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Thursday, July 12, 2007
Median ERA?
There was a discussion on Baseball Fever about using median ERA, because one bad game can really kill you in ERA. I wrote the following:
The ERA “problem” is that it doesn’t (can’t) follow a normal distribution. It’s bound by 0 on one side and infinity on the other.
OBP however doesn’t have that problem, and neither does winning %. I think converting ERA up to winning percentage (runs to wins) or down to OBP (runs to base/outs) is a sensible approach.
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I just did a little test, where I took games, with an OBP of .135 to .535 (player mean of .335, uniform distribution, league mean also .335).
While the league mean of runs allowed per 9IP is 5.00, this pitcher had an RA of 5.66. However, when I converted it to win% instead, I got a win % of .498.
Essentially, what I did was construct an average pitcher; and his OBP and win% both gave me an average pitcher, but his runs allowed was 13% higher than the league average.
Therefore, you *cannot* look at the runs allowed figure, precisely because of the skew issue. Of course, when you look at it over a period of years, all the pitchers should have the same skew, and therefore, balance out that this is not an issue. On a seasonal basis? Definitely a problem.
You’re correct in pointing out the problem with bounds. It is possible to correct for this in a theoretical sense.
http://www.hardballtimes.com/main/article/moving-beyond-era/
http://www.hardballtimes.com/main/article/more-on-mera/
However, it is not possible to correct for this on a seasonal basis because most pitchers only start 20-30 games and therefore rarely follow the theoretical distribution (on an individual basis). If one were interested detailed accounting, using individual game results would be better, in which case it is *better* if a pitcher is inconsistent rather than consistent.
http://www.hardballtimes.com/main/article/same-old-same-old/
http://www.hardballtimes.com/main/article/are-foolish-conistencies-the-hobgoblins-of-starting-pitchers/
Now, having said all that, it’s only a value judgement since we don’t know if there is a skill in the way a pitcher distributes his performances. Anecdotally, I believe the answer to be “no”, but I haven’t done a rigorous study.