A swinging strike is arguably the most important pitch result from the perspective of a pitcher. A strike, not matter how it is obtained, is a strike when you look at a scorecard. However, when evaluating and predicting the performance of a pitcher, swinging strike rates are vital. A swinging strike is different than a foul ball: in the case of a foul ball the batter makes contact with the pitch. A swinging strike is different from a called strike: in the case of a called strike the batter does not swing, thus we cannot know the effectiveness of the pitch if the batter swung. The swinging strike is the outcome that gives us, as analysts, the most positive information of the pitcher. We see the batter makes the decision to swing at the pitch and upon making that decision he misses. So while all strikes are technically equal, the swinging strike gives us the most information about the effectiveness of a pitch.
For these reasons, modelling pitches in terms of their probability of generating a swinging strike is the best way in gauging pitch quality. What goes into a swinging strike? Well we know velocity and spin rate are essential factors. Higher velocities give batters less time to make the optimal decision. Higher spin rates allow pitches to move as much as possible given their spin axis (transverse spin and seam-shifted wakes play into pitch movement but all else being equal spinning the ball as much as possible is beneficial, sometimes with the exception of changeups and splitters. That is a topic for another time).
Once the pitcher makes the decision to swing at a pitch, attempting to disguise its movement is of the utmost importance. Pitchers that throw both a fastball and a curveball have the benefits of deception because the spin of the pitches are opposite. Four-seam fastballs have close to perfect back spin (depending on the pitcher). Curveballs have close to perfect top spin (again, depending on the pitcher). To the batter, these pitchers look eminently similar. The orientation of the seams are seemingly the same, but the actual spin is the opposite. Leveraging the spin characteristics of these two pitches can give the pitchers advantages in terms of deception.
With the implementation of Hawk-Eye cameras in all MLB stadiums in 2020, the spin axis of every pitch can be directly tracked. Previously with Trackman, MLBAM tracked the spin axis of pitches by inferring the axis from the movement of the pitch. The Hawk-Eye cameras can directly track the spin axis of the pitch. This gives analysts a better understanding of how pitches pair with each other and gives insight into pitches the move more than their movement-inferred spin axes would indicate.
In this post I wanted to look at the effect of spin axis differential between curveballs and four-seam fastballs on those pitches swinging strike rates. There is a lot of research into the effect of spin axis on the effectiveness of pitches, all else being equal, but I wanted to look at how pitchers who throw both of these pitches can get an extra edge. I built a model for pitchers who throw both of these pitches and how often they should generate swinging strikes.
First let us look at which pitchers generate the most spin on both four-seam fastballs and curveballs. I took all pitchers in 2020 who threw 100 four-seamers and 100 curveballs and compared their spin efficiencies on each spin type (the percent of spin that contributes to transverse movement).
There is not much of a relationship between the two quantitates. Lance Lynn is notable because despite the fact that he does not have great spin efficiency on either pitch he is supremely effective. I will note that Lynn dos not throw his curveball often and is known to manipulate the shape of his fastball. He is unusual in his ability to throw different fastballs to great effect. Shane Bieber was the best pitcher in the league in the shortened 2020 season and he shows well by these measures. Lucas Sims has elite spin rates overall but seems to have trouble generating high-end transverse movement given the ample spin he imparts on the ball. Hyun Jin-Ryu does not throw with great velocity but maintains great results threw efficient spin. For further insight into spin rates and spin efficiency on four-seamers and curveballs I direct the reader to the following visual where the reader can get an idea of which pitchers have the best raw pitch characteristics (without consideration of arsenal and seam-shifted wake. Bauer, Lugo, and Sims stand out here):
For all pitchers who threw 100 curveballs and four-seam fastballs, I binned the swinging strike rates of the curveballs and fastballs by swinging strike rate (the percentage of pitches that resulted in swinging strikes). I also gave context into the effectiveness of the pitchers in each bin by summarizing the pitchers in each bin by wOBA allowed. The spin axis differential should be important but there are other factors at play so the qualitative importance of the the spin axis differential can be derived from this visual:
The spin axis and spin axis differential is displayed in terms on arms on a clock. For example, a curveball with perfect top spin has a spin axis of 6:00 (it moves straight down). A fastball with perfect backspin has a spin axis of 12:00 (relative to other pitches it has ride. Obviously in an absolute sense the pitch does not rise). The spin axes were taken from the perspective of the batter. I will not that this is not literally the axis around which the ball spins. It describes the axis of rotation in terms of how the ball should move from transverse spin.
The visual above gives the reader a qualitative idea of the importance of spin axis differential between curveballs and four-seamers in a pitcher's arsenal. In the case of generating swinging strikes on either pitch there is not a clear relationship. I wanted to account of the overall effectiveness of the pitchers in each bucket by accounting for their wOBA allowed. My thought was maybe the axis differential matters, but so do other aspects of a pitch. Maybe pitchers who happened to be really good do not get optimal axis differential on their four-seamers and curveballs and derive value via other means? It is impossible to totally discern these relationships from a chart. So I built a model to empirically evaluate the importance of the spin axis differential.
The model is a general additive model that takes the smoothed relationship between a pitch's velocity, location, and movement, whether or not the pitcher has the platoon advantage, and a variable for spin axis differential modelled as a random effect. The model was trained on 80 percent of the pitches thrown by the pitchers who threw 100 four-seamers and curveballs. It was then tested on the remaining 20 percent of those pitches. The model had an accuracy of 89.8 percent in that it was correct 89.8 percent of the time when it predicted whether or not a pitch would be a swinging strike. From here I could apply the model to every pitch in the data set. There are many ways you can look at this data. I created a column in the data frame that I called expected swinging strike rate, the probability that the pitch was a swinging strike. I grouped and summarized the expected swinging strike rate data by pitcher and
posted a thread on twitter for those who are interested in which pitches faired best. Guys like Bieber, Glasnow, Gray, and Cole have curveballs at the top of this leaderboard but worth noting Griffin Canning by pure "stuff" has an excellent curveball. And Josh Staumont has the only fastball that appears at the top when you combine four-seamers and curveballs.
As interesting as the player-level data is, ultimately I wanted to check the importance of spin axis differential for a pitcher's four-seamer and curveball. The variable for spin axis differential was significantly significant based on its p value, though much less vital to predicting swinging strikes than the pitches velocity, movement, and location. This p value in general is
often misinterpreted but is encouraging nonetheless. Similar to my last post about park effects, I could extract the distribution of possible effects for each spin-axis deviation. Here are the results:
Remember 6:00 is perfect spin mirroring. Based on the model while this spin axis differential is important in predicting swinging strike rates but much less so than the other characteristics. Here you can see that while the spin axis differential is important, there is no discernable pattern. Perfect spin-mirroring has almost no effect while 6:30 has a negative effect. On the other hand 7:00 and 5:00 have the highest positive effects followed by 8:30, the latter of which is far off from perfect spin-mirroring.
What can we conclude from this? I think spin mirroring is still very important. Making your pitches appear the same to the batter's eye is essential in deceiving him. However, my model does not capture this phenomenon and my hypothesis is that the random effect in my model is not really addressing the effect of the axis differential. Instead it is capturing the effect of the pitcher overall and the best pitchers at generating swinging strikes happen to fall into the 7:00, 5:00, and 8:30 buckets. I will point out the if you look at the twitter thread with the expected swinging strike rate leaders, the top pitchers cluster around axis differentials between 5:30 and 6:30 (Bieber, Canning, Ray, Glasnow, Duffey, Cole, and Young) which is close to perfect mirroring and from the standpoint of the batter is probably barely discernable. Those guys make up half of the top of the leaderboard. Still, velocity and movement remain the most important factors in getting hitters to whiff but I remain convinced that small edges are to be had with effective spin-mirroring. That does not mean work on this type of data is over. There are better models that can be built that better isolate the effect of spin-mirroring from the overall quality of the pitcher. And we will have more data. Hawk-Eye was implemented in the shortened 2020 season so we have barely any pitch data relative to other seasons. I only had 82 pitchers who threw 100 four-seamers and curveballs and the pitchers who met this threshold obviously did not throw a full season's worth of pitches. In a sport with as much variation as baseball, this is not a sufficient sample. In the future, as our Hawk-Eye based dataset grows, analysts (including myself) will be able to generate better insights on the effects of spin and learn more about the hitter-pitcher interaction, the most consequential part of any baseball game.
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