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Friday, December 29, 2006
Pitch Sequences
Fantastic article by Sal Baxamusa. One of the little things I’ve done, which I’ve set aside for… I don’t know why… was to extend my Markov chains to counts. I could, in effect, tell you how many pitches Christy Mathewson threw, with just a few reasonable assumptions.
Sal however is making me think that one of my assumptions may not be reasonable. He says:
When the first pitch is a ball and the second pitch a strike (called, swinging, or foul), batters have a line of .243/.312/.378. Curiously, batters perform better when the all-important first pitch is a strike and the second pitch is a ball; they hit at a .257/.314/.402. That’s a 25-point difference in OPS; not world-breaking but statistically significant (p<0.001 for you stat wonks) nevertheless.
I’ve always wondered if the path to a particular state (1-1, 3-2, etc) matters. That is, is 1-1 itself a state, or do I now have to say the state was “0-1 to 1-1”, and “1-0 to 1-1”. What I would consider one state for Markov chain purposes is actually better described as two states. The interesting work is to see how far back the states need to go. That is, if you have a 3-2 state, how far back in the count do you have to go, in order to establish the state you are in.
Most pitch data research should be recognized and applauded, and this article, as well as all of the Appelman articles, fits the bill.
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