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Monday, July 27, 2009
Most people still don’t understand the concept of regression toward the mean…
There is a thread on BTF about Sabathia’s “numbers,” particularly his BB and K rates, being down this year, as compared to last year, although he is still pitching very well of course.
While the quality of the posts on BTF is nowhere near that of this blog (although they beat us easily in quantity), there are some reasonably intelligent regulars on that site (if anyone interprets that as a dig, it is).
Anyway, no one mentions the obvious so far. Any player who posts a better than average number in any category for one year or for 100 years is EXPECTED to do worse in any other time period you look at, even if that player’s true talent never changes. In fact, when we talk about regression toward the mean in a mathematical sense, we are talking about the exact same player - no change in true talent, just another “sample” of his performance. Changes in true talent are another issue altogether.
On top of that, ALL pitchers’ true talent is expected to get worse in every subsequent year, although we don’t exactly know why.
Put those two things together, and you fully expect every pitcher who has been better than average previously to get considerably worse in any subsequent time period.
Now I don’t know if Sabathia’s drop-offs in K and BB rates are exactly what we would have expected, but it couldn’t be that far off.
The thing that people don’t understand (actually one of the things) about regression toward the mean in baseball is that the reason any above or below average player will always regress, on the average, towards average, is that they were not really as good or bad as we thought in the first place, based on any of their stats. That goes for Sabathia, Halladay, Bonds, Chipper Jones, etc., etc. Chipper Jones is not as good as his career stats tell us, even after you do all the appropriate adjustments. Same for Halladay. And Sabathia. And everyone else who has been above average and we think has true talent X. When I say “as we think” I mean as their stats suggest, not as we think based on a credible projection which already does the regression. And of course, there is some chance that any given player is better than his prior stats - it is just that the chances of him being worse is greater than the chances of him being better. That is ALWAYS the case, as long as we properly define the mean for that player.
That is the KEY to understanding regression toward the mean and is what most people don’t understand, even if they think they understand the concept.
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