Kurtz wrote:You're basically right. If year 1 every team scores 4 runs, and you score 6, then the standard deviation for that year will be something like 0.1. So the difference in mean (between what ur team produces vs league average) will be 2, which will be 20 standard deviations above the mean.
But year 2 you may have normal binomial distribution of runs, which means that the unit of standard deviation may be 0.5 or more. So even if you again produce 2 runs above the mean, now you're only 4 standard deviations above the mean.
That's the trouble with using such a small sample size (15 AL teams in that year), and why Skin points out that this is a pretty weak argument.
I don't think this is an argument about using Z-scores, but rather how they come up with both the mean and standard deviation to determine the z-scores.
It would be better to determine an 'expected' average run scoring each year through regression analysis.
Then you could adjust all historical year's data to this year's expected run scoring (actual runs scored * this year's expected runs / actual year's expected runs) and use all the data to determine a single z-score for the current year. This accounts for the impact that a higher run scoring environment should produce a higher absolute standard deviation, but gives you a larger data set with which to set your standard deviation and remove the impact of outliers.
Only stats geeks like myself would appreciate the additional effort though.
