Fresh from the PITCHf/x Summit, I mean BASEBALLf/x Summit, my mind is full of questions about batted balls and fielder positions. While HITf/x and BASEBALLf/x are not ready for prime time (HITf/x may be close), I’m thrilled to have a little bit of data on batted balls. By combining April’s HITf/x data and Matt Thomas’ photogrammetry, I can present a few examples of issues we’ll someday be able to explore in every game. I hope reading this article will be at least half as fun as it was putting it together.

### Photo what?

Thomas specializes in using photographs to take measurements of physical space. That’s his day job. On some nights, you’ll find Thomas in the press box at Busch III working as a stringer. Thomas uses a camera to capture stills of the action, creating a record of locations, and timings, of movement on the field. Thomas happened to be working at Busch two nights in April that were also captured by HITf/x. He was kind enough to send me the data from April 24 and 26, Cubs at Cardinals, in all their glory.

### The data

Thomas provided some interesting information for each batted ball, measuring the point of contact, passing through the infield (when applicable) and reaching a fielder (or sometimes the ground or a wall). The specific data points include:

- x,y coordinates relative to the foul lines
- distance from home plate
- angle off the first base line
- time to glove/turf/wall
- time through the infield
- approximate distance above ground when caught (or where ball struck a wall)
- base states, outcomes etc. as coded by Thomas

HITf/x provides:

- Speed of bat
- Horizontal, or spray, angle
- Vertical, or launch, angle

Gameday adds in:

- Its own x/y coordinates
- Location where fielded
- Outcome of the play
- Description of batted ball (grounder, liner etc.)

Seeing how Thomas, as the stringer, feeds Gameday, there should be plenty of overlap. There is, and I’m going to use a limited set of factors, but I should point out I found one play that was coded differently in Gameday than in Thomas’ data file.

My question is simple, as hinted at in the title: Will two batted balls with similar or nearly identical initial characteristics result in different outcomes? Will they be described differently within Gameday? What other factors seem to be associated with these discrepancies? In other words, can the same thing happen twice and either end up differently or be described differently? If so, what other piece of information helps us explain that subjective difference?

To attack this question, I used HITf/x data (SOB, Launch and Spray) to pick similar batted balls. Gameday provided the outcome, and Thomas’ data (along with HITf/x and Gameday itself) are used to explore/explain the differences.

###### The plays

I found at least four pairs of interest, but I’m limited this discussion to two of them.

The first pair of hits I picked differ in one important way—speed.

**Ball 1**

SOB 98.3

Horiz. half-way between second and third, a little closer to third (114.9 in the raw HITf/x data)

Vert. -13.1 degrees

**Ball 2**

SOB 73.0

Horiz. same as above, within .1 degree, Thomas’ found “theta” to be within 1 degree for the two hits, also (114.8)

Vert. -13.6, slightly lower than above

Here we have two hard-hit grounders. One was hit very hard. They went to almost the identical spot, but ended up with very different results.

Ball 1

“Alfonso Soriano reaches on fielding error by shortstop Khalil Greene.”

Ball 2

“Reed Johnson singles on a sharp ground ball to left fielder Chris Duncan. Geovany Soto to 2nd.”

First, the “sharp” notation appears on ball two but not ball one. I believe Gameday doesn’t allow for the sharp/normal/soft distinction on errors. Still, given the slower speed, I found it curious. Second, while both plays occurred with one out, it was ball two that came with a runner on first.

While Greene did field the first ball cleanly, it was smashed probably a little bit to his right. The second ball, despite being hit slower, made it through for a single. Why? I would guess Greene was pulled over towards second base, cheating for the double play. According to Thomas, Greene reached (or was reached by) ball one 1 in 1.6 seconds. Ball two passed the infield in 1.5 seconds. What I don’t know is the nature of the hop, as that could matter if this ball was just on the edge of Greene’s range.

The next pair had a lot more in common.

**Ball 3**

SOB 78.3

Horiz. about the same as 1 and 2, just a little more toward second base (114)

Vert. 25 degrees

**Ball 4**

SOB 75.0

Horiz. 4 degrees closer to second base (108.2)

Vert. 29.7 degrees

So, ball three was hit a little bit harder, a little more towards the gap, and on a lower trajectory (at least initially). So, what happened?

Ball 3

“Alfonso Soriano lines out to left fielder Colby Rasmus.”

Ball 4

“Mike Fontenot flies out to left fielder Colby Rasmus. “

Have we really found the line between a fly ball and a line drive? Were these both fliners in BIS lingo? What else was different?

- Ball three was pulled; ball four was hit the other way.. (Fontenot is a left-handed batter)
- Ball three was caught somewhere between two and three feet off the ground, according to Thomas
- Ball four was caught between five and six feet above ground
- Rasmus caught ball three 3.33 seconds after contact; ball four 4 hit his glove 3.5 seconds post-contact

So, we have a pulled line drive caught below the waist and an opposite field fly caught chin-high. Otherwise, they’re very much alike. I wonder if positioning could explain why Rasmus seemingly arrives later to ball three (perhaps the .17 seconds of time difference is accurate).

I realize I’ve raised more questions than I’ve answered—to address the two pairs discussed above, a review of the video tape and some details on player positioning could provide simple answers to the questions raised. But there are other plays I need to review, such as:

- Hard hit grounders turned more easily into double-plays?
- How fast does a ball need to get through the infield at different locations, depending on the fielder’s location?
- Can we use time to the outfielder on singles to evaluate a runner’s ability to take (or not take) an extra base?

Other ideas? Leave ’em in the comments.

### Summary

While the data for this study were a lucky break, we’re months, not years, away from this being a regular thing. Even with limited data, this baseball nerd was well entertained.

**References & Resources**

Thanks to Sportivision for the HITf/x data and Matt Thomas for putting his photogrammetry data together for me.

Harry Pavlidis said...

@Dan I’m pretty sure they are measuring different things. Sometime it could work out that the fielding/infield point would be similar across some batted balls, but I would assume they’re not the same.

@Laura Very good points. We talked a bit about ground ball spin at the Summit, and the conventional wisdom seemed to indicate the first bounce would have spin effects, but after that the spin the batter put on the ball will be gone. As you’ve pointed out, countless variables come into play beyond spin.

@Joe thanks for checking the vids. I’ll try and grab some screenshots for a follow up

Peter Jensen said...

Harry – I checked the MLB.com videos of all 4 balls as well. On the Johnson ground ball the SS was playing further in than on the Soriano ground ball. From the way the Johnson ball hopped it appears that he topped it and it hit the ground in the dirt surrounding home plate on the first bounce. If that is so it is probable that Hit f/x had to few frames to calculate the speed off the bat and that what is given is the speed after the first bounce. I talked to Greg Moore about this at the Summit and told him that when he did this it should be noted in the file somewhere. I don’t think he realized that how much of the original speed would be absorbed by the impact with the ground. So I think both balls were initially hit with about the same speed off the bat. Johnson’s ball took one big hope and then skipped by the drawn in SS. Soriano’s ball was not topped as much, took several bounces before reaching the SS near the outfield grass and he just misplayed it.

The two balls hit in the air had much different spins. Fontenot’s ball was sliced and undercut which caused it to curve more and stay in the air longer. Soriano’s pulled ball was hit way out in front of the plate where his swing arc was rising. It had much less undercut so it curved less and stayed in the air less time. Since the perception of line drive and fly ball is governed not just by the initial angle off the bat, but also by the height the ball reached Soriano’s was really a line drive and Fontenot’s was really a fly ball.

Harry Pavlidis said...

Peter: “Since the perception of line drive and fly ball is governed not just by the initial angle off the bat, but also by the height the ball reached Soriano’s was really a line drive and Fontenot’s was really a fly ball. “

What would one expect the contributions of the spin and the difference in launch (4 degrees in this case) in that height/perception? Is the 4 degree delta enough to explain it?

joe arthur said...

Peter,

In his presentation, Greg Moore certainly indicated that HITf/x would report a misleading positive verticle angle and a slower speed for chopped balls they picked up only on the way up from the first bounce. In this case, since both ground balls were assigned downward angles, the vertical angle of the Johnson ground ball was measured on the way down to initial contact with the ground (which was near the edge of the circle of dirt surrounding the plate, as you suggest). I suppose it’s possible the velocity measure nonetheless could commingle frames before and after the bounce – did Greg say something to you personally to suggest that? This is worth a very close look to decide whether we can take the speed off the bat of these two balls as directly comparable. It would be surprising (to me) if the speeds off the bat are accurate and comparable, and yet the 73 mph ground ball could get to the infieder faster than the 98 mph ground ball.

Peter Jensen said...

Joe – Greg did commumicate to me in a private conversation after his talk that what he did on balls that hit the ground too quickly to get enough data to calculate the Hit f/x data on the way to the ground, was to take the positive verticle angle of the ball after it strikes the ground and just take the mirror image of that, and for speed he used only the speed after it struck the ground. This is misleading on both counts as a ball hit with topspin will come off the ground at a lower angle than its incoming angle and at a much reduced speed. Sportvision needs to flag the plays where they use this method so the data will not be commingled with actual off the bat data.

Mike Fast said...

@Joe

The energy of the bat is propelling the ball parallel to the ground (or a little upward). The rebound of the ball off the bat is what creates the downward component of the velocity. Because Soriano’s bat was moving faster at the point of contact than Johnson’s bat, in order to produce roughly the same initial vertical angle, he had to be on top of the ball a little more than Johnson. This creates more topspin on the ball hit by Soriano. That would make the Soriano ball bounce lower on at least the first bounce and consequently hit the ground more often on its way to the shortstop.

According to my bat-ball collision model, the Soriano ball had about twice as much topspin as the Johnson ball, about 1100 rpm vs. 500 rpm, created by an offset between the center of ball and bat of about -.67 inches for Soriano and -.54 inches for Johnson, generated by a bat speed at point of contact of about 59 mph for Soriano and 29 mph for Johnson.

Both balls also had significant sidespin, ~2500 and ~1900 rpm, but the sidespin shouldn’t affect the bounce much and 1.5 seconds isn’t much time for the sidespin to affect the trajectory in the air.

@Harry

I missed the ground ball spin discussion at the summit, but my own experiments with bouncing a rubber ball on a tile floor do show that the ball loses much of its spin after the first bounce. A baseball on grass/dirt would probably experience more friction and lose even more of its spin when it bounced.

Mike Fast said...

I agree with Peter that that is important information to know as it would certainly change the dynamics of all the calculations.

joe arthur said...

Peter, agreed about the desired resolution, but I am not sure about HITf/x using the “mirror image” of the angle after ground impact, since there are ground balls in the april data with large

positivevertical angles [like plus 50-60 degrees – just like a fly ball] and very slow speeds off the bat [like 20 mph]. I looked at several of these on video, all chopped nearly straight down. Definitely no adjustment to the mirror angle on those balls …Greg Rybarczyk said...

Harry, I think this sort of study is great, and I encourage you to keep doing as much of it as you can.

One thing about referring to batted balls as the same, though, is that TO THE FIELDER, they are “the same” only if they get to the same landing spot (or CPA – closest point of approach – spot) at the same time. And it is the presentation of the ball to the fielder that is most important to the outcome (along with, of course, the fielder’s initial positioning and range).

So, comparing similar ground balls off the bat, according to launch parameters, may not be the way to do it, since the literally unpredictable ball-ground collision will alter the balls’ trajectories in different ways every time.

A better way is to identify two grounders that passed through the same spot (ideally the infield arc) after the same amount of time), and then compare the outcomes. I did a comparison like this in my 2008 THT Annual article, to show the importance of infielder positioning…

Incidentally, I think you know all this, I am writing it primarily to stir the pot a bit for further discussion…

Peter Jensen said...

Harry – This site lets you change Magnus force and shows you its affect on the trajectory and the distance. Unfortunately it doesn’t give you the time to that distance. But time is directly proportional to maximum height. You don’t mention what distances Matt had for these two hit balls. My translation of the Gameday hit locations has them only a foot apart at arouond 240 feet where they were caught.

http://faculty.tcc.fl.edu/scma/carrj/Java/baseball4.html

Peter Jensen said...

Joe – I haven’t looked at those videos, but I’ll take your word for it. It may be that they haven’t developed a consistent policy on how to handle chopped balls. Here is data for one ground ball that I calculated by hand last year that had enough frames to calculate both before and after it hit the ground.

SOB HA VA

After 77.7 46.5 4.7

Before 95.5 44.5 -7.1

Harry Pavlidis said...

@Greg

good point. From the fielder perspective it isn’t _as much_ how the ball got there, but when it got there. I’m still intrigued by the hop characteristics, though.

I can’t help but think judging and handling different hop types is a skill, and that where the fielder got the ball relative to their normal throwing position has an impact on converting a fielded ball into an out.

Caught on heels vs. charging the ball, etc etc

Alan Nathan said...

@Mike on spin:

Not sure I agree with the statement about the ball losing spin when striking the ground, at least in the case of a topspin grounder. Suppose a ball is hit with a large horizontal velocity and topspin. When the ball hits the ground, it starts to slide and the surface velocity is slowed down by friction. The direction of the frictional force will be opposite to the direction of the surface velocity. The surface velocity has a forward component due to the horizontal velocity and backward component due to the topspin. Almost always (I would bet) the forward component is larger. That means the frictional force is backwards, which tends to slow down the horizontal velocity speed up (not slow down) the topspin on the ball. You can try this for yourself by throwing a ball with no spin at an oblique angle to the floor and it bounces with topspin.

An interesting effect is theoretically possible, although probably never happens in practice. If the topspin on the batted ball is such that the surface velocity due to the spin is larger than the horizontal velocity, then the friction acts in the forward direction, speeding up the bouncing ball (and reducing the topspin). Adair discusses this in his book (3rd ed, p. 92). As Adair points out, for such an effect to occur, it would require more topspin on the ball than is likely to happen.

The situation is very different when the ball has backspin, since in that case both the forward velocity and the backspin are slowed down by friction. In this case, the loss of horizontal velocity is greater than in the topspin case, resulting in a higher bounce angle (as Mike points out).

Alan Nathan said...

@Peter: Interesting “before/after” analysis you did of a grounder. Carrying the analysis a bit further, the normal (vertical) component went from 11.8 mph before to 6.4 mph after, implying a COR of 0.54, more or less what I would expect. The horizontal component went from 94.8 to 77.4. If the fractional loss in velocity were the same for horizontal and vertical components, then the “mirror” prescription would be correct. However, you can seen that there is a much larger fractional loss in the vertical direction, so that the bounce angle (relative to the ground) will always be less than the initial angle. That is exactly what the data shows. For a ball hit with topspin (and most grounders are), it will always be the case that the bounce angle will be less than the initial angle.

It would be very interesting to see more analysis of this type.

Alan Nathan said...

Harry referred to a link to Jim Carr’s flight simulator (like me Jim is a nuclear physicist, although he is a theorist and I am an experimentalist). For those of you interested, you can download an Excel spreadsheet to do your own trajectory calculations, including effects of wind, altitude, temperature and using what I believe are the best available models for the drag and Magnus forces. I put this together for Colin Wyers just in the last day or so and it hasn’t been completely checked out yet. If you find any mistakes, please let me know. Colin is working on preparing some instructions about how to set the input parameters (although it is probably pretty self-explanatory).

http://online.physics.uiuc.edu/courses/phys199bb/fall07/Programs/full-3d-trajectory.xls

Harry Pavlidis said...

@Peter – here are the fielding locations for the two outfield flies

Definitions from Matt:

x

feet off the third-base foul line, along x-axis

y

feet off the first-base foul line, along y-axis

r

feet from home plate = sqrt(x^2 + y^2)

theta

angle off 1B foul line = arctan(y/x)

Fontenot

59, 227, 234, 76

Soriano

60, 241, 248, 76

Peter Jensen said...

Using Matt’s hit ball locations and the initial Hit f/x parameters and Alan’s 3D trajectory calculator I calculate a backspin of 1300 and a sidespin of 725 for Soriano’s line drive. It would have a maximum height of about 40 feet with the distance of 248 feet.

Fontenot’s fly ball had a backspin of 1600 and a sidspin of 1985 and a maximum height of 47.3 feet over a distance of 234 feet.

If you did enough of these you might find that line drives and fly balls have a dividing point of a constant ratio of distance to height. Or you might not.

Alan Nathan said...

Peter: nice work! Matt sent me all of his data prior to the summit but I did not have the time to go through an analysis that I would be happy with. My goal was to do an analysis similar to what I did with Greg’s hittracker data for home runs. Namely, adjust the two spin components to reproduce the landing point and flight time. I did all that but have not had a chance to look critically at the results.

For those of you familiar with the Solver macro in Excel, you can do this yourself using my spread sheet. Perhaps that is what you used, Peter.

joe arthur said...

To go back to one question asked by Harry in the article, it appears that Soriano’s ball hit to left (vertical launch 25 degrees) was scored as a fliner(liner) by BIS, whereas Fontenot’s (vertical launch 29.7) was scored as a fliner(fly). [Fangraphs has pbp data supplied by BIS, and the hit type is embedded in their descriptions.] For those interested, the ground balls occurred in the 5th and 6th innings of the 4/24 game, and the fliners in the 3rd and 8th innnings of the 4/26 game.

joe arthur said...

Peter may be correct in one of his comments that HIT f/x has not been consistent about converting the observed angle to the “mirror angle”. There are 40 “ground outs” in the database with vertical angle < -50, and 5 with vertical angle > +50.

Peter Jensen said...

Joe – I sent Sportvision a list of about 30 plays that looked like errors to me. I think GBs with a vertical angle greater than 40 degrees were on the list but I’ll double check.

Dan Turkenkopf said...

Very cool stuff Harry (or should I say Matt?).

On the first set of balls, are the 1.6s and the 1.5s measuring the same thing?

I’m assuming the first one is a timing to wherever Greene was standing and the second one is when the ball crossed the line into the outfield. So to get an accurate comparison we’ll need to know where Greene was when he made the first play.

Unless he’s on the outfield grass when he makes that play it’s somewhat counter-intuitive that the harder hit ball takes longer to get where it was going. Is this due to the hops? Spin on the ball?

I’ve seen a lot of talk about the physics of fly balls and liners, but is there any way to model the physics of a ground ball?

Laura said...

The problem with measuring the motion of a ground ball is that the ground, which isn’t close to constant between fields, has a huge effect. Turf will have a different effect than short grass which will have a different effect than long grass. Plus, any spot where the ground isn’t uniform would be extremely difficult to model.

joe arthur said...

After looking at the video of the Soriano and Johnson ground balls, I wonder if we are seeing the effects of batted ball spin … in spite of the similar horizontal angles as measured by HIT f/x, Soriano’s ball ended up about 6 feet closer to 2nd (you can tell by the mowing pattern on the infield). Also Johnson’s ball seemed to bounce higher (and made contact with the ground fewer times?) than Soriano’s, so that it may have lost velocity less quickly, so that it could get through the infield faster in spite of a much slower initial velocity [assuming the HIT f/x measurement is correct].

Alan Nathan said...

Question for Peter, re Balls 3 and 4. You said you used my trajectory spreadsheet to adjust the two spin components to reproduce the landing point. Did you use the hang time information when doing that? I ask that for the following reason. There are three pieces of data (x,y,z) at the measured hang time. You are only adjusting two parameters (backspin and sidespin). You are not always guaranteed a good solution unless everything else is right (namely, the drag). When doing a similar analysis with hitf/x and hittracker data, I found I also needed to vary the drag to get a good fit. What I did was simply assume a constant cd, then adjust it (along with the spins) to fit the data. With three pieces of data and three parameters to vary, you can always get a perfect fit.

You can also get a perfect fit by varying the two spin components if the flight time is ignored. I suspect that is what you did. When I use my own procedure in with the constant Cd, I get very different spins than you got. That is why I am asking how you did it.

Alan Nathan said...

One clarification on my previous message:

One way to think about the procedure I outlined is that, given the initial position and velocity as well as the landing position and flight time, that uniquely determines the *average* acceleration in each of the coordinates (x,y,z). In some sense, the backspin, sidespin, and drag coefficient are surrogates the three accelerations. The backspin roughly determines the vertical acceleration, the sidespin determines the acceleration in the horizontal plane perpendicular to the initial velocity, and the drag coefficient determines the acceleration in the horizonatal plane parallel to the velocity.

Peter Jensen said...

Alan – I did use the hang time. Did you take into account the height at which the ball was caught?

Matt Thomas said...

Kudos, Harry, on a well-scribed thought provoker. Wanted to pass along a few more recently determined data points that are pertinent to your choice of balls 1 and 2. For ball 1 (off which Soriano reached base on Greene’s fielding error), Greene’s initial position—or at least that of his right foot, as viewed about 300 ft from the lens of a ten-megapixel Digital Rebel XTi w/ lens set to 18mm—was 148 ft from the apex of home plate, 65 degrees off the 1B foul line. He should have been able to handle a ball four degrees to his right. For ball 2 (Johnson’s single), Greene’s initial (right foot) position was 133 ft from the apex of home plate, 62 degrees off the 1B foul line. The speculation within your article about Greene cheating toward second vs. Reed Johnson was thus correct; Peter’s 7/21 11:32am video-based assertion that Greene was playing Soriano closer (relative to Johnson) was also correct.

Best,

Matt (now a well-provoked thought-scriber)