Couldn’t decide on the right forum for this. It may just be GQ. It may be debateable, but it doesn’t seem like the stuff of Great Debates.
By Simpson’s Paradox, we know that it’s possible for this to occur:
Batter A is better than Batter B against left-handed pitchers.
Batter A is better than Batter B against right-handed pitchers.
Batter B is better than Batter A against pitchers in general.
So my question is–what are you supposed to do with this information when deciding what batter to use? If it’s a left-handed pitcher, you might think you should send in batter A since A’s better against lefties. But since a left-handed pitcher is also a “pitcher in general,” you might think you should send in batter B, since B is better against pitchers in general.
So is the answer that it’s just indeterminate? Or is there something more that can be said here?
No pitcher is a “pitcher in general”. If you know the handedness of the pitcher they are going to face (as you seem to be stipulating) the decision is straightforward.
But also, what ITR champion said. Either there is something relevant that you are not telling us about how “good” the batters are, or your scenario is not possible.
What ITR champion said. Batter A is better than Batter B. The only reason B looks better is because he’s faced fewer left-handed pitchers. If they had faced the same ratio, B’s batting average would be .270.
That is a plainly false statement. Every pitcher is a “pitcher in general,” since the phrase “pitchers in general” refers to the class of all pitchers.
Did you read the Wikipedia article on Simpson’s paradox?
ETA: I thought I linked it. Here it is. The situation I described is definitely possible, because actual.
I think another right thing to say here is that, in a scenario where Simpson’s Paradox applies, it will be illicit to make generalizations like the ones found in the OP. It may be true that Batter A has outperformed Batter B for a certain sample set etc but that particular sample set will turn out not to support a generalization that Batter A is “better than” Batter B against X-type pitchers.
I swear I thought this thread was going to be about the Simpsons episode Homer at the Bat when Burns pulls Darryl Strawberry for Homer against a lefty.
Burns: You, Strawberry, hit a home run.
Strawberry: Okay, skip.
(hits a home run)
Burns: Ha-ha! I told him to do that.
Smithers: Brilliant strategy sir.
When Burns pinch hits Homer for Strawberry because of the LH/RH pitcher match up at the end of the game.
Burns: “It’s called playing the percentages.”
I actually was reading about the Paradox earlier today before I saw the thread.
So a higher percentage of Southern Democrats (7% and 5%) voted in favor of the law over Southern Republicans (0% and 0%). And a higher percentage of Northern Democrats (94% and 98%) voted in favor of the law over Northern Republicans (85% and 84%). But overall, a higher percentage of Republicans (80% and 82%) voted in favor of the law over Democrats (61% and 69%).