On Pitch Sequences and Spin Mirroring

With the adoption of the Hawk-Eye tracking system before the 2020 season, analysts and fans alike can directly measure the orientation of the baseball’s spin axis as it heads towards the pitcher. Previously the readings we would see on Baseball Savant were based on the movement of the pitch; the spin axis was inferred. Tom Tango, Senior Data Architect over at MLBAM and author of The Book, delves into the nuances between the spin axis readings here. The differences are derived from the nature of the tracking system before (TrackMan radar) and after (the aforementioned technology from Hawk-Eye, which consists of a series of high-speed cameras placed around the ballpark) 2020. During the offseason, the good people at Baseball Savant rolled out some leaderboards with the new measured spin axis data and compared that to inferred spin axis by pitcher and pitch type. The deviation between the two quantities is the result of the seam-shifted wake effect, a new idea permeating the baseball analyst community. Christian Hook from Driveline has a good piece introducing the phenomenon, as do our very own Ben Clemens and The Athletic’s Eno Sarris; I’d also point you to Barton Smith, Alan Nathan, and Harry Pavlidis’ excellent piece at Baseball Prospectus, as well as Barton’s other work on the subject.

At some point in the future, I hope to add to the discourse regarding seam-shifted wake. For now, though, I want to look into another idea we can analyze with this new access to measured spin axis. Until recently the ability to dive deep into the new spin axis data has been limited. We, the public, only had access to data summarized by pitcher and pitch type. Now, thanks to the wonderful work of Bill Petti and his baseballR package (and MLBAM for deciding to release the information), we can extract the measured spin axis on the pitch level in 2020. With this influx of new data, I re-scraped and stored the pitch-by-pitch data in my Statcast database (which I could not have done without Bill’s tutorial).

With that being said, my first inclination was to look at how pitches paired together in the context of spin mirroring. The idea behind spin mirroring is to deceive the hitter. Two pitches that rotate about the same axis but in opposite directions are hard to discern by the batter. For insight into spin axis and how it differs for different pitch types, I recommend checking out this comprehensive piece from Dan Aucoin at Driveline where he explains the importance of understanding a pitch’s spin axis, how it explains pitch movement, and deviations between axis and expected movement based on the axis via the magnus force. Mike Petriello at MLB.com has also given good insight into how spin axis allows certain pairs of pitches and repertoire’s to yield better results than just velocity and movement would indicate. He specifically dug into Shane Bieber’s diverse repertoire, which lacks elite velocity and correspondingly elite spin.

Being able to mirror the spin axis between two pitches has been the source of many great Pitching Ninja GIFS. Hitters can pick up a pitch just by the orientation of the seams as it moves towards home plate. If the orientation of the seams on two different pitches are the same but the rotation is different, the hitter has trouble deciding on the pitch type and consequently whether to swing. Eno talked about this in his own research, which included quotes from ballplayers and numerical analysis. Eno gauged the importance of the how a fastball pairs with a breaking ball with respect to velocity differential, movement differential, and spin axis differential in how well the breaking ball plays in a pitcher’s arsenal. I will note that Eno’s analysis considered the average values for velocity, movement, and spin axis as opposed to more granular pitch-level data, which was not available to the public at the time of his piece’s publication.

Joe Schwarz, earlier in the same year that Eno’s piece was published, explored the concept and its application to John Gant’s diverse repertoire. Joe found that despite imparting high-level spin rates on his curveball, the way it played off his fastball made it an eminently hittable pitch. He also opined that the way his changeup and slider play off his fastball gave him three potential plus pitches and those three pitches would help drive him to success as a starting pitcher. Also prior to the measured spin axis data becoming available, Michael Augustine explored the concept in a two-part series here and here. Michael has some intuitive visuals and GIFS of his own that give the reader good examples of how spin mirroring is leveraged by the pitcher to fool the batter into making disadvantageous swing decisions. For an overview on batter decision-making in general, I recommend this piece from Eno back in 2016. The lessons from Eno’s piece help explain the trouble posed by spin mirroring for the batter.

Pitch types are derived from their movement and velocity. The former is mainly derived from the axis of rotation and the spin rate; sometimes the effect of seam shifted wake is sprinkled in, too. Based on 2020 data, here is the average axis of rotation and spin rates for the main pitch types for right-handed pitchers directly from the Statcast data (left-handed pitches are the opposite so I filtered by handedness):

My interpretation of the unfiltered spin axis reported by Statcast here is the direction of the spin going into the plane parallel to the front of the strike zone (i.e. the plane formed by the x and z axes) from the perspective of the pitcher. After reaching out to Tom Tango on twitter, he confirmed my suspicion: what is published in the Statcast .CSV is the spin entering the x-z plane. The three-dimensional information can only be obtained on Baseball Savant at the player-level (i.e. player averages) instead of the pitch-level. Nevertheless, using the two-dimensional information, fastballs spin opposite curveballs (about a 180 degree difference) as expected, while sliders spin about 90 degrees away from either.

My goal here is to see if the spin axis differential between two pitches thrown in sequence alone can be a driving force behind generating swinging strikes and suppressing batter production overall. First, here is the distribution of spin axis differentials for sequences involving four-seamers and the two curveball variants:

The first pitch type in the sequence is the pitch being thrown while the second is the pitch preceding it. As you can see, the peaks of these distributions are around 180 degrees. Similarly, here are the distributions for sequences involving fastballs and sliders:

Now the peaks are not as well defined. I would guess this is a product of the fact that there is more variance in slider movement profiles than curveballs. Next, I took every pitch sequence from the 2020 season and binned them in buckets of 20 degrees of spin axis differential. I took the swinging strike rate of each bin and the wOBA allowed (for sequences that ended plate appearances) to account for the possibility that mirroring pitches well has other benefits like suppressing contact.

There is not much rhyme or reason to the swinging strike rates besides the fact that pitches with similar spin axes do not lead to many swinging strikes. Remember, pitches with a differential of 180 degrees are perfectly mirrored. The lack of signal in the swinging strike rates makes me think that pitchers with good sliders can still sequence those well with fastballs and generate swinging strikes. This piece by Wes Jenkins over at The Hardball Times is from a few years back, but it makes a cogent argument that sliders are truly the most difficult pitch to hit. This analysis fails to capture that, hence the seeming lack of importance of spin mirroring. In the future it would probably be worth looking at sequences between just curveballs and fastballs and seeing if for those specific pitches, mirroring the spin is a significant driver of swinging strikes. If you squint at the wOBA plot maybe you can argue that spin mirroring drives positive outcomes from the pitcher’s perspective (maybe because this takes into account some pitchers being able to induce groundballs with their curveballs), but just binning data is not a sufficient solution. Incorporating this information into a model and gauging its importance is probably required.

Clearly just looking at how well pitches are mirrored is not the be all, end all in determining the effectiveness of a pitch sequence. My analysis ignored velocity and movement, which we know are driving factors in the ability flummox hitters. This type of analysis, where I look at sequences and their spin axis differentials, neglects all other context on a pitch’s or pair of pitches’ effectiveness. Slicing and bucketing data has its limitations. Determining a features importance among other factors requires a more robust modeling process, which I did not include in this analysis. Thus, a future project would include incorporating this information into a model predicting swinging strike rate and seeing how that property interacts with parameters such as velocity, location, movement, and deception via the effect of seam shifted wake. In the meantime, I think it is still interesting to peek at. We can conclude the spin mirroring in and of itself is not the deciding factor in the merits of a pitch sequence. That does not preclude spin axis differential’s importance in conjunction with other variables, but I think we can be relatively certain it lacks weight on its own in terms of judging pitch quality. However, with this new data in hand, the possibilities for understanding the merits of a pitch or pitch sequence are endless. Hopefully, this is just a jumping off point.