Similarity Scoring College Pitchers
Note: This post was co-authored by Reed Zahradnik and Kitae Kim
Introduction
Baseball is chock-full of pitcher comparisons. Developing players are benchmarked by the nastiness of their curveball to Clayton Kershaw or heralded by fans as having the same “stuff” as Gerrit Cole. While it is fun to imagine a favorite pitcher throwing like one of the greats, how can you use hard science to draw these parallels? We want to take this question and bring it to the college level with two objectives: scoring the similarity of individual pitches and finding college arsenal similarity scores. This score will focus on pitch characteristics and will not be based on their results.
To come up with scores, we need to turn to the quantitative data in the University of Iowa’s Trackman data set. Seems simple enough, Trackman gives us a lot of numeric data to work with. We only need to make one small change before we begin building. Normalizing our variables gives us the opportunity to capture full relationships within each variable. One mph in pitch speed and 1 foot of vertical movement belong to vastly different scales and have vastly different pitch implications until normalized. Moving to a 0 to 1 scale for all our numeric variables moves everything to the same scale, at which point we can begin scoring. However, we need different algorithms to answer each objective. We’ll start with examining individual pitch similarity.
Scoring Pitches First
Euclidean distance measures the shortest distance between points in a multidimensional space. Each dimension is defined by a different metric of interest, so we have to determine the most important characteristics of a throw. We ignored underlying determinants of profile such as spin rate and spin axis and narrowed our focus to four key delivery metrics.
- Pitch Velocity
- Vertical Break
- Horizontal Break
- Arm Slot Angle
Velocity drives a lot of player development at the college rank, so release speed is vital to building a comprehensive model. What explains why two balls thrown at the same speed from the same point end up over different parts of the plate? Horizontal and vertical break capture that movement, so we will use these variables as well. And because we are focusing on metrics that define delivery profile, we round out our last dimension with arm slot angle.
To calculate arm slot angle we need to recall some high school trigonometry. Arctangent of a pitcher’s release height divided by the horizontal release distance delivers a release angle. A good start, but we can actually do one better. We can amplify the release angle by moving our calculation origin to the minimum of our release height range. We do this by subtracting the lowest data set release point from the release height before calculating arctangent to get our lowest release on the x-axis. Imagine how a ¾ arm slot from an overhand pitcher varies from a sidearm pitcher when examined from the ground versus the catcher’s eye level.
Taking averages of our four metrics from two pitchers creates two points in our four dimensional space that we can then apply our Euclidean distance function to. The result is a score that gives us a quantified description of distance between points, also known as dissimilarity.
Feeding our output into a Shiny application gives us a quick and efficient tool to present our work. We sort on lowest dissimilarity and you can input however many pitchers you want to compare. You can see below that when we examine our target pitcher’s curveball to the five closest curveball throwers, we find some incredibly similar deliveries.
Combining Pitches in an Arsenal
Scoring a pitcher’s arsenal is a bit more complex because we need to take into account what pitches a pitcher currently throws and at what rate. Enter our second algorithm. Earth Mover’s Distance takes the idea of Euclidean distance and adds weights to the movement through dimensions. The clearest weight for this task is how often each pitch is used and can be visualized as the cluster size of each pitch.
We cannot compare pitches that one or both pitchers do not throw. Let’s look at a quick example. Say we have Pitcher A who throws a fastball 50% of the time, a changeup at 10%, a curveball at 20%, and a slider at 20%. If we compare him to Pitcher B who throws a fastball 60% of the time and a slider the other 40%, we can only score the fastballs and sliders weighted by their usage. The 30% of Pitcher A’s throws that Pitcher B does not use will add 0 to the score. To aid the intuition of our scores we reverse scale from 0 to 1 so that higher scores represent higher similarity. You may identify there is a major limitation to this method. We will address that limitation in the next section.
Our Shiny application arsenal option is most informative when paired with a score matrix. Each matrix is the product of scoring arsenals of interest. This means either the full data set or some tuned version like instituting a minimum pitch count. Note that we coerced diagonal values to NA to remove comparing players to themselves. Coaches can easily scan one of our score matrices for two players of interest. They can then turn to the Shiny application if they wish to understand which metrics are driving the high or low score.
Arsenal Limitations
For the highest scores, a deep dive is incredibly important because of the limitation we foreshadowed earlier. A high score arises when pitchers have common pitches with similar profiles, creating low dissimilarity. But when pitchers don’t share a pitch type, no dissimilarity score is added because there is no shared weight to use the function on. This gives rise to situations where pitchers with vastly different arsenals lack great comparison and receive dissimilarity scores closer to 0. Given our reverse scaling, you ultimately end up with a high score. To this end, we can add context by creating visuals like Baseball Savant’s Pitch Similarity engine. This engine takes the disadvantage of inflated scores and visually demonstrates bubbles for percentage of arsenal. In the example below, the two most similar pitchers to Gerrit Cole are Brandon Woodruff and Dinelson Lamet. Woodruff uses four of the same pitches while Lamet uses two. Anthony DeSclafani throws four of the same pitches as Cole, so why would his score be lower than Lamet’s? The simple answer is that even with four scorable pitches, DeSclafani’s pitch characteristics are dissimilar enough from Cole’s compared to Lamet’s two shared pitches that the resulting score is worse. The more complex intuition is only gleaned by scanning the scored metrics. Search for Yu Darvish’s seven pitch arsenal to see another great example.
While our visuals are not shown as nodes, we are taking the same strategy as Baseball Savant in our current experimentation with what the best representation for our team would look like. Covering player identities would cover too much of our built visuals, so we won’t be able to share them at this time. Ultimately, however we represent the arsenal score there will be give and take with balancing scores and pitch types.
Final Thoughts
The best application of our model for our pitchers will come with offseason pitch design goals. We will be able to ask ourselves why other college pitchers are having more or less success with similar pitches and train our pitchers towards or away from comparable pitch characteristics. Batters will similarly be able to use pitch similarity for practice in the offseason and should be able to take advantage of arsenal scores in-season as well. We can use this information to convey to our batters how similar an upcoming pitcher is to what they have been seeing recently. Practice adjustments can be made accordingly.
Taking this project a step further, we hope to develop recommendations for added pitches when pitch characteristics match between pitchers with different arsenals. This recommendation would be heavily reliant on a player’s current release angle. To find our best path forward we will continue to dive deep into individual pitch similarity while also adding weight to the biomechanics of release angle. This step will add to pitch design goals and drive a feedback mechanism for better scoring. Despite the difficulty in interpreting arsenal scores, we are excited by the opportunities opened with this project. We believe the quantitative description of similarity gives our program a new edge and will greatly assist player development and decision making.
