pfx data.

Mike: if we use human beings (as is currently done) to determine batted ball location, can we then say that given this data, we can determine hang time?

I would love to see some Hit-f/x next year. This way, we might be able to delve deeper into how the different atmospheres and winds in different cities effects the balls movement and distance traveled.

would it be at all possible to use the pitch-f/x measures of how a pitch moves prior to being hit to correlate how a ball moves once it gets hit? Is there even a correlation?  That might be a way to have a better ‘guess’ to the spin of the ball after it gets hit which, along with the other hit f/x data that *crossing fingers* will be available, might be able to give you a decent idea where the ball will land.

More data is always better, right? =)

Color me excited.

HOT/COLD ZONES!

Boy.. I’ve been waiting for that for forever, haha.

@Gumbotsu

The velocity and spin of a pitch does affect the outcome of the batted ball, but not as much as you might think. I don’t have my Physics of Baseball with me at the moment, but if memory serves, it is on the order of a few feet for a 5 mph difference in speed. Also, a fastball suppresses backspin and a curveball enhances it. Once again, if memory serves, the difference in speeds between those two pitches is just about compensated by the difference in spins.

Backspin as a component of hitting for power and average is one of the least appreciated aspects of hitting. Given the same launch speed and optimal launch angle, a ball with no spin that goes 360 ft will travel 400 ft with 2000 rpm of backspin and arrive sooner due to a flatter trajectory. I have an article brewing on just that topic. No promises when it will be done though.

Tango/#5, in order to calculate the trajectory of a fly ball, we need to know the initial position, initial velocity, and acceleration of the ball.  We know the initial position, and HITf/x will provide us with a good measurement of the initial velocity. 

The acceleration is a combination of the effects of gravity, the drag force, and the Magnus (spin) force.  We know gravity, and between some atmospheric data and what we have learned from PITCHf/x about the coefficient of drag on a spinning baseball as a function of velocity, we have a good enough handle on the drag force that it is not our biggest source of error.  We don’t know what the spin on the batted ball is, unfortunately, and HITf/x won’t tell us that.

If we knew the final position and the hang time, we could determine the spin force.  If all we know is the final position, we have to estimate the spin force in order to determine hang time.

Hit Tracker has always looked at the whole trajectory, and using some informed assumptions about spin, and a best estimate of wind, arrived at launch characteristics.  Naturally, since spin does not always conform to the spin model (which is not a constant model, by the way), and since wind can’t always be accurately estimated (and varies across the flight of the ball as well), the launch characteristics from Hit Tracker have always had more uncertainty than the distances (which are well-constrained due to the method, and thus very accurate in all but the most unusual cases).

I think a combination of true measurement of the launch parameters, combined with Hit Tracker’s use of flight time and landing point measurement, could yield even more accurate trajectory data, very accurate spin info, and excellent insight into the wind impact across the flight of the ball.

Paging Dr. Alan Nathan…

Couple of points with Hit F/X

Absolute, Relative, Dew Point numbers for humidity are almost never kept historically and equally between towns.  If it goes into effect, the data might need to be collect on a game by game basis

In Retro sheet there is no 7 wind (in from RF) in the last 4 year at any game.  I would exactly trust the wind data, but it is all we have to work with.

Jeff #14

The weather recorded in the boxscore for a game is typically captured several minutes before the beginning of the game, and is thus of questionable value from the very beginning if you are looking past the first inning or so.

I use weather data from the Internet, choosing available weather stations that are closest to the ballpark.  As for the exact timing of the batted balls, I wrote some code to estimate this and interpolate within the weather data stream, but the component data has the exact timestamp for each pitch, so half that work won’t be needed any more.  That all works fine for temperature and humidity, which won’t be hugely different a few blocks away, but for wind, I try to make an observation from within the park off the video.  A lot of work, but probably worth it most of the time.  I wish MLB would place a weather station in the park at field level (CF fence would be my vote), and tie it in to the component database so for every pitch, we have a timestamp and a set of weather conditions for the park.  This should be easy.

Hi guys.  Good discussion.  Sorry I don’t have time for a full response right now.  Suffice it to say that I am very much in favor of getting the initial trajectory with HITf/x.  For sure, that can be combined with Greg’s landing point and time-of-flight data to pretty much constrain the spin and therefore the full trajectory.  I did such an analysis for the Barry Bonds’ 756th home run.  See
http://webusers.npl.uiuc.edu/~a-nathan/pob/bonds/b756.html
For that analysis, I got the PITCHf/x videos and analyzed the hit ball by hand, then used the camera transformation to convert to an initial trajectory.

All for now…

I am not sure I agree with one of Matt’s points.  He says that a ball hit with backspin will have a flatter trajectory than one hit without backspin and therefore have a shorter flight time.  Perhaps I misunderstood, but it is exactly the opposite.  The upward Magnus force of a ball hit with backspin give a higher trajectory, a longer trajectory (assuming the launch angle is reasonable), and a longer flight time.

Mike Fast said he is working on a model for the spin of a batted ball.  I have my own model I have been working on, based in large part on experimental data that I took.  Not quite ready for publication yet (but will be soon).  The new Trackman radar system that some of you may know about has the ability to measure the initial spin on the ball also.  So, we are likely to get lots of data on this in the coming year.

If we knew the final position and the hang time, we could determine the spin force.  If all we know is the final position, we have to estimate the spin force in order to determine hang time

Mike - I believe that if you know accurately the final position, the initial factors and the wind, temp and altitude, that there is only one spin rate that will have the ball land at that location, and that the hang time can be calculated.  The problem is that the exact wind factor is only accurately known for enclosed stadiums, and the exact models for drag and spin force for the all the speeds of a hit ball are not universally agreed upon.

Peter/#18, on second thought I believe you are right.

Alan/#17, the model I am working on is for ball-bat collisions with a generalized bat orientation at contact.  At the current time I am assuming an elastic collision for my purposes, but the adaptation to a model with friction and deformation of the ball could/should follow.  Right now I am more interested in the direction of the batted ball than the velocity or spin, so the assumption of an elastic collision works fairly well.

Mike - Email me.  I might be able to provide some data that will be useful to you in your project.

Peter/#18:  Actually, I don’t agree with you (and therefore, I would have to disagree with Mike/#19 also).  That is, I think the trajectory is not fully constrained by the initial conditions and the landing point.  You really do need the hang time to get the spin.  That is, balls hit with the same initial velocity (including angle) and ending up at the same landing location can get there by different paths depending on the spin.  The flight time sorts all that out.  I actually prepared a slide about that for the PITCHf/x summit, but never got a chance to show it as the HITf/x session was running too long.  I’ll see if I can dig that up.

Mike/#19 (and other that might be interested):  The formalism for the ball-bat collision (including getting the spin), can be found in a paper I wrote.  Here is a link:
http://webusers.npl.uiuc.edu/~a-nathan/pob/AJP-Oct2006.pdf.  I would say that this formalism has the minimum of complexity in terms of the number of parameters needed to describe the collision.  The data shown are low-speed data and not necessarily relevant to realistic collisions.  The newer data I referred to in my earlier post was taken at much higher speed and should be more relevant to the game.  Based on those data, I have my own model.

Re my last post (#21), let me back off on my disagreement with Peter and Mike.  I want to think more about it and post again later.

Alan, I’ll certainly defer to you as the expert. 

I initially thought as you say in #21, but I could convince myself either way if I think too hard about it.  I think I need to work out an actual example rather than just trying to think it through in my head.

In terms of the ball-bat collision model, I am definitely building off of the model you presented in the Scattering paper.  What I am trying to do, however, is to generalize it for a bat that is not oriented parallel to any axis (and a pitch that is also not oriented parallel to the y-axis, although that varies less than bat orientation).  This generalization has not been trivial for me to accomplish.  Perhaps I am missing something from your formalism that would have made my task easier?

Alan - You may be correct in the special case where the spin is oriented only vertically, but where the spin has both a vertical and horizontal component I think that the simultaneous equations computing vertical and horizontal movement yield a singular spin RPM and angle.

Re Peter Jensen’s post #18, I dug out a plot I made but never showed at the summit.  Here is a link to it:

http://webusers.npl.uiuc.edu/~a-nathan/pob/trajectory.JPG

What is shown are three calculated trajectories for identical initial velocity (90 mph, 35 deg) but for three different values of the spin (indicated on plot).  I did not constrain the calculations to go through the same landing point, but they did anyway, within 4 ft.  The spread of spins shown represent the uncertainly in spin due to my collision model, in which the spin is a function of the initial speed and launch angle.  The remarkable thing is that the trajectories all look roughly the same.  This plot gives me confidence that HITf/x will be able to tell us quite a bit about the trajectory, even without knowledge of the spin.

FYI, the collision model I used is as follows:
w/v = -23.1 + 1.24*theta
with v in mph, theta in deg, w in rpm
e.g., v=110 mph, theta=30 deg gives w=1550 rpm
Overall accuracy:  I estimate at no better than +/-20%

Of course, the calculation uses a particular model for drag and Magnus forces, which are known only imperfectly.

This should help resolve the definitions of line drives that I pointed out last week. It doesn’t give us hang time, but the speed off bat and angle of elevation will be quite helpful in objectively classifying batted balls.

If nothing else, the data can be used to fill in other parts of the picture that we don’t have today. 

Being interested in how effective a pitch in a location in a count is, I’m pleased hfx will provide an incomplete, but more direct, measure than slugging rates and the like.  But this isn’t just another color on the palette, it’s a new brush.

Peter, I emailed you at the address from the Pfx Summit list.  Alternatively, you can email me by clicking on my name on this post.  Thanks.

With regards to my comment: I was comparing two balls that travel the same distance - One with backspin (~2000rpm) and one without. Also, both initial trajectories have to be less than 45 deg. For popups we get the opposite effect. 

A baseball example would be two hard line drives (one with backspin and one with no spin) that hit the base of the wall. Both balls having been hit with the same initial velocity. The backspining ball would have arrived sooner by taking a straighter path to its destination. Therefore, more likely to not be caught and be an XBH.

I might still be wrong, but I wanted to clear up what I was talking about. 

Matt

One more clarification: Those two hit balls would have different launch angles as well. The backspinning ball would have a lower angle.

You could imagine the backspinning ball hit with a fairly level swing by ARod (who, as I understand hits with a lot of backspin) and the other ball hit by Jack Cust with his big, loopy uppercut swing.

Matt...given that last clarification (#30), I withdraw my objection and agree with you.

It occurred to me that it might be tricky to figure out the precise initial spin, even with the landing point and time of flight, because we might not be able to *measure* spin-down.  I am not sure if it will be possible to distinguish a high initial spin and high rate of spin-down from a lower initial spin with a lower rate of spin-down, as they could conceivably average out over the flight of the ball.  The hope would be that in the brief interval of camera observation at launch, we could measure ball positions precisely enough to nail initial spin and spin-down, but I am not sure about this.

What do you all think?

Re Greg/#32:  I have some recent data on spin-down (I like to call it “spin decay”, from my nuclear physics background!) using the Trackman radar system.  The time constant for spin decay is very long, perhaps 40 or 50 seconds.  If it is, say, 30 seconds, that means the spin decrease by about 3% (1/30) every second.  Whether it is 30, 40, or 50 doesn’t matter a great deal.  The main point is that it is long compared to a typical flight time, so that it can safely be ignored when calculating a trajectory from the initial conditions.  I should point out that this is ongoing research.  There are *no* published data on spin decay for a baseball.  The data that we will publish will be the first.  I expect to have a conference paper written that (in part) addresses this issue by the end of March.  There are data on a golf ball, where the time constant is about 20-25 sec.

BTW, in his book Adair has the time constant at 5 sec.  That is almost surely not right.  Nor is it based on any careful measurements.  As with many things in his book, it is a “seat of the pants” estimate.  To his credit, I don’t think he characterizes his number as anything other than a best guess.

Alan, using a good number for spin decay constant should work fine, it sounds.  Question: are there any factors that might change that constant significantly, e.g. humidity, temperature, altitude, variations in ball size/weight, etc.?  I am guessing not, but wondering if your data had anything to say about that?  Also, it seems that the seam orientation might influence spin decay, did your experiments allow you to know the seam orientation for each tracked ball?

Everything I’ve read about two-seam vs. four-seam spin has said that there is no appreciable difference in Magnus effect. That would also imply no difference in decay rate.

So why do pitchers bother to spin the ball with two or four seam spin? I think it all has to do with deception and not tipping the batter. Four seam pitches have a dot at the spin axis, but for fastballs and curveballs it is not observable because of the orientation of the spin. Two seam spins don’t show this dot so are useful for pitches where the spin axis is observable, like a slider.

Two seam spins show stripes when observed side-on, so they may not be appropriate for fastballs and curveballs. Admittedly, I don’t know if those stripes are detectable by batters in game situations. There’s no baseball lore that I am aware of about stripes like there is for dots. 

For sure there are some biomechanical reasons for throwing with a two-seam grip. A sinker is a good example since there has to be purchase on the ball for the flip the hand does at the end of the pitch.

Just more stuff I’m working on…

Matt

Matt, are you saying that the same arm motion used with a 2-seam and 4-seam grip will result in the same pitch trajectory?  If so, I don’t think I buy that.  I’m willing to be convinced, but I don’t think the difference between two and four seams is exclusively deception…

I had always thought that the arm delivery was the same for 2- vs. 4-seam fastball, but that the pressure applied by the fingers was different.  As a result, a 4-seam fastball has primarily backspin, resulting in a very straight pitch.  And a 2-seam fastball has just as much spin but less backspin and more sidespin, resulting in a tailing action (break towards arm side).  When I look at pitchf/x data, I can easily distinguish the two pitches in a plot of vertical vs. horizontal movement (pfx_z vs. pfx_x).

Two- and four-seam are distinct in terms of movement.  They fall along the opposite sides of the arm axis you can SWAG from a pfx plot.  The lower the arm angle, the more likely the two-seam is to be referred to as a sinker.  And one man’s four-seam can move like another man’s two-seam, in terms of spin movement.

Greg,

Yes, that’s essentially what I am saying. I agree it’s a non-intuitive result.

Here’s a quote:

Physical tests show negligible differences in deflection magnitude between the two- and four-seam fastballs, curveballs or sliders. The big differences seem to be psychological—specifically perceptual. The batter can see the two red stripes and the flicker of the two-seam fastball and palmball, the two red stripes of the two-seam curveball and the red dot on a four-seam slider. All of these clues alert the batter to the type of spin on the ball and help him predict its movement.
In conclusion, the pitcher should use a four-seam grip for fastballs and curveballs to remove the perceptual clue of the two red stripes and the flicker. Then, he should use the two-seam grip for the slider, to remove the clue of the red dot. These techniques could make a fearsome pitcher even more difficult to hit. But if you’re in luck, he hasn’t read this article.

From this article (from 2005):

http://www.americanscientist.org/issues/id.962,y.2005,no.3,content.true,page.1,css.print/issue.aspx

Unfortunately, I wasn’t able to find the “physical tests” mentioned in the article online. I realize just stating this as fact without data backing it up is less than 100% convincing.

Matt

As I understand it, the key to the quote in #39 is “deflection magnitude”, which (since it is not deflection vector) is determined by, as the authors say, “the spin rate and forward velocity of the ball”.  It says nothing at all about the direction of spin. 

The linked article also claims:

a two-seam fastball does not look like a four-seam fastball, although the speed and spin rates of these pitches are the same.

From what I have seen, neither the speed nor the spin rate nor the spin direction are the same for the two-seamer and the four-seamer.

The authors also reference “1,200 revolutions per minute—the typical spin rate for a fastball”.  Mike Fast, if I recall correctly (and please excuse me if I am incorrect), has shown much higher spin rates for fastballs than this. 

Regardless, I see no reason to believe that different grips should produce the same spin rate, but rather that different gripping of the seams would allow for the production of different spin rates, due to greater leverage on the ball via the seams. 

Same for the spin direction.  The four-seam grip should allow for greater leverage in the backspin direction, whereas the two-seam grip should allow greater leverage in the side-spin direction.

Pitch speed is obviously dictated by grip as the change-up is supposed to be just a change in grip, not arm speed.

All true, and yes there are some inaccuracies in that article based on PITCHf/x data gathered just in the last couple years.

The fundamental question is whether two balls, one with with two seam spin and one with four seam spin, will have the same deflection (or close enough not to matter) given all other factors (rpm, velocity, atmospheric conditions) are equal.

I think they are saying that the two spins are not important compared to other larger effects.

Matt

I wrote the following comment prior to seeing Matt’s response #41, but since most of still seems interesting/applicable, I’ll go ahead and post it.
------------

It’s worth noting that the Bahill and Baldwin article referenced by Matt/#39 was written before the advent of PITCHf/x.  So they were looking at laboratory data and wind-tunnel data and didn’t have the advantage of the million-pitch data set collected in real-baseball conditions by Pfx.

Most pitching coaches recommend a four-seam grip for the fastball. They presume that a seam perpendicular to the trajectory of the pitch encounters greater air resistance than the smooth surface of the ball. Therefore, they speculate that a four-seam fastball encounters greater air resistance than a two-seam fastball, which might create a stronger Magnus force on the ball. Pitchers assume this produces a greater lift on the overhand fastball. Indeed, pitchers have written that the four-seam grip is more effective than the two-seam grip in producing rising fastballs. However, wind-tunnel tests have shown no significant differences in lift between two- and four-seam orientations. Two of us (Baldwin and Bahill) have explained that the perceived rise of the four-seam fastball is probably a perceptual illusion.

I agree with SirKodiak that the primary difference between the two-seam and four-seam orientation is not in the lift coefficient (magnitude of the deflection) but in the direction of the deflection.

With PITCHf/x, we don’t directly measure the spin rate.  However, with the assumption that the lift coefficient is approximately equal to the spin parameter (S = radius * spin rate / translational velocity), we can calculate a spin rate.  (This spin rate is really a projection onto the x-z plane, meaning that we miss the football spiral component of the spin around the direction of travel.) The typical spin rates we calculate for fastballs are in the 1500-3500 rpm range.  Two-seam and four-seam fastballs have similar spin rates (but different spin axis) when looking at the major league population as a whole, but for individual pitchers the spin rate may vary significantly between the two types.

With the Trackman radar system, we can make more direct measurements of the spin rate by looking at the spacing of the harmonic sideband peaks in the radar returns.  I haven’t personally seen any of the Trackman data yet, but perhaps Alan could comment on what he has seen.  I know he’s taken Trackman data on batted balls, but I think perhaps he’s seen some data from pitched balls as well.

However, ultimately what a two-seamer and four-seamer do depends a lot on the pitcher and how he grips and releases the ball.  Look at Kenny Rogers or Jon Lester and you’ll see very distinct four-seam and two-seam fastballs.  Look at Josh Beckett, Cliff Lee, or Jamie Moyer and you’ll have a much tougher time distinguishing the 2-seam and 4-seam fastballs.

Just a few words about the potential of the new Trackman radar.  The radar was originally developed for golf (see http://www.trackmangolf.com/index) and those of you who watch major golf tournaments on tv have probably seen it in action.  It has recently been adapted for use in baseball.  It is a so-called phased-array Doppler radar and has the ability to track the ball through its entire flight--not only pitched baseballs but also batted balls, and in addition it provides information on the spin.

Not being a shy person, I have been nurturing a relationship with ISG, the company that developed the Trackman, much in the same way that I have developed a relationship with Sportvision.  I have visited the company twice, which is no small feat given that they are in Copenhagen.  I have learned quite a lot from them about how the device works and some of its limitations.  As far as I know, the only device currently in use in the US is owned by Rawlings, and they call it SciFly.  They are using it to measure batted-ball speed as a way to help batters choose an appropriate bat.  I have also developed a pretty good working relationship with Rawlings, and they have been very helpful in allowing me to use the SciFly for some experiments and sharing some of their own data with me.  I have lots of data, all of which were taken with a pitching machine (both balls projected horizontally as in a pitch and balls projected like fly balls).  I (and my principal collaborator Mont Hubbard from UC/Davis) have lots of data to pore through.  There is absolutely no question that this device has the potential to be of enormous value in tracking hit baseballs.  Not so clear is how competitive it is with PITCHf/x in tracking pitched baseballs.  My own analysis indicates that the typical single-point precision of PITCHf/x is about 1 inch.  I don’t yet know what the comparable number is for Trackman.  Mont and I have committed to writing a paper on our measurements for a conference and papers are due at the end of March.  I will know much more (hopefully) by then.

I gave a bad link in my previous post.  Here is the correct link to Trackman:
http://www.trackmangolf.com
Also, Rawlings has put together a short video on the SciFly:
http://www.baseballwebtv.com/Video.aspx?videoID=23814