THE BOOK--Playing The Percentages In Baseball

One more piece (of about 100,000) of the puzzle to unravel what makes pitchers good/bad, etc.

I wish he would write a little more like he was talking to a 10 year old.  I have to read each sentence sometimes about 5 times.

For example, this sentence is an abomination, although I THINK I know what he means:

The vertical axis shows the time, in seconds, for the pitch to travel from 50 feet from the point of home plate (the origin in the PITCHf/x coordinate system) to the front of home plate (1.417 feet).

Now, how does he compute the spin rate and spin axis of each pitch?  I don’t think the pitch f/x data provides that, does it?  Does he use some algorithm that takes the x and y coordinates of break along with the speed in order to calculate spin rate and spin axis?

I am starting to think that there is no real good way of presenting the data.

MGL—Dr Alan Nathan provides all the equations you need, although I suspect you’ll find that paper heavy going too.

http://webusers.npl.uiuc.edu/~a-nathan/pob/pitchtracker.html

Tango, thanks for the link here and for the kind words.

The spin direction I use is the direction of the spin axis, i.e., the north pole around which the ball is spinning, according to the “right-hand rule”.  That’s a convention from physics, and I assumed it made sense to everyone else, but that may not be the case.

The direction you are talking about, if I understand you correctly, is the direction in which the Magnus (spin) force is acting. Thus, it’s the direction in which the spin causes the ball to move.  An overhand curveball moves down, a slider/cutter move to the side.

In terms of what the ball is doing, describing the direction the ball moves due to spin may be more transparent to the reader.  On the other hand, it was easier for me to understand what the pitcher is doing with his hand/wrist/arm to provide spin to the ball when I describe it by the direction of the spin axis.

I’d be interested in getting more feedback on this from others, too.

I was just thinking in compass/navigation terms.  If the convention is what you say, that’s fine.  I understand either way.  The key is to follow the common convention.

Yes, the spin is purely a parameter from the pitch thrown (i.e., means something to the pitcher), and should be described in those terms (spin axis and spin revolutions).  So, it’s great that you show it in these terms, since that’s how a lay person will see it.  Whether it should be rpm or rps, I don’t know.

I’ve never been a fan of showing the x/y inch movement representation for spin (the gravity-less movement).  It really means nothing to me.

Your last graph, which shows the actual physical movement (due to the spin, gravity, AND time) is how the common person will think of it, and so, it’s great that you show it like that.

The other question is whether we prefer things from the batter/catcher view or from the pitcher view.  Tough call either way.  My guess is that since the ESPN and Fox graphics will certainly become more common in the years to come, they will certainly continue to show their charts from the pitcher’s viewpoint, which is the same viewpoint the viewer has when watching a ballgame.  And for consistency’s sake, that probably would be the tipping point for me.  It’s also nice that when you look at the right-side of a chart that this represents the RH batter.  I’m 51/49 on this.

I agree, it will be interesting to see how the common folk like me see these charts.

MGL, I feel sometimes with the PITCHf/x data like we are almost in the shoes of Henry Chadwick, trying to organize something meaningful out of a myriad of options.  Just as Chadwick drew on his cricket background to decipher baseball, we can draw on the existing baseball lexicon to describe the PITCHf/x data, but ultimately we’re going to have to develop a new vocabulary for PITCHf/x, just as Chadwick invented batting average and the box score. 

Our existing sabermetric vocabulary revolves around the game and the plate appearance as its fundamental units.  That framework can be stretched a little to describe pitch sequences as is done in a Retrosheet event file, but it stretches beyond the breaking point when trying to describe the level of pitch detail we now have.  So we work on a new vocabulary in hopes of developing something that is accurate, meaningful, concise, and easily understandable.  I especially appreciate the efforts here at this blog to further that process.

One thing we are fighting is the inherent difficulty in describing a four-dimensional (x, y, z, time) event in a two-dimensional image.  That inherently requires compromises.  The skill comes in deciding which compromises to make depending on what needs to be communicated in a particular instance.  I don’t think we’ll ever come up with THE perfect way to describe a pitch for all applications.  We have developed very different vocabularies for the same plate appearance depending on whether we are talking about hitting or pitching, and we can do similar things at the pitch level.

I don’t know if we’re ever going to standardize on a best terminology, but if some of us can work together to find what makes the most sense, hopefully it will gain traction and wider acceptance over time.

Regarding the abominable sentence, I have to agree that one is almost painful.  Writing on my blog is always a struggle between publishing the article and perfecting and clarifying.  That sentence clearly lost the battle.  What I was trying to communicate was that the graph was showing the time from shortly after the pitcher released the ball until it crossed home plate.  But then I tried to mix in specifics about the initial and final points, while condensing them for brevity, and that’s where it descended into disaster.

The origin in the PITCHf/x coordinate system is at the point of home plate.  That’s x=0, y=0, z=0.  The initial measurement of position is made by the PITCHf/x system at the point in the baseball’s trajectory 50 feet from the point of home plate.  The final measurement of position is made where the baseball crosses the front of home plate.  Home plate is a pentagon cut from a 17-inch square, so the front of home plate is 17 inches, or 1.417 feet, from y=0.  So, the pitch time shown in my graph is the time from the point y=50 feet (shortly after release) to the point y=1.417 feet (front of home plate).

John is correct about the basis of my spin calculations.  I should probably provide a link back in all of my new articles to previous more detailed discussions.  I went into depth about how I calculate spin in an article about Jonathan Papelbon: http://fastballs.wordpress.com/2007/09/07/magnus-papelbonus/

I derived my formulas from Dr. Nathan’s paper analyzing a Jon Lester start that is linked at the site which John Beamer mentioned.  In his paper he presented some approximate formulas which do not require actually solving the equations of motion for every pitch.  I solved these formulas for spin direction and spin rate, and I’ve found them to work quite well in the regime of motion that we can expect from a pitched baseball.

And regarding conciseness, I’m clearly not the guy to turn to for that perspective.

Don’t worry about MGL’s criticism, which are always (or usually) meant to be constructive.  (Always = if he respects you; usually = if he’s perturbed by you.) He’s certainly directed a few of those my way, which I take in the “always” vain, regardless of his intent!  And we know that if you see a very long single-paragraph post, a three-letter handle is sure to be at the end of that.  He may sound gruff, but he’s just like the rest of us.

Back to the matter at hand: yup, the 4-D thing is tough.  Using color coding as a 3rd dimension definitely helps. Another thing that you can use (which studes has used alot) is size the point as an additional dimension.

For your chart, one thing I thought of is: concentric circles.  Create your standard xy quadrant, where x=y=0 is the center of the chart.  A point along the y axis, above y=0 (at x=0) means the spin is backspin (North).  To measure speed, it’s the distance from the x=y=0 point.  The farther away you are from that point, the faster the pitch is thrown.  You can set the x=y=0 point as 50mph.  A pitch thrown at 100 mph is twice as far away (using the radius) from the center point as a pitch thrown at 75 mph.  You can imagine therefore a circle that represents 100 mph all around the zero (50 mph) point.  And where it lies in the quadrant is the spin axis of the pitch. 

It’s really limitless the way you can represent all the parameters you have.

***

Another presentation that Joe Sheehan did was to show the data, based on where the ball was at T-0.25 seconds.  Basically, what’s the reaction distance for the batter.  I think it’s alot easier to tell someone that he’s got to make a decision to swing or not when a pitch is 32 feet away or 42 feet away, than to tell someone he’s got 0.32 seconds or 0.26 second to react when the ball is 40 feet away.  This is just like when you cross a busy street.  You need a reaction distance.  No one thinks in terms of 0.25 or 1.22 seconds.

Briefly…

I love your (and Joe P. and Walsh’s) work, of course.  Let’s make no mistake about that.  If I were in charge of a team, I’d hire you for a lot of money!

Sure, I knew what you meant with that sentence:  “From 50 feet from the back of the plate, to the front of the plate, which is 50 - 1.417, or around 48.6, feet” would have sufficed, even though that is awkward. Trivial though.

Another question:  How can you estimate the spin axis and rate (especially rate) if you don’t know the orientation of the seams?  Or is the spin rate just a “fiction” which “includes” the actual spin rate AND the orientation of the seams (which we don’t know)?

For example, if the pitch f/x data tells us that the ball was travelling at 90 mph and had no horizontal break (a 100% overhand pitch), and a vertical break of 6 inches less than a no-spin ball, couldn’t that be a 4-seam fastball with X amount of spin or a 2-seam fastball with Y amount of spin?  Wouldn’t the spin rate be different depending on the orientation of the seams even for the same velocity and movement?  So without knowing the orientation of the seams, how can we estimate spin rate from the pitch f/x data?

MGL, no, we don’t know the orientation of the seams.  From what I understand from reading Alan Nathan’s work, the orientation of the seams has negligible effect on movement for a pitch that is spinning quickly (i.e., everything but a knuckleball).

That conclusion is contrary to what I’ve read of Robert Adair’s work.  Apparently Adair indicated in the Physics of Baseball that seam orientation mattered, but Dr. Nathan’s experiments are better and more complete than Dr. Adair’s.  Nathan was certainly aware of Adair’s work in constructing his experiments. 

Plus Nathan had access to at least some of the PITCHf/x raw trajectory data to validate his conclusions during this season, which is a wealth of data far beyond what was available to Adair.  Although Nathan noted the seam orientation effect as an area of further study in his June 2006 presentation to SABR, all of his work since then assumes that effect can be ignored, and I believe I’ve seen him make that statement explicitly somewhere, although I can’t find it right now.

Maybe Nathan could clarify this point since it seems to come up repeatedly, not only here but elsewhere as well.

Perhaps I just don’t understand what you are talking about, but I used to pitch and I’m 99.9% certain that the orientation of the seams makes a difference in the movement of a pitch.

Are you saying it doesn’t matter how you hold the ball before throwing, the only thing that matters is the rotational force put on it?

Rally, I’m saying that once the pitch is released, the orientation of the seams doesn’t matter very much in affecting the drag force or Magnus force on the ball compared to the Magnus force generated on the ball by the spin itself.  This is my understanding of Dr. Nathan’s work.

Clearly, seam orientation in the pitcher’s hand matters a great deal in terms of what kind of spin the pitcher can put on the ball in the first place.

Hi...Alan Nathan here.  I’ll try to find some time tonight to weigh in on the discussion here, especially about seam orientation.

It sounds like what Mike is saying is that how you grip the ball (seam, cross-seam, or anything in-between; different amount of pressure; etc) lets you control the spin axis and spin rpm, but that once the ball is out of your hand, the orientation of the seams don’t matter (to any measurable degree).

Sounds like DIPSf/x!

And just as in DIPS, knuckleballers are the exception.

Hi...Alan Nathan again (please forget the Dr. stuff!).  Some points:

1.  Regarding seam orientation and its effect on the trajectory, Adair covers that in his book to some extent (pp 61-62, 3rd edition).  I don’t disagree with anything he says.  The effects are not large if the ball is spinning, since the rotation averages over many different seam orientations.  He makes the point (and, again, I agree) that a 4-seamer on the average looks like a “rougher” surface (to the on-coming air flow) than a 2-seamer.  Rougher means less drag, so that a 4-seamer has an average speed about 1 mph faster than a 2-seamer.  That is a small effect.  The Magnus force might also be different for the two orientations, being somewhat larger for 4-seam than 2-seam.  This will affect the break of the ball due to its spin (as Adair points out), so that there will be a bit more “hop” to the 4-seam fastball than the 2-seam fastball.  Adair goes on to point out that a 2-seam fastball might be gripped with the fingers on the smooth part of the ball rather than the stitches, thereby reducing the friction between fingers and ball.  Such a ball will be thrown will less backspin and therefore more vertical drop.

2. For what it’s worth, I understood perfectly what Mike Fast meant in his sentence about the travel time.

3. Regarding the spin and spin axis, as Mike points out, I have given approximate expressions in the short writeup I did on an analysis of one of Jon Lester’s outings.  Some people prefer to see the spin axis (that tells us what the pitcher is doing to the ball); some people prefer to see the break direction (sort of the batter’s point of view).  I find merit to both of these points of view (and, by the way, if you want to know the break angle, just take the spin angle and subtract 90 degrees).

4. There is a related question as to whether you show the “movement” (pfx_x and pfx_y) or the “break”.  I defined precisely what these mean in the link you have referred to.  I think the “movement” numbers are kind of numbers that physicists like since they tell us what the effect is of the Magnus force.  I think players prefer “break”, since they give a better view of what the ball is actually doing.  Just to be sure we are all on the same page, the break is defined as follows.  Draw a straight line from initial to final point.  The break is the maximum deviation of the actual trajectory from that line.  For a hard fastball thrown with backspin, the break is very small.  So, for a point of comparision, the break measure (roughly) the deviation of the ball from a hard fastball trajectory.  That is much easier for most people to visualize (and to put into some overall context).  For classifying pitches, however, I prefer using the “movement” numbers.

5.  Someone meantioned in post#7 about concentric circles.  I think that is the “polar plot” technique I used in the Lester analysis.  The velocity is measured radially outward from the center in concentric circles.  I very much like that way of presenting the data for the purposes of classifying pitches.  Of course, there are many ways.

6.  I wish I had as much time as many of you seem to have to devote to this exercise!

I think we are all on the same page here. 

The thrown pitch can be broken up into several independent parameters.  And it is those parameters that point to the description of the pitch (speed, release point and tangent, spin axis and rpm, high point, and final location).  If we are concerned about what the pitcher is throwing, I’m fine with showing any of the “physics” parameters.

When it comes to human terms, if we want to know how the batter sees it, the effect of time and gravity has to be included.

I think it’s incumbent on the analysts, when presenting this data, to make quite clear what is being presented.  I can guarantee you that 90% of the people will think that all the charts reflect “human” terms, not the individual parameters.

“break” is the proper human term.  “movement” I would prefer to go away, and be replaced with something less ambiguous, like “gravity-less movement”, or “Magnus movement”.

I agree that the data is robust enough to tell us pretty much all we (and the batter and pitcher) need to know about each pitch, but when I see someone (for the first time) give the rotational speed and axis, when that is not actually measured by the pitch f/x equipment, I want to know where it comes from and if it is accurate, even though it does not really matter.

If a 2-seam fastball thrown with the same initial velocity and the same rotational speed is indeed around 1 mph slower than a 4-seam fastball, that is a lot, I think.  Plus Dr. Nathan also says that a 2-seamer will have more Magnus force and thus a 2-seamer with an orientation other than “level” (over the top) will apparently break or move more than a 4-seamer. 

Given those 2 things, I still (and now even more so) fail to see how anyone can list the spin angle and spin speed without knowing the orientation of the seams (e.g., whether it is a 2-seamer or a 4-seamer).  I may be missing something though.

Not to mention that, but I seem to recall that some of the pitch f/x researchers differentiate between 2 seam and 4 seam fastballs (maybe not).  If there is only around a 1 mph difference, how can one know which fastball is thrown with what seam orientation?

So, again, my question to Mike and somewhat to Allen, is, for example, if a pitch (say a fastball) has an X horizontal break, how do we know whether it was a 2 seam with a Y spin orientation or a 4 seam with a Z orientation, if the 2 and 4 seam pitches will break differently?  Same thing with speed and verical break.  There have to be different formulas for computing spin speed based on vertical break, depending on the orientation of the seams.

IOW, as was my original contention, it seems to me that we can only estimate spin speed and axis based on the observed vertical and horizontal breaks, only if we know the seam orientation.

No time right now, but when I get a chance I till try to clear up the confusion that MGL is having.

Responding to MGL (#16):

As I have tried to emphasize in the various things I have written about PITCHf/x, the magnitude of the spin (rpm) is only a crude estimate.  The estimate is based on the relationship between the size of the Magnus force and the spin magnitude.  The size of the Magnus force is reasonably well determined by the trajectory.  However, the relationship of the force to the spin magnitude is not perfectly well established (including the dependence on seam orientation).  So, the estimate that Mike and other (including myself) use is just that:  an estimate.  Do not overinterpret it.

On the other hand, the direction of the Magnus force (and therefore the direction of the spin axis) is very well determined from the pitchf/x trajectory.  It does not depend on the seam orientation.  The numbers used by Mike are very robust, except in the (rare) case where the movement on the pitch is very small.  In that case, the Magnus force is very small and it is hard to determine its direction accurately.  For those of you mathematically inclined, it is the
“zero divided by zero” problem.

One final word:  MGL cautions against using “computed” quantities (such as the spin direction) that are not part of the pitchf/x data base.  I want to remind everyone who uses pitchf/x data that the only thing that is determined from the trajectory data is the 9-parameter fit.  From that fit, ALL other quantities in the data base are computed (the initial and final velocities, the break, the movement, etc.), based on the fit to the trajectory.  You could compute these quantites yourself (I do) and compare them with the number in the data base.  Although the data base does not give the spin direction, it could have been given (I have urged the Sportvison people to do so).

I think distinguishing 2-seam and 4-seam fastballs with pitch-f/x data is still in its initial stages. I know Mike and Josh Kalk (maybe others) have done some work in this area, but I don’t think we’ve yet seen a convincing separation of the two pitch types.

A comment on the spin issue: the formulas from Alan that Mike is using make the assumption that the spin axis lies in a plane that is perpendicular to the pitch direction. (Alan, please correct me if I’m wrong about this.) I do believe there are some pitches where this doesn’t hold, many sliders for example. 

A pitch thrown with its spin axis aligned with the direction of the pitch (like a football spiral) will have very little movement.  This kind of pitch would have a very small spin-rate using the approximate formulas and a spin-axis that is not well defined (as Alan mentioned above). 

There are not a large number of such pitches: I find around 6000 with abs(pfx_x/z)<2 (out of 300K pitches).  Still, I’m not sure in general how well we know that the spin-axis generally lies in the x-z plane.

John, I agree with your general sentiment on pitch classification.  In fact, I think the curveball is really the only pitch we have a great handle on.  Other pitches can be distinguished well depending on the pitcher but not consistently across the spectrum of all pitchers. 

I would put the 2-seam and 4-seam fastballs in that category.  For some pitchers they are two distinct pitches or the pitcher throws only one of them exclusively or almost exclusively, but for other pitchers the spin/break of their fastballs vary more on a continuum.

Regarding the spin axis, the formulas I took from Alan’s paper are really about a projection of the spin axis on the x-z plane.  The y-component on the spin has little effect on the movement of the pitch, so we ignore it.  Alan and I have both stated that explicitly a few places, but I know I haven’t repeated that every time I’ve written about computing spin axis and spin rate.

Where that has its biggest practical effect is with the slider (and the gyroball), as you noted. I don’t have any trouble identifying the slider with the spin axis/rate method, but the spin rate the formulas produce for the slider are much lower than reality since there is a large component of spin about the y-axis.  As a matter of pitch classification, this is actually a way to identify the slider, but in terms of describing the real spin rate of the pitch, it produces incorrect values. 

We still get a well-defined projection of the spin axis on the x-z plane for the slider, however, which is all we need in order to know which direction the pitch will break.

Tango/Alan/others have mentioned graphing spin axis versus pitch speed or other quantities on a polar plot.  I agree that, at least in theory, this makes the most sense.

I’ve found myself not doing that for practical reasons, however.  Foremost is the fact that Excel doesn’t do polar plots, and I’ve found it easiest to do a lot of the other analysis in Excel.  I experimented with plotting in R, and it certainly had some advantages, but overall I found it harder to manipulate the data in R.

Alan mentioned to me that he did his graphs using Kaleidagraph, but at this point I didn’t want to lay out money for a graphing program, so I haven’t tried that one.

Secondly, for some reason I can’t quite explain, I found the graphs easier or just as easy to interpret in Cartesian format even though I thought they would be easier to interpret in polar format.  If I could find a better way to create the polar plots in the first place, maybe I could experiment some with formats and find a polar plot format that communicated the message better.

Mike:

I generated this in Excel:
http://www.tangotiger.net/files/spin_speed.JPG

And this is the Excel file:
http://www.tangotiger.net/files/converting_ball_tracking_to_quadrants.xls

Just put your data in the A and B columns, rows 2 through 25.  You can of course collapse all the other intermediary columns, but they illustrate what is happening.

The only question is to set your 4 quadrants approporiate to your spin axis, but that should be a very quick change, if needed.

Thanks, Tom.  I used your Excel graphing method and incorporated the results into my latest article:
http://fastballs.wordpress.com/2007/11/15/appeasement/

I had thought about doing something similar with Excel but had never been able to work out the details, so your example spreadsheet was very helpful.