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Visualizing Pitch Transitions

Pitch transition diagrams show how often one pitch type is followed by another (e.g., a fastball by a slider). Diagrams for Clayton Kershaw and Yu Darvish show how two artists sequence their pitch types.

Matt Kartozian-USA TODAY Sports

It seems to me that pitch sequencing should be a big thing.  If a hitter has a good idea of what’s coming next (or can rule out an option), he ought to be better prepared to make contact—right?  Robert Arthur has a really innovative approach to quantifying these effects by adapting the concept of entropy.  I highly recommend his work.  Read also Max Weinstein’s well-researched work on fastball mixing.

Before I wade too deeply into a topic I like to step back and figure out a way to visualize the data so I can figure out what it might be trying to say.  So that’s the purpose of this article, to take a look at how to visualize pitch selection.  I’m going to keep the data set consistent with Robert’s early 2014 work (2012 and 2013) and look at two of the pitchers Robert discussed at some length, Clayton Kershaw (a "power pitcher") and Yu Darvish (a "slower ace").

A chord diagram is a great tool for looking at the frequency of transitions between discrete states.  The first diagram shows Clayton Kershaw’s pitch transitions from 2012 and 2013.  Besides being an interesting pitcher, Kershaw is a great visualization example for a few reasons:

  • He’s shown a tendency to have low pitch type entropy (as found by Robert) which is similar to being "streaky" (as found by Max)
  • He throws four pitches, each with a fairly high "usage"
  • PITCHf/x tends to auto-classify his pitches correctly (e.g., the same as Brook’s pitch usage)

The labels in the html should help guide you through the diagram.  In summary, the width of each chord end is significant and shows how often a pitch type was followed by the next pitch type (or PA result).  It’s neat to see that Clayton almost never follows a slider with a change (I suppose that makes sense).  Kershaw starts off most plate appearances with a fastball (~80 percent).  If the previous batter reaches base, there’s about a five percent increase in likelihood that the next batter will see a fourseam first (~85 percent).  Similarly, if the previous batter strikes out, there’s about a five percent decrease in the likelihood that the next batter will see a fourseam fastball first (~75 percent).  I know there’s more to be mined from this data set.  What do you see?

Remember how many pitches Yu Darvish throws?  Fourseam, sinker, cutter, slider, curve, slow curve, change, and splitter.  Yup, he throws them all.  PITCHf/x auto-classification gets boogered on Darvish’s pitches.  I had to separate his curve from his slider.  I’m not totally sure I split his change and splitter correctly.  All the pitch totals are close to how Brooks has them classified.

Got that? Put yourself in the batters shoes—try to narrow down what’s coming next based on what you just saw.

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The chord diagrams are built on the D3 javascript library, read all about it here.  This implementation is derived from Steven Hall’s examples and uses underscore.js.  I used ColorBrewer to assist with the palette. Thanks also to my buddy Rob H.

Jonathan Luman is a system engineer with a background in aerospace. You can contact him at or follow him on twitter @LumanJonathan.