## Color Me Skeptical

I am mulling over the following, which I posted as a comment here.

I have a question about Iowahawk’s analysis. In his follow-up post he describes Simpson’s paradox…:

“Hitter B has a higher batting average against both righties and lefties, but Hitter A has a higher overall average by dint of facing a different mix of pitchers. Now comes the question: it’s the bottom of the 9th, two out, and you need a base hit. Who would you insert as a pinch hitter, A or B? The detailed data suggests Hitter B, irrespective of whether the pitcher was right- or left-handed. The overall average, in this context, is worse than meaningless – it leads you to exactly the wrong conclusion.”

If this is legit analysis, it opens a can of worms, I think. Suppose that instead of handedness, we had pitchers with and without some “X Factor.” Suppose we didn’t even know what the X Factor is. Suppose we didn’t even know what the proportion of pitchers in the league have the X Factor. But suppose some third party did know, and simply provided us with a breakdown of our two hitters’ averages against the two types of pitchers, and they formed a Simpson’s paradox. Would it still be “wrong” to put in hitter A? Is it better to put in B, because he is better at hitting against both X and not-X pitchers? Color me skeptical.