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Thursday, August 06, 2009
More regression from Colin
Some very lovely work.
I’m going to be picky here, because it’s important to make the huge distinction between the uncertainty around the true talent level, and the spread in observed performance centered around that true talent level.
For example, Colin says this:
In the case of Pujols, we would estimate his OBP going forward as .424, with an uncertainty (expressed in standard deviation) of .006. In other words, about 68 percent of the time, Pujols’ OBP should be between .418 and .430.
The uncertainty that Colin suggests is the uncertainty of his true talent level. That is, he’s got Pujols pegged as a true .424 OBP hitter, with one sigma of .006. So, he’s 68% certain that it’s between .418 and .430. It’s not 68% of the time.
Indeed, in order to say something like “68% of the time”, you have to know what the “time” is. Is it 100PA, 1000 PA, or 10000 PA? If you have a true .424 hitter, he will PERFORM at .419 to .429 68% of the time if given 10000 PA. If you only give him 100 PA, then the 68% range is +/- .049 points.
However, we don’t know if Pujols is a true .424 hitter. We estimate he is a true .424, with a certain amount of uncertainty. Colin has that pegged at .006 for Pujols. So, the observed range of Pujols will be a bit bigger than .419 to .429, because we aren’t sure he’s a true .424 to begin with.
As for Colin’s league average hitter having an OBP of .356, that can only be true in a certain era, or if he only considers regular players. Since Pujols is a decidely regular player, then that mean is the population he is bring drawm from. It’s not the “league” as in everyone in MLB, including pitchers and callups. Pujols’ population is made up of whoever most closely resembles his actual population WITHOUT looking at his performance numbers. (The problem is that for some players, their performance numbers do drive their playing time, as opposed to their scouting driving their playing time. I have no idea what category Francoeur falls into.)
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