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November 19, 2012

Baseball Therapy

Defining Change in Player Performance from Year to Year

by Russell A. Carleton

Quick, which player had the greatest change in on-base percentage from 2011 to 2012? Did you say Houston Astros pitcher Aneury Rodriguez? In 2011, Rodriguez went 0-for-9 with two sac bunts. In 2012, Rodriguez appeared in only one major-league game, but he came to the plate once and got a hit. Rodriguez went from a seasonal OBP of .000 to 1.000. It doesn't get bigger than that.

But then you might have already recoiled at the thought of using sample sizes of nine PA and one PA in any sort of analysis. At those sample sizes, OBP isn't stable enough to mean anything at all. Especially, y'know... one PA. Can we say anything about whether his performance changed? How would we know?

There are several statistical problems that get in the way in these sorts of analyses. It's easy enough to take this year's OBP and subtract last year's and get the difference between the two, but what sort of context should we place around it? For one, there are some statistics which naturally vary more from year to year than do others, but for issues of statistical reliability. If a pitcher's BABIP goes from .250 to .350, that is certainly unfortunate, but there's an understanding that because the stat is so unreliable, huge swings are to be expected. If a hitter's OBP did similarly, this would be a cause for investigation.

Then there's the matter of sample size. We instinctively treat Aneury Rodriguez with caution because of the small sample size. But had the case been that he had jumped from .000 to 1.000 and had 500 PA in both seasons, people would probably skip the PED investigation and just investigate Rodriguez's ties to the dark arts.

Finally, there's a question of cut-offs. What "counts" as enough of a jump (or drop) in OBP to warrant further explanation? Is it a certain number of points? (20 points? 30?) Perhaps a certain percentage change from year to year? And of course, what happens to the guy who adds 19 points? He gets tossed into the "didn't change" bin? Where do these numbers even come from, other than just being pulled out of the air?

There needs to be some sort of sensible framework for identifying players who made changes from year to year. Let's see what I can do. As always, if you just want to see the list, skip the next section, although this week, the whole point is the gory stuff.