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February 17, 2014

Baseball Therapy

Looking for Meaning Amid the Small-Sample Flukes

by Russell A. Carleton


Last week, we discussed a new method for looking at how players change within a season. Baseball stats are normally denominated in years, but the problem with yearly stats is that they obscure any growth and development—or regression—that might have taken place. Six months is a long time. Players can change. This week, I want to look at how we might use that method to teach us something about the growth of individual players.

I’ve been focusing my attention on one specific decision that a hitter makes, the decision of whether or not to swing at a pitch. It’s a decision that the batter gets to make every time the ball is thrown his way, so we have a large number of data points to work with.

Warning! Gory Mathematical Details Ahead!
First off, if you haven’t read last week’s piece, you’ll need it to understand what’s going on here. The basic idea is that for some hitters, we can see evidence that their recent swing rate over their last certain number of pitches is a better predictor of what they’re about to do than is their seasonal average. I take that as evidence that within the season, something is changing. The nice thing is that we can track those changes.

I looked only at the 2013 season to see which players had a swing rate that could be best described, from pitch to pitch, by some sort of moving average. Out of 258 qualifying players—min. 250 PA and 1200 pitches faced—146 (64.4 percent) fell into this category. For some of them, the best moving average was the swing rate from the last 100 pitches. For others, 500. I tested everything from 50 to 1000 by 50s and let a regression pick the best fit for each player.

For each player in that 64.4 percent, I ran a logistic regression (and by that, I mean 146 separate logistic regressions) predicting the chances that each plate appearance they had would end in an on-base event (walk, HBP, or hit). I keyed the moving average to reflect what it was during the first pitch of the plate appearance. This told me whether there were players who had better (or worse) OBP results when they swung more. There were 17 players who had a significant association between in-season swing rate and their chances of getting on base.

Let me show you a few case studies and how we might use their examples.

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<< Previous Article
Baseball Prospectus Ne... (02/17)
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