Magnus Models and Constant Acceleration Assumptions: Post 46

There are two major issues with current pitch tracking in the MLB.

  1. The measurement system, Trackman, does not make a direct measurement of the spin that contributes to Magnus force.
  2. It assumes all accelerations are constant over the entire flight of the ball.

Each of these is important. I know the Hawkeye system that will replace Trackman next year will eliminate (1). But, most non-MLB folks will still be using Trackman or Rapsodo and will still have this issue.

The constant acceleration assumption seems like a way to reduce the amount of data that needs to be recorded and perhaps a way to smooth noisy data. I have no idea whether or not Hawkeye will solve (2). At minimum, it would be nice if acceleration could be a bit more nuanced than constant. Maybe linear or even a polynomial. It is unknown to me if the Trackman (or future Hawkeye) data are sufficiently resolved in time and space to support this.

One other thing I’d like to point out is that the impact of (1) is different with Trackman than it is with Rapsodo. In fact, Rapsodo 1.0 and 2.0, which measure the ball’s rotation at different points in the flight, are impacted differently. They all work great if the ball isn’t experiencing a non-Magnus force.

If you want to find out what your Trackman or Rapsodo will make of a Seam-Shifted Wake pitch, just scuff a ball on its pole and see what it says. It can’t read that. An example is shown below. This is Rapsodo 1.0

Rapsodo result from a scuffed baseball

The ball is scuffed significantly on the right side. Note that while the ball broke left about two feet (0 would be about the vertical pole on the L screen), Rapsodo says -1 inch. That’s because it correctly got the tilt near 12:00 and that axis gives 0 horizontal break from Magnus. Note that Rapsodo 1.0 accurately tells you the pitch location independent of these issues.

Related Post

25 thoughts on “Magnus Models and Constant Acceleration Assumptions: Post 46

  1. Barton, You are making wrong conclusions on how TrackMan works. We need to talk. Send a pm on
    TrackMan measures the spin rate completely independent of any modelling. Also the trajectory is measured without any modelling. Now what is true, but will change, is that the output trajectory data from TrackMan is a result of a constant acceleration smooting.
    You really need see a scuffed ball being measured by TrackMan so you can see the above yourself.
    Looking forward to our talk.

    1. I am happy to talk about it and admit that I have little first hand knowledge of your system. Perhaps you can point me to someplace that your system’s method is described in detail? Where can I see the scuffed ball results? That would be quite convincing.

      And if the user sees only the result of the constant acceleration smoothing, the fact that the measurement system could do better is irrelevant. I understand that constant acceleration probably works well for golf and that was the original application.

      It’d be nice to have the chat here (since I know others may have the same question), but if you want it private,

      1. I gave a talk at the 2012 Saberseminar on how Trackman works. You can look at the slides here: In recent years, the system has been upgraded to employ a camera as a supplement to the phase shift method of measuring angles. I am in total agreement with what Fredrik has said in his post (How could I not be in agreement; he taught me everything I know about the system!)

          1. Sorry, Alan. Fredrik said I made wrong conclusions and you said you agreed with him, so I guess I am asking you what I said that was wrong.

      2. As a supplement to my previous reply, I add the following: It definitely is true that Trackman measures the spin rate (rpm) but not the spin axis. The transverse (“useful”) part of the spin axis is inferred from the trajectory and that can be done without any model, assuming the movement is due entirely to the spin (and gravity). To infer the transverse spin rate requires a model relating the movement to the transverse spin rate. I have written about that also. I believe it is true that I am the very first person to write about it.

          1. Yes. Of course, it is physically not possible for transverse spin to exceed total spin. However, there is considerable measurement noise on the transverse spin rate (due to measurement noise on the movement). As a result, it can happen that transverse (enhanced with noise) can exceed total. This was something I recognized in my first article on the subject. For that reason, I do not recommend determining “spin efficiency” for a single pitch, which might be quite noisy, but rather averaging over many pitches to, in effect, average out the noise.

        1. “assuming the movement is due entirely to the spin (and gravity)”

          I should have said “assumptions that may not be true” instead of “model”

          This is a much bigger discussion, but the practice of calling spin that contributes to Magnus Force while the ball is moving horizontally “useful” may be something the community needs to reconsider.

    2. I missed that my post said “ball RPM and axis” instead of “ball axis”. I have updated it and appreciate the comment.

      I stand by my original point: A Magnus model is used and the axis is not measured directly.

  2. Frederik, my understanding is that TrackMan measures the spin rate directly and the position of the ball over the course of its flight. It then assumes a constant spin rate and fits to the 9 parameter model ( in order to get initial conditions at release.

    From your post, it sounds like you will be changing the output trajectory ball flight model using the fitted release conditions. Is that correct?

    Thanks to Barton for posting this. I’m one of the people interested in the discussion. Diamond Kinetics has been pushing on this and even released the ball flight model code we’ve been using ( for any external validation/input.

  3. More comments from me: I don’t think the issue with Trackman is the constant acceleration assumption. My own modeling shows that this is an excellent approximation, even for most knuckleballs. See my web site for details. The issue, as far as I can tell, is the interpretation of the movement as being the result of the Magnus force. Of course, Trackman doesn’t do that. But people who use Trackman do it. Trackman measure the trajectory, from which one gets the movement. How one interprets that movement is up to the user.

      1. Yes, I guess Trackman gives tilt, which is a derived quantity showing the direction of the movement (without gravity). It is model independent and needn’t be interpreted as a Magnus effect.

  4. Bart….I’m not sure you have said anything that is incorrect. However, I repeat what I just posted that I don’t think the constant acceleration approximation is such a big issue. It would not be so difficult to do a more sophisticated smoothing (e.g., constant jerk, which is the derivative of acceleration). I do think the interpretation of the movement in terms of spin rate or spin axis *is* an issue if one has conclusive proof that there are other causes of movement. Indeed there must be. Otherwise the knuckleball would’t move nor would we have been completely flummoxed (?) by the Freddie Garcia pitch. Not to mention scuffs.

    1. Right. My complaint is that I believe systems like this prohibit “late break” and other phenomena that may be happening. Maybe complaint is a bad word, since they are clearly amazing systems and have improved the game. But there is no reason that I can see to stick with these limitations.

      1. As I have said, it would be very straightforward to relax the constant acceleration assumption. I have access to some “raw” Trackman data and have tried alternate smoothing methods. The most sophisticated is a non-linear fit assuming “lift” and drag depend quadratically on the instantaneous speed. I put lift in quotes to signify a force transverse to the velocity, regardless of the origin of that force (Magnus or something else). Having done such analyses, I have concluded that constant acceleration is “good enough”, in the sense that any deviation from that assumption is not warranted, given the overall precision of the data. That may not be true with HawkEye (i.e., perhaps the measurement of the trajectory has vastly improved precision over TM). But I don’t know.

        1. Hoping for one more reply. Relaxing constant acceleration and finding anything meaningful in the results relies on the raw data being sufficiently resolved. If it is not, you can’t eek out addition information. I suspect that is where we are.

          1. I think what you just said is essentially what I said: ” Having done such analyses, I have concluded that constant acceleration is “good enough”, in the sense that any deviation from that assumption is not warranted, given the overall precision of the data.”

  5. After this discussion, I have revised the text. Thanks to Alan, Fredrik, and Trip for straightening me out. Trackman doesn’t use a Magnus model, but it does not measure the ball axis either. I had several misstatements that have now been corrected.

Leave a Reply