THE BOOK--Playing The Percentages In Baseball

Good point on the axis.  It does obliterate interesting information as you noted.

I think your labels for the angles are a good convention, as they make sense intuitively.  I’ll incorporate both of these in my upcoming stuff at BtBS

A question for you and the readers, the double peak in ground balls in SOB and in launch angle (hard to see, it follows the y-axis down) - related? artefacts?

Regarding the GB: I’d like to see the plane of the swing.

Your GB hitters are going to have a slice down, and so, the launch angle will be low.  I presume it’s launch angle off a bat that is parallel to the ground, correct, and not the angle off the plane of the bat?  So, I expect peaks there.

And a ground ball launched at 0 degrees means that it’s a one-hopper most likely, right?  So, there are your two peaks.

If you plot the launch angle on the y-axis, and the speed of the bat on the x-axis, I will presume that you will get a cluster of data points so that the SOB will be high for the 0 launch degrees, as well as the -45 launch degrees.

If instead you had launch point off the plane of the bat, you’d get one peak, probably at around -10 degrees off the plane of the bat.

***

Btw, is “speed of the bat” the horizontal speed of the bat, or purely the speed of the bat?

Tom, I can answer a few of your questions, but I’m not sure I understand your answer.

Yes, launch angle is the angle between the initial velocity vector and the plane of the ground.

A ground ball launched at 0 degrees with decent speed would probably be a one hopper.  But why does that mean there would be two peaks?  I don’t follow that logic.

I’m pretty sure Harry is reporting the initial speed in all three dimensions, not just the horizontal plane.

Tango - Its not the “speed of the bat”, its the speed of the ball as it comes off the bat.

Following Mike’s notes in #3

- agreed on the launch angle
- I’m not following Tom on this either
- the initial speed is made up of all three dimensions, but we do have the xyz velocities, too

Typo.  This:
speed of the bat
is supposed to be this:
speed off the bat

***

“A ground ball launched at 0 degrees with decent speed would probably be a one hopper.  But why does that mean there would be two peaks?  I don’t follow that logic. “

Presume that there are two ways to hit a ball: on a downward plane (say Endy Chavez), and on an upward plane (say Ken Griffey).

A groundball hit by Endy Chavez means that the bat is on a downward angle.  If the launch point of the ball off Endy’s bat is minus 30 degrees TO THE GROUND, it might be 0 degrees TO THE BAT.  So, that’s a hard hit ball.  He got “all of it”.

So, all those GB that are at minus 45 degrees are likely all coming off the bat of groundball hitters (guys with a downward plane of swing).  That’s why the results of those GB have a good success.

The question we really want to know is: “How much of that pitch did that swing get?”.  So, you need the plane of the swing to answer that.

Tom, I think I understand your explanation now.  I’m not sure I agree with it, though.  I would expect much more of a continuum than two distinct populations or groups.  But your explanation is plausible, I suppose.

I wonder if we can estimate a swing plane from the data. Upper cut = hard hit flies and weak grounders (Thome), chop swing is the opposite.

Well, we do indeed observe two peaks.  Therefore, we are left to explain it.  Either it’s sample size, or we have fairly disproportionate representation, or ???

“Mathematically bees shouldn’t be able to fly. Their size and weight seem to be too large for their wings in some people’s perspective.”
-- Barry B. Benson

I think we may want to take the data on grounders with a grain of salt, compared to balls hit in the air. 

From what I know of HitFx, the way the launch parameters are calculated is by observing a number of “blobs” which represent the ball position on a camera at a known time, and then calculating a constant velocity (zero acceleration) best-fit trajectory for those points that also passes through the launch point (which is determined by analysis of both the incoming (PitchFx) and outgoing (HitFx) ball data). 

Note that the HitFx constant velocity fit method is different from PitchFx, due to the smaller number of “blobs” to work with.

But getting to my point now, when a ball is hit towards the ground (i.e. launch angle < 0) there must be even fewer blobs to work with before the ball hits the ground, at which point the blobs are no longer usable.  This would seem to make the data on grounders less solid than that of line drives and fly balls.

Anyone who knows more about the derivation of the HitFx parameters, please chime in…

The dip at 0 deg is very suspicious to me because it seems to be right at 0 deg. My first reaction is that it is a data artefact either in the measuring or the calculation. I think that’s the most plausible answer until more evidence can be acquired.

Does Endy Chavez swing down? I would be very surprised if he did. That would not be the optimal approach (not even close actually).

If a player wants to maximize his contact ability he should swing inside out (to get the longest time possible to react to the ball), swing his bat in the same plane as the pitch (about 7 deg up to meet the typical fastball) and aim center of mass on the baseball.

That’s a ground ball hitter. If you notice from Harry’s plots the line between line drives and grounders crosses at about 6 deg. That’s for an average hitter. For a contact oriented swing it would be higher since the balls will not be travelling as fast off the bat.

Now if we assumed that the optimal launch angle was 30 deg would that mean that the best power hitters would swing up at that angle? No, actually. The optimal swing for power is IIRC 11 deg up and striking the ball about 1 inch below center of mass. That is because of the beneficial effects of backspin. The velocity you lose from not hitting the ball perfectly square is made up by the backspin you get.

Also, swing up at 30 deg means you’re going to miss a lot of balls because your swing plane is so out of whack in comparison to the path of the pitched ball. Using the benefits of backspin also makes you a better hitter for average also.

Of course not everyone swings optimally. Jack Cust comes to mind. And there are guys who do chop at the ball (at least in the minors), but they are all handicapping themselves. Jack only gets away with it because of this plus bat speed and plus plus pitch recognition abilities. Ground ball hitters who also strike out a lot are *really* unlikely to make it to the majors.

The physics of hit ball is actually quite messy and complex. Simple models are not that useful.

Regards,

Matt

Greg, you are correct, except that the model is a constant-acceleration model, not constant-velocity.

I think that ground balls with launch angles of, say, -10 degrees or higher, probably have fairly reliable data, but as the launch angle decreases, I become more suspect of the accuracy of the data as well as wondering how big of a sample Sportvision was able to transcribe from the video.  So I take any conclusions about balls pounded into the ground with a full shaker of salt.

Greg - It doesn’t take many frames (1 1/2 to 2) to be able to make an accurate calculation and a ground ball at all but an extreme downward angle (greater than -20 degrees) has plenty of frames available before it hits the ground unless the ball is obscured by the bat, the batter, or the foul lines.  I am assuming that the 8% of the hit balls that Sportvision couldn’t calculate data for are the ones that were either at an extreme angle or were obscured.  Of the data reported, I have only found 30 or 40 balls out of nearly 15000 that seem to be odd data and that I am reporting to Sportvision fo ra second look.

Matt #11, thank you for saying what I was thinking but couldn’t put into words.

The physics of hit ball is actually quite messy and complex. Simple models are not that useful.

Yes!  I have a model of the ball-bat collision that I have finally worked out, but the math is so messy that I haven’t been able to put it into a nice widely-applicable format, and I have been reduced to solving each batted ball one by one.  When I get some spare time I’m going to work on streamlining my equations so they can be applied more easily.

Mike #12:

In the HitFx data, the “Hit_ax”, “Hit_ay” and “Hit_az” parameters are all zero for all the batted balls.  Zero acceleration means constant v.

In the PitchFx data, the “ax”, “ay” and “az” parameters are all non-zero constants, and so the v’s vary throughout the pitch, as we all know.

I don’t think this is the last word on the modeling for HitFx, but for this is it, as far as I know…

Hmm, you are correct, Greg, about what the data says.  I assumed they were using the same model as for PITCHf/x since it was coming from the same video source, but perhaps not.  Maybe you don’t gain much accuracy in your estimation of the initial velocity by going to a constant-acceleration model for the batted ball, whereas for the pitched ball, of course knowing the acceleration is paramount because you want to know more than just the initial velocity out of the pitcher’s hand.

"Spray” and “launch” seem much less clear to me than horizontal and vertical, or azimuth and elevation. Why insist on inventing new terminology when something perfectly clear already exists?

Agree with andeux #17, although what is clear to some people is ocnfusing to others. 

Btw, Greg, I’ve been meaning to ask you, when you set your reference line for the azimuth in your coordinate system, why did you choose what is the -x direction in the Pfx coordinate world?  Was it just arbitrary?  Knowing you did navigation in the Navy, I guess I always assumed you had a reason, but I didn’t know what it was.

I have found it more useful to set the +y direction as the reference line, and then if I want to transform azimuths from right-handed batters to left-handed batters, I can just flip a sign.

I get something a little different than Harry when I plot horizontal angle by hit type:

http://i110.photobucket.com/albums/n85/JnaiJnai/wherehitsaremade.jpg

Which I think more clearly reflects the fact that singles are hit between infielders and doubles are hit at them but over them…

Matt - You are confusing the optimum launch angle for hitting a home run with the optimum launch angle that produces the highest average linear weight.  Thirty degrees may give the best chance at a home run, but the highest average linear weight is for hit balls with a launch angle between 10 and 15 degrees.  Home run hitters will have an average launch angle somewhere between 20 and 25 degrees and those who get a low percentage of there value from home runs between 0 and 10 degrees.

Dan - I think your chart represents pretty much of a tautology.  Almost all doubles are either balls hit in the air between the outfielders or ground balls hit down the line.  By far the majority of singles are ground balls hit between the infielders.  Your chart just indicates where the fielders are playing.

I have the graphs that I think Tom was asking for in #2, as well as my replication of Harry’s graphs, but using only the horizontal component of the initial speed.

I’m not sure why there are “ground” balls with elevation angles of >10 degrees.  These are a few but may represent errors in the data (possibly errors in my classification of batted ball types rather than errors in the Hfx data set).

Peter - Right, of course. Wasn’t saying there was anything deep there.

Tom, if I’m posting too many graphs in these threads, please let me know.  I seem to have killed the Ortiz thread with them.  I love the fact that you have opened up image posting here and am going a little crazy, but if I’m making it hard for people to read the threads, I’ll back off.

Mike #18:

The coordinates that underly HT have the +x axis pointing from home through second base, and the +z axis passing through home plate also, but in a “third to first” direction.  +y is straight up through home plate (well, the back apex of it).  Don’t ask me why I used y for height instead of z, I think I started out just looking at trajectories in 2D, and then moved on th 3D, and by the time I got serious, I didn’t feel like changing it. 

I use these coordinates for plotting things, but when I express azimuth in degrees, I set the RF line as 45 degrees so I wouldn’t have any odd boundary issues over fair/foul.  Something to do with trigonometry - sines are always positive this way, even for balls that land on the foul side of the extended line, something like that…

Incidentally, all this took place back in Spring, 2005, so well before I knew anything about PitchFx…

Mike, if one of us were to hit MLB pitching, our launch angle could be +45 degrees, and the ball would travel 30 feet.  ergo, groundball.

That’s the problem with the designation of GB, FB, LD, etc.  You can have the same everything.  But if one is a HR and the other is a checked swing, one is marked as a FB and the other as a GB.

***

1. Me: Spray is clearer
2. You: Why use spray if horizontal is clearer.
3. Go to 1.

Greg: since you are a Navy man, what words are used when a plane takes off?  Would you say that the plane’s takeoff angle is 30 degrees, or that the plane’s vertical angle is 30 degrees?

Mike,

I don’t have a problem.  If you want, you can code your images like this:

That makes the image smaller (a regular blog post is 400 or 425 or so), but it makes it clickable.

Whatever you think looks better…

Over in this thread I’ve been splitting SLGCON and BABIP against launch angle (or wtvr) by SOB buckets.  Animated, no less. With and without homers.

http://www.beyondtheboxscore.com/2009/6/9/903793/optimal-launch-speed-and-angle-for

Peter #20:

I’m not confused but my writing was - there was a sentence missing there about optimal homerun launch angles. Agree 100% with what you posted.

What you said also reinforces my point that no MLB batter is (or shouldn’t be) deliberately trying to beat the ball into the ground - either by aiming at the top of the ball or chopping at it.

With regards to the naming conventions my opinion is that the colloquial names (launch, spray) are better. Less precise, but more friendly to the layman who will be the one reading what we write.

Vertical is a little ambiguous, could mean the elevation above the horizontal (which is what we’re talking about), or it could maybe mean the angle down from straight up.

I’ve used VLA - Vertical Launch Angle for this, and HLA - Horizontal Launch Angle, for the azimuth.  And SOB (Speed Off Bat) to complete the perfect trio of TLA’s (Three Letter Acronyms)…

I don’t know that my Navy experience will help here: in celestial navigation, what I’ve been calling VLA would be referred to as an “altitude” angle, which would probably confuse things even more…

Re Peter #20:  I am finding that the mean launch angle for home runs is about 29 deg (larger than your 20-25 deg) and for hits other than home runs is about 10 deg.

Alan - I didn’t say that the mean launch angle for home runs was between 20 and 25 degrees.  What I said was that the optimum launch angle (the angle that produces the lighest linear weight) for HR hitters was likely to be between 20 and 25 degrees.  Big difference.  I am running the numbers now to be more precise.

Greg, have you done any spot checking to see how the hitf/x data matches up with your Hit Tracker calculations?

Peter (#33):  Sorry, I don’t understand what you mean by the “lightest linear weight”. 

Re the discussion of constant velocity vs. constant acceleration:  I suspect there simply are not enough frames of hfx data to allow a statistically meaningful constant-acceleration (9-parameter) fit to the data, so they opted for the simpler constant-velocity (6-parameter) fit.  It is a simple matter to test this with a simulation, which I will try to get to sometime this week.

Pretty sure Peter #33 is supposed to say “highest linear weight”, i.e., highest run value as determined by linear weights.  So while the HR% might be lower at lower angles, the optimum overall run value even for a power hitter might be to average hitting the ball at lower angles, trading some HR for more inside-the-park hits and less outs.

JBrew #34:

There is a systemic bias between Hit Tracker’s SOB (Speed Off Bat) and HitFx’s “hit_initial_speed”, because they do not represent exactly the same thing, despite the names.

In Hit Tracker, SOB represents the instantaneous speed of the ball off the bat. It is derived by establishing the atmospheric conditions, then postulating a set of launch parameters (SOB, VLA, HLA as defined above) and evaluating how closely the trajectory comes to the observed landing spot.  Then the launch parameters are adjusted until the trajectory passes through the landing point at the proper moment in time.  Drag and lift are calculated according to the atmospheric conditions and the trajectory of the ball, with spin an assumed value based on a complicated combination of the launch parameters.  Since Hit Tracker is an analytical model, I have no trouble at all picking the initial speed out of the model.

HitFx is an empirical model that calculates hit_initial_speed by creating a best fit straight line path for the ball, based on a zero acceleration model, that minimizes the time/position error to the various observed “blobs” that the cameras capture.  As such the parameter hit_initial_speed does not represent the instantaneous speed as the ball leaves the bat, but rather the average speed of the ball along a hypothetical constant velocity straight line path over the first few hundredths of a second of the ball’s flight.

Since we know that the ball begins to decelerate the instant it separates from the bat, it’s speed a few hundredths of a second later as it passes out of the field of view of the cameras is of course lower than it was when it left the bat, and so naturally the average speed across the camera’s field of view is less than the instantaneous speed off the bat.  Think of how much the pitches slow from release to crossing the plate, as revealed by PitchFx.  The same thing goes for batted balls, of course…

Data comparison between Hit Tracker and HitFx confirms this: hit_initial_speed from HitFx averages about 2 mph lower than the SOB numbers from Hit Tracker.  I don’t know yet how consistent this bias is, but it is based at least in part on the number of “blobs” used to derive the HitFx fitted line path, so if the number of blobs changes, so would the length of the path across which speed is averaged, and so hit_inital_speed would change… I’m hoping to learn more about this at the conference…

There is of course a lot of variation around the 2 mph average, attributable primarily to Hit Tracker, which is rather sensitive to the atmospheric conditions used as inputs for the calculation.  If I estimate the wind to have been a 7 mph tail wind, and it really averaged out to be an 8 mph tail wind, the calculated SOB will be higher than the actual value.  This dependence on accurate wind data that is often just not available is a weakness of Hit Tracker, one I hope to mitigate in the future with better wind modeling inside the stadiums.

I concur with Mike Fast that that is exactly what Peter is talking about.

If you were to create profile of hitters, say Ryan Howard and Ichiro, the claim being made is that the optimum launch angle for the power hitters would be in the low 20s (that even though they can get more HR at higher angles, it would cost them elsewhere), and I presume for the non-power hitters would be something below 10 degrees.

It’s unclear to me if this includes swing-and-misses in the linear weights.

Re Mike and Tango (#36,38):  OK, I sort of get it.  But what exactly does “optimum” mean?  Does it mean optimizing the chance of getting on base?  If so, then it is straighforward to investigate with hfx.  You just plot on-base probability vs. launch angle and see where the maximum is.  Or does optimum mean something more complicated?

Re Greg and hfx vs. hittracker:  Just to clarify a bit further, for hittracker data to determine the initial conditions, two things are needed:

1.  an aerodynamic model of lift and drag
2.  a ball-bat collision model to determine the two components of spin on the batted ball

Greg in his post talked only about the first of these.  But even if we had perfect knowledge of the aerodynamics (including, but not only, the wind), we would still not be able to accurately predict the initial conditions without somehow constraining the spin.  Mike Fast talked about his model in an earlier post.  Greg has his model.  I suspect neither of them work all that well, based on my own experience in construction such models.  And this is not meant to be a criticism of anybody (except perhaps myself and my own lack of knowledge).  It is really a statement about where I believe we are scientifically on being able to calculate the spin on a batted ball.

So, while hfx has its limitations, as Greg has noted, I would argue that hittracker has probably even more severe limitations.  At least, that is my opinion (and I know Greg disagrees with me, but reasonable people can disagree), based on what I know (and don’t know) about items 1 and 2.  My fond hope is to use data such as hfx and hittracker to try to constrain better the things we don’t know, leading to better understanding and better models.

Alan, “optimum” means optimizing your team’s run scoring chances.  Each offensive event is assigned a run value using a run estimator (e.g., Base Runs or Bill James’ Runs Created, etc.).  Off the top of my head, a walk is worth something like 0.3 runs, a single 0.5, a double 0.8, a triple 1.0, and a home run 1.4 runs.  An out costs your team 0.3 runs.  Those are approximations but should give you the basic picture.

A simple approach would be to assign a run value to each batted ball in the Hfx data set and then find the launch angle that optimizes overall run value.  However, as Tango points out, a batter’s approach may also affect how often he walks and strikes out, which are not captured in the Hfx data set.

Alan,

Were you able to collect good data about spin put on the ball at different bat alignments? (not tilt, and not variations perpendicular to the barrel, but the other one - what do we call it? bat advancement? pull angle?)

For those of you who like seat-of-the-pants estimates, here is a very rough estimate of how much hfx underestimates the actual SOB, based on the effect Greg mentions, looking only at home runs.  From hfx, the mean approximate hit ball speed for a home run is about 100 mph.  A ball loses about 10% of its speed in 50 ft, or about 0.2% per foot.  Suppose the hit ball is tracked in the range 5-20 ft from the contact point, so that the mean distance is about 12 ft from the contact point.  The fitting will approximately determine the speed at that point in a constant-velocity fit.  At 0.2% per foot, the SOB will be systematically low by about 2.4%, or 2,4 mph.  Pretty close to Greg’s number.

I have some tracking data from some spring training games in Arizona this past March.  I will see if I can get a more quantitative estimate of the effect.

Re Matt, #43:  Long story and Red Sox v. NYY is about to start, so my attention is very much divided.  I’ll tell my story about spin measurements a bit later.

Alan #40

I cringed when I read hfx vs. hittracker, because I don’t see it that way, although I may project that sometimes (sorry).  I think the two are quite complementary, in that each measures something (launch & immediate post-launch position & time for HfX, landing position & time for HT), and each uses the principles of aerodynamics to figure out some of the other parameters of interest. 

HT’s got plenty of limitations that affect its internal derivation of the launch parameters, chiefly the uncertainty about weather and the generic spin model.  It’s been a continuous splinter in my mind to not be able to model those things better, so I share your hopes about gaining a better understanding by learning from the measurements HitFx will provide…

Fortunately, the distance numbers that HT generates are much more robust to the weather and spin uncertainties thanks to the constraining effect of the landing point observation (extreme example: if the ball lands 400 feet away at field level, it doesn’t matter what the weather or spin were, it’s 400.)

I’m hoping something similar to this can eventually become part of the automatic data intake and output of HitFx.  I’m truly looking forward to the opportunity to spend more of my time analyzing and less time gathering.  Not to mention catching up on my sleep…

Yes, “highest linear weight” is what I meant, but I miss typed. Alan, optimum vertical angle means the angle that the batter should attempt to hit the ball so that his actual distribution of hit balls yields the maximum total linear weight and thus the maximum number of runs for his team.  And the approximate answer is 25 degrees for home run hitters.  I took 25 hitters that hit more than 15 HRs and had the highest HR rates in 2008 and looked at their average linear weights +-8 around various vertical launch angles.  The highest was .480 per hit ball for the 306 balls hit by these batters between 17 and 33 degrees.

Alan,

Batting average treats all hits the same, putting a “1” in the numerator for all hits.

However, we know that a single and a HR are not worth the same.  If you give a weight of 0.9 for a single (or reaching on error), a 1.3 for double or triple, and a 2 for a HR, you get the proper balance for the hits.

Add them up, and divide by the balls in play, and you get a “weighted” batting average per ball in play.

aka, linear weights on BIP

I just added two animations to the thread linked in #28. Using 10mph and 10 degree buckets and the weights from #47 ...

Re Greg #45:

I completely agree with you on two important points:

1.  hfx and ht provide complementary information and together they ought to teach us a lot about baseball aerodynamics and batted ball spin

2.  the uncertainties in the initial conditions do not significantly affect your determination of the home run distance

Thanks to Tango, Mike, Peter for explaining linear weights to me.

I just puttered around a bit, brushed up on my physics a bit, and THINK I figured out how to estimate hang time (crudely) from the Hit F/X data. Here’s the formula I used in SQL:

2 * (((hit_initial_speed* 0.44704) * SIN(RADIANS(hit_vertical_angle))) / 9.8)

This, as they say, ignores air resistance. (And several other variables, like the height of the bat/ball when contact occured.) It LOOKS reasonable to me, when I look over the results. Am I way off base here?

Colin,

Try your equation on the home runs, and I’ll send you my observation data on them that includes my measurement of hang time.

Greg

Greg:

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

That’s everything matching event = “Home Run”. My distance estimates are all high by a good deal, which is a consequence of ignoring the decreasing speed of a batted ball over time. I presume the same is true for the hang time estimates.

Looking over it some more, the solution to my problem seems to be to run the simple formula repeatedly at one-second intervals, modifying the input speed each time based upon the deceleration of the ball. I even found an example that uses a baseball:

http://wps.aw.com/wps/media/objects/877/898586/topics/topic01.pdf

It looks like a bear to program, however.

Greg and Alan, thanks for your thorough responses.  I can understand some of the limitations you outlined above.

I should have elaborated more but my question was more along the lines of checking the hitf/x data (which is new and raw) against some actual results while also confirming/checking your HT calculations, not just SOB but also VLA/launch and HLA/spray.  I would expect some differences (like the average 2 mph you mentioned above) but just to provide some validation/comparison before accepting something as truth.  The amount of information that can be gleaned from these will exciting to follow in the coming years.

Colin, the way to solve the equations for the trajectory of the batted ball is to use a numerical method for integrating differential equations called fourth-order Runge-Kutta.  It’s based on Taylor series expansion.

Also, you need to include the effects of drag and the spin.  Drag is dependent on the velocity, which is known, and the atmospheric conditions--air density (can be calculated from known parameters) and wind (must be estimated, I believe Greg does this from video and weather data).  Spin is not known from this data set--estimates can be made but this is a more complex topic.

Mike (#55) beat me to the punch with his response to Colin.  I have Greg’s data for the April home runs.  When combined with hitf/x data, I find that the hang time computed with your formula (which assumes the vertical acceleration is just from gravity) is underestimated by an amount that varies from case to case but averages about 15%.  Drag and spin go in opposite directions here.  Spin (assumed backspin) makes the hang time longer.  Drag acts in the direction of gravity (down) on the way up and opposite to gravity on the way down.  The up and down effects don’t quite cancel, however, since the ball is moving faster on the way up so the drag is larger.  So, the net effect of the drag is to reduce the hang time.

"Spin (assumed backspin) makes the hang time longer.  “

I presume that the amount of backspin off the bat is proportional to some degree to the amount of backspin prior to the point of contact which is proportional to the amount of backspin off the pitcher’s hand correct?

So when you say this:

“...is underestimated by an amount that varies from case to case but averages about 15%.”

then can I presume that if you considered the spin of the ball prior to contact, that this would be one source of bias that can be (easily) accounted for?

then can I presume that if you considered the spin of the ball prior to contact, that this would be one source of bias that can be (easily) accounted for?

It’s true that the spin on the incoming pitch is one source of the spin on the outgoing batted ball.  The other source is from the ball rolling on the bat during the collision, which is dependent on the offset distance between the centers of the bat and the ball.  The direction in which this spin is applied depends on the position of the bat at contact.

Generally speaking, however, the higher the fly ball, the greater the offset between bat and ball centers at collision, and the greater the backspin.

I should add to #58 that the magnitude of the spin is not well understood by physics at this point, unless Alan has gotten results yet from his spring experiments that have bearing on this question.  Trackman is also collecting data this summer which should illuminate our understanding of spin on batted balls, although I haven’t had the opportunity to see any of it yet.

Low-speed laboratory experiments imply some things about the tangential coefficient of restitution and conservation of angular momentum that do not appear to hold at the higher-speed ball-bat collisions in the actual game of baseball.

Generally speaking, however, the higher the fly ball, the greater the offset between bat and ball centers at collision, and the greater the backspin.

Although this is an OK general principal for home runs, the tilt of the bat at the time the ball is hit varies so much more for all hit balls than it does with home runs that calculating hit ball spin is much more complex.

Tango - Incoming pitch spin is a relatively minor factor on hit ball spin compared to the spin created by the bat/ball offset at impact that Mike mentioned.

Re spin on the batted ball, Mike #59 says:

Low-speed laboratory experiments imply some things about the tangential coefficient of restitution and conservation of angular momentum that do not appear to hold at the higher-speed ball-bat collisions in the actual game of baseball.

The low-speed experiments he refers to are mine and are published in a paper you can download at this link
http://webusers.npl.illinois.edu/~a-nathan/pob/AJP-Oct2006.pdf:

The paper is technical in nature and probably not easy to read.  But the issues are easy to state, so let me try to do that here.

When ball meets bat, there is a component of the ball-bat relative velocity that is tangential to the surface of the bat, and it is this component that is responsible for the spin on the batted ball.  The tangential component could arise from several sources: 
1.  The vertical offset between the ball and bat
2.  The spin of the pitched ball
3.  The bat is “out in front” or “behind”, so that the axis of the bat is not parallel to the x axis (using the pitchf/x coordinate system).
4.  The bat is tilted out of the horizontal plane

Whatever the reason, if there is a tangential component, the ball “slides” along the surface of the bat during contact.  The friction between the two surfaces slows down the relative tangential motion and exerts a torque that causes the ball to rotate (or changes the spin if it is already spinning).  The “standard” way to describe what happens is that the friction slows down the tangential motion until it stops, whereup the ball rolls on the surface.  You can see the same effect by tossing a bowling ball down the lane.  The ball slides until friction stops the relative motion at the surface, then the ball starts to roll.  A standard “physics 101” problem is to calculate the speed of the bowling ball after it starts rolling, given the initial speed.  The usual treatment of the ball-bat collision assumes that the rolling condition is met, allowing one to calculate the spin of the batted ball.  As a technical point, the additional assumption is made that the angular momentum of the ball about the initial contact point is conserved. 

Now, the low-speed experiments that Mike referred to (and that I referenced above) show that the rolling assumption is wrong.  Instead the ball “grips” the surface, resulting in much more spin than one gets from the rolling assumption.  This is precisely what happens with a superball, resulting in some really weird motion (try tossing a superball at an angle onto the floor and watch the subsequent motion).

And there is still more to the story.  In experiments I did last year but have not yet published, I looked at 100 mph collisions and used high-speed video to measure the spin.  I found even higher spin than one would expect based on the low-speed collision.  These spins, when translated to typical ball-bat collision one might encounter in a game, are much larger than I would expect.  However, I am skeptical that the data, taken at face value, actually describe what happens in a game situation.  So, until I sort this all out, the new data stay unpublished.  My gut instinct is that the predictions based on the rolling assumption are closer to correct.  But a gut instinct is not science, so until I sort all this out, my data remain unpublished.

Mike referred to the Trackman radar system, which has the ability to measure the spin on the batted ball and will ultimately provide the data needed to refine the collision models.  Or at least allow for empirical expressions relating the spin to the two angles and SOB.

Sorry that this is so long-winded.  The chief message you should take away from this is that our ability to predict the spin of a batted ball is not so great.