THE BOOK--Playing The Percentages In Baseball

That is the Freddy Garcia “super-splitter” to Juan Rivera that Lucas discovered on April 29 and which I captured on video and passed along to Alan, and which Alan then discussed with Rod Cross, who proposed the cricket swing theory.

I’ll have to watch the video and see if Dr. Cross has done any laboratory measurements of the force on the baseball yet.

In #1, I should say “cricket reverse-swing theory.”

Rod Cross and I have indeed been “partners” for many years.  We have published multiple papers together and are in quite regular contact, despite being separated by many thousands of miles. 

Mike has it right in his comment.  Mike originally contacted me about the Garcia pitch.  I then contacted Rod, who then started doing a number of experiments to see if he could simulate the effect (i.e., the ball breaking in a direction inconsistent with the Magnus effect, given the spin axis).  To enhance the effect, he used a lighter ball.  He used tape to simulate the seams.  He did not measure any forces and if I recall, he did not even do careful measurements of the trajectory.  He did, however, do qualitative measurements.  He wrote a paper that he submitted to American Journal of Physics; most likely it is currently under review.  I have a copy and I’ll ask Rod if it is ok to post on my web site.  If so, I’ll post a link here.

Just watched the video, which I had not seen before.  Rod and I spent quite a bit of time last summer looking at the Garcia pitch that he shows on the video.  It is the same clip that Mike Fast sent me and I sent Rod.  We both understood very well the effect of scuffs on the ball, which is very well documented for cricket balls, as the video discusses.  What we were trying to figure out was whether the spin axis was such that the ball appeared “rougher” on the pitcher’s left than on the right (due to the seams).  I was never as convinced as Rod that that was the case for the Garcia pitch.

One minor point:  Mike refereed to “cricket swing” in #1, then corrected to “cricket reverse swing” in #2.  Actually, he had it right the first time.  Cricket swing occurs when the ball breaks in the direction of the seam (opposite to the smooth side). Reverse swing does the opposite.  If I recall, reverse swing occurs when the smooth side of the ball actually gets roughened up in such a way that it triggers the transition to turbulant flow rather than the seam.  The ball then breaks in a direction away from the seam (hence “reverse swing").

OK, I’ve said enough and now I’ll shut up.

But Alan, isn’t reverse swing what happened on the Garcia pitch? The ball broke toward the smooth patch.

Mike:  That’s not what Rod claims in the video.  He says it breaks away from the smooth patch.  Have a look at it and let me know what you think (look at around 3:10 in the video, which is a cartoon of the effect).  As I said above, the real issue is whether or not there is a smooth patch.  I couldn’t convince myself but Rod could.

Ah, I think I see what is going on.  When we discussed this in May, I thought we were talking about reverse swing.  But there are two smooth patches, on opposite sides of the ball.  How the flow of air comes over the ball and interacts with the seams could determine which of those smooth patches is creating the most force on the ball.  If it’s the smooth patch that is mostly hidden in the video (toward the third-base side and underside of the ball), then it would be the usual cricket swing, I guess.  If it’s the smooth patch that is on the topside and first-base side of the ball, then it would be reverse swing.  I don’t know how Rod determined that from the video, or if he did.

I imagine it would have to be the “smooth patch that is mostly hidden in the video (toward the third-base side and underside of the ball)” since that patch is the one that is most directly facing the direction of the path of the ball and therefore is interacting with the air the most.

Geri:  I have looked at the Garcia video countless time, most recently just now.  The only way I can get a smooth patch on the left side of the ball (catcher’s view) that persists through one revolution is if the spin axis is tilted toward the batter (i.e., if there is a significant “gyro” component to the spin). Probably that is what is going on but it is not so easy to verify from the video.  Without the tilting, it looks like two seams pass through the upper left-hand quadrant of the ball (again, catcher’s view) during one revolution.

I think this might be a good way to explain what I’m seeing in the Garcia video:

Look at the simulated view in the video linked above that starts at 3:04.  Now, flip that view upside down.  That is from the catcher’s view, the “bald spot” is to the lower left.  The opposing bald spot is to the upper right behind the ball (upper left from the pitcher’s point of view).

This would match the force vectors shown in the Garcia video at 3:25 with the “side force” up and to the right from the catcher’s point of view.  That vector arrow matches my view of the Garcia video that the ball should curve away from the bald spot facing the catcher.

Thus, the ball thrown the way that Garcia threw it should curve higher and to the right than what gravity plus the magnus force alone would predict.

Maybe I am being particularly dense tonight--or perhaps just distracted by the #CNNdebate--but I can’t reconcile what I see in the cartoon with what I see from the actual video. 

Cartoon:  spin axis is such that the ball should break down and to the left (catcher’s view)

Actual video:  ball should break up and to the right (pitcher’s view), or up and to the left (catcher’s view). 

Or, said differently, the cartoon appears to me to have topspin whereas the actual video has backspin.

Where am I going wrong?

Just to clarify my last post, for both the cartoon and the actual pitch, I am talking about the break due to the conventional Magnus force.

Good point.  The 3:05 “cartoon” both has to be flipped and the ball has to spin the other direction in order to match Garcia’s pitch.  Garcia’s pitch, from the point of view of the catcher, has the lower right side of the ball spinning toward the catcher, so the Magus force will be up and to the left from the catcher’s point of view.  So, the force arrows shown on the diagram at 3:26 are correct.

So, in Garcia’s video, but from the point of view of the catcher, there are two effects besides gravity:

1) The magus force with the ball spinning toward the catcher from the lower right, causing the ball to go up and to the left.

2) The “side force” with the “bald patch” to the lower left that causes the ball to go up and to the right.

Geri:  your understanding in #14 exactly coincides with mine.  Now, the real question is whether or now there is a bald patch on the left (catcher’s view).  I have yet to be completely convinced that there is.  I have asked Rod to send me a sketch that convinces me of the white patch.  That is, a catcher’s view of the ball showing the location of the spin axis.

Meanwhile, Rod just told me to ignore the cartoon, which was put in by the interviewer at the last minute.  Rod agrees it does not correctly represent the actual pitch.  So, we all seem to agree on that point.

Alan, I don’t know if it helps you the way it did for me, but looking at an actual baseball was helpful.  If you take a splitter grip like Garcia’s, with fingers just outside the seams where the seams are at their narrowest point, you can see that there is a “bald patch” both to the left of your index finger and to the right of your middle finger (as the pitcher).  You can also see that the axis of rotation could go roughly through the center of both of the bald patches.

In the Garcia video, you can see the bald patch to the pitcher’s left.  The corresponding bald patch on the other side of the ball is hidden in the Garcia video, but it must be there, too.

What I can’t reconcile for myself is where the airflow is laminar and where it turns turbulent.  I think that matters quite a bit, and the exact orientation of the seams and spin axis relative to the direction of travel are quite important to whether the cricket swing (or reverse swing) effects actually happen to the baseball.  So I find Rod’s explanation plausible as to how it COULD happen to baseball.  But I’m not necessarily convinced that it DID happen to this specific pitch.

Mike...thanks for the comment.  I actually have now done a frame grab so I can more easily see the orientation of the seams frame by frame.  There is clearly a white patch in the upper left quadrant, which mean the batter sees a white patch in his lower left quadrant.  So the side of the ball to the batter’s left is smooth and the side to the batter’s right is rough, so the ball moves to the batter’s right.  To make this happen requires that the spin axis be tilted into the -y direction (PFX coordinates).  In fact, it might be totally contained in the x-y plane.

I will write something up about this tomorrow and put it on my web site, with a link here.

It’s a shame that the “side force” and magnus force are working in opposite directions side-to-side.  I’ve been trying to think of ways that you could get them to work together at least side-to-side, which would basically require one to pitch with top-spin or change the axis of orientation.  Perhaps a submariner would be able to do it.

Alan - I count 5 revolutions of the ball from the pitcher’s hand to the catcher’s mitt which should be somewhere around 650 to 680 RPM.  The seam orientation of the splitter is going to be almost exactly the same as a two seam fastball.  Is the theory that Cross is proposing that the “side” force on the smooth side is greater when the ball is spinning less?  Therefore causing the side force to be proportionaly greater than the magnus force for a splitter, but for a two seam fastball with the same seam orientation but greater spin the magnus force would more than counteract the smooth side force and cause the ball to move in the opposite direction?  That’s the only reason that I can think of why the pitch being analyzed moves away from the right handed batter but a two two seam fastball would move toward him.

It would be interesting to analyze some knuckleballs with a similar super slow motion video to see whether smooth side forces offer a better explanation for the erratic movement of the knuckleball.

Geri (#18):  Actually, if the pitch had not moved in the “wrong” direction based on the Magnus force, then no one would have noticed it and we would all be talking about something else.  But I agree with your point.

Peter (#19):  I don’t know how the side force depends on the spin, except when the spin is very low (as in a k-ball).  I would guess that once the ball makes at least one complete revolution, that is enough to average over the instantaneous orientation of the seams to produce an average force.  Of course, at low spin, the Magnus force is lower, so the side force in this particular case dominates.  For a normal 2-seam fastball, the spin is larger and the Magnus force dominates.

By the way, the side force in this case has its origin in the flow of air over the seams, just as it does for the knuckleball.  Be on the lookout for my ProGuestus article about knuckleballs, which should appear next week at BPro.

I would love to get more slo-mo video of unusual pitches.

Peter, one of the biggest questions I had when Alan and I were discussing this pitch back in May was whether this had happened on any other pitches.  If so, why, and if not, why not?

I have not yet been able to find another pitch where we can conclusively identify this happening.  Part of the challenge is that you really need a very good slow-motion video where you can identify the rotation of the seams.  Last year, at least, the Yankees YES-MO seemed to be the only slow-motion capture with the quality of video to do that from pitcher’s release to the plate.  Other teams’ slow-motion video does pretty good with capturing the pitcher’s release, but you usually can’t see the seams while the ball is traveling to the plate; thus, it’s useless for this exercise.

Given that limitation, I examined a few dozen pitches made in Yankees games.  In particular, I looked at other splitters from Freddy Garcia.  I never found another pitch that moved the “wrong way” anywhere near that dramatically.  I considered several possibilities for why that might be:

(1) the orientation of the spin axis varies somewhat from pitch to pitch, both relative to a field coordinate system and relative to the direction of travel of the ball (based on where it was aimed).  It’s possible the effect is very sensitive to the orientation of the bald patch and the seams relative to the airflow over the ball.  There is some indication that is true with a knuckleball based on the wind tunnel tests by Watts and Sawyer.

(2) or perhaps small variations in the orientation of the spin axis are not so important, but instead, the size of the bald patch is the key.  Many pitches have some precession.  Even if the spin axis initially passes through the area in the middle of the horseshoe seam, if the axis precesses too much, there won’t be a consistent bald spot.  I’ve observed significant precession on other pitches.  Alan has suggested that might be due to torque-free precession caused by asymmetries in the baseball.  Perhaps what is unique about this pitch from Freddy Garcia is not what he did to the baseball but that it was an unusually symmetrical baseball such that it did not experience significant precession and was able to maintain a bald patch throughout its whole flight.

(3) the ball may have been scuffed, either intentionally or unintentionally.  This baseball was hit to the outfield prior to this pitch, but it was caught in the air and thrown back to the infield.  I don’t see it ever touching the ground on the video.  Of course, someone might have cut it on something on their uniform, but it’s not a particularly crucial game situation.  Also, the catcher seems to be surprised that the pitch moved the way it did since he lunged for it at the end.  I don’t proof that the ball wasn’t scuffed and can’t discount it, but it seems odd for that to only happen on this one pitch and not again, as far as we can tell, for Garcia the rest of the season.  I’d put spit or some other foreign substance on the ball in this category, too.

(4) something else we haven’t thought of.  I will say there is no evidence on video of a wind gust, and the weather was not windy at the time.

Back in May I shared this image of the spin deflection of Freddy Garcia off-speed pitches from three games and the pitches whose spin I had been able to identify from YES-MO video:
http://twitpic.com/5cttcm
It may be of some interest in the discussion.

Peter/19, you also asked whether we should see this effect on two-seam fastballs.  I answered that obliquely by noting that we don’t even see this on other splitters.

But to address your question more directly, I think that if we did see this on two-seam fastballs, the side force would make them move more like four-seam fastballs or cut fastballs.  That makes it tough to identify such pitches using the spin deflection from PITCHf/x.  Whereas if a splitter has a lot of side force, depending on what other pitch types a pitcher throws, it can end up in a distinct region in the spin deflection space.  The slower rotation of the splitter means it starts out closer to the origin in that space, and a strong side force moves it into a region where we don’t normally see pitches from right-handed pitchers (though a few pitchers’ sliders or cutters can be over there).

So it’s possible that (1) this doesn’t happen to two-seam fastballs or (2) it happens but we don’t have any way to notice it.

By the way, my theory #2 in post #21 is new since Alan and I last discussed this side force phenomenon.  Our discussion of torque-free precession came at a later point when I had captured some slo-mo video of sliders and was looking at red dots that came and went.

When I get the chance, I should examine the slo-mo video I captured of Garcia’s other splitters and see if they have more precession of the spin axis than this pitch.

I reviewed the video that I have for nine of the Garcia splitters.  I observed significant precession of the spin axis on two of the pitches, some precession on four, and no noticeable precession on three.

The presence or absence of precession is not enough to explain the effect on its own, but perhaps in combination with the orientation of the spin axis it could.  I would need probably three or four times as much video as I have before I think I could make that determination with good confidence.

I will say that there is one pitch (May 10, 5th inning, 0-1 pitch to Escobar) with fairly similar spin axis orientation, with respect to field coordinates, to the pitch in question (April 29, 1st inning, 1-1 pitch to Rivera), with no noticeable precession, and it did not exhibit this phenomenon (the large side force).  The pitch to Rivera was aimed higher in the strike zone than the pitch to Escobar, so perhaps that change in the direction of the airflow was enough to make the large difference in movement?

One of the things I have found puzzling about the Garcia splitter is that the catcher seemed not to be fooled by movement, despite its apparent rarity.

Alan/25, it’s true that Russell Martin caught the pitch, but I thought he definitely had to lunge for it at the last minute.  The catcher’s movements were quite a bit a different on this pitch than on other splitters from Garcia to Martin that I’ve watched.

Thinking more about I wrote in #24, many of Garcia’s splitters are buried in the dirt.  But we have slo-mo video on another high splitter that he threw to Arencibia in the 5th inning on April 29.  There was no noticeable precession on the spin axis of that pitch, either, but its spin axis differed from that on the pitch to Rivera by about 20 degrees (my estimate from video).  The pitch to Arencibia was also aimed about half a foot higher than the pitch to Rivera, so perhaps that, too, contributed to the difference in movement.

Mike - My problem with the “smooth spot side force” explanation alone as being a cause of significant movement is that an axis of rotation directly through the large smooth spots indicated by Cross creates two smooth spots directly opposite each other that would tend to cancel each other out unless it is a very specific orientation of the seams to the direction of travel that causes an unusually strong force.  Cross discusses this aspect in relation to the cricket ball.  Whatever is happening to the baseball essentially has to get it to act like Cross’s wiffle ball with the asymetrical string attached.  A baseball thrown from Garcia’s splitter grip might move like the subject pitch if it met certain very specific conditions.  It would have to have a low backspin rate which would limit the movement due to Magnus force.  It would have to have a spin axis through the large smooth areas that Cross suggests.  It would have to have no precession from that spin axis.  These conditions would create a baseball where the seams would be acting like two strings set equidistant from the center line of the backspin.  If you then add an additional condition that the seams/string closest to the batter is exactly on the line of the direction of motion of the ball toward the plate then the force created by its air turbulence is neutral since it is acting on the center of the ball.  Leaving the air turbulence caused by the seam/string away from the batter as the major force causing the ball to break to the outside part of the plate.

This explanation would also help to explain why some two seam fastballs thrown by right handed pitchers sometimes break down and in to right handed batters more than would be predicted by a lower Magnus effect than 4 seam fastballs.  If instead of the seam closest to the batter aligning with the balls velocity path it is the outside seam than aligns then the inside seam would create the turbulence causing the additional down and in movement.

Sportvision might have to add a couple of additional parameters to its 9 parameter model.

Sportvision might have to add a couple of additional parameters to its 9 parameter model.

Hmm...Alan, would it be possible to get the raw tracking data from Sportvision for this pitch and apply the same method to it as you did for your knuckleball analysis?

Mike - That’s a great idea, but be forewarned that there won’t be any tracking data for the last 8 or 9 feet before the pitch reaches the front edge of home plate.  You may want to request the video from all three cameras for the the pitch as well. from that you can get the coordinates for the last couple of ball positions as the ball reaches the plate.

Peter #27:  I’m not sure I followed completely what you were saying.  Let me say things a bit differently and you can tell me if that is what you meant.  As you point out, there are two white patches, diametrically opposite to each other.  Presumably, the spin axis needs to pass along that diameter so the the orientation of the patches does not change during the trajectory.  In addition, there must be little or no precession of the spin axis.  Now, if the spin axis (and white patches) were parallel to the x axis (PFX coordinates), the ball would look left-right symmetric and there would be no effect.  Instead, the spin axis is tilted a bit forward, with a component parallel to the y axis.  Under such conditions, the white patch on one side would be at the front of the ball while the opposite one would be at the rear (batter’s view).  The movement would then be determined by the one on the front.

Actually, way back in May, I asked Sportvision for the video but never heard back from them.  With the renewed interest, I will try again.  I don’t really want the video, only the raw tracking data (the pixel location of the blobs in camera coordinates and the transformation matrices).  I don’t think it matters a great deal that the ball is not tracked over the last bunch of feet.  The trajectory surely is smooth, so fitting to a reasonable function allows a pretty good extrapolation to the home plate region.  Moreover, I doubt than more parameters are needed than 9, but that will be pretty easy to check.  I would use a different 9 parameter function, however, one involve drag and lift coefficients.  That ought to provide a somewhat improved description of the data.

Having said all that, I am not sure what we will learn from such an analysis.  It might turn out that the simple parametrizations fit the trajectory poorly, in which case we would have learned something new.  But I suspect we will simply learn that the 9P fit we already have is an adequate description.

Inspired by all this discussion, I have written an article about the Garcia pitch which includes a link to Cross’s paper.  I had originally planned to put it up on my web site today.  However Dave Studenmund has kindly agreed to put it on The Hardball Times site sometime this week.  Stay tuned.

Studes is amazingly quick.  Here is the link to the THT article:

http://www.hardballtimes.com/main/dispatch_article/dissecting-a-mystery-pitch/