# Simpson's Paradox--so what are you supposed to \_do\_?
**URL:** https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572
**Category:** The Game Room
**Created:** [November 22, 2013, 10:48pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572 "2013-11-22T22:48:42Z")
**Posts on this page:** 19
**Page:** 1
### Author:  [@Frylock](https://boards.straightdope.com/u/Frylock)
#### Post date: [November 22, 2013, 10:48pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/1 "2013-11-22T22:48:42Z")
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?
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### Author:  [@ITR\_champion](https://boards.straightdope.com/u/ITR_champion)
#### Post date: [November 22, 2013, 11:00pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/2 "2013-11-22T23:00:03Z")
> [@Frylock](#):
>
> 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.
Only in strange circumstances. Specifically, if they face different numbers of left-handed and right-handed pitchers.
Imagine the following:
A bats .200 against lefties and .400 against righties. He’s faced lefties 100 times and righties 100 times. Total batting average: .300
B bats .150 against lefties and .390 against righties. He’s faced lefties 20 times and righties 180 times. Total batting average: .365
But if A and B face exactly the same pitchers, then the scenario you described is not possible.
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### Author:  [@njtt](https://boards.straightdope.com/u/njtt)
#### Post date: [November 22, 2013, 11:13pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/3 "2013-11-22T23:13:08Z")
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.
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### Author:  [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)
#### Post date: [November 22, 2013, 11:59pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/4 "2013-11-22T23:59:51Z")
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.
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### Author:  [@Frylock](https://boards.straightdope.com/u/Frylock)
#### Post date: [November 23, 2013, 1:12am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/5 "2013-11-23T01:12:24Z")
> [@njtt](#):
>
> No pitcher is a “pitcher in general”.
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.
> [@](#):
>
> 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.
Did you read the Wikipedia article on Simpson’s paradox?
ETA: I thought I linked it. [Here it is](http://en.wikipedia.org/wiki/Simpson's_paradox). The situation I described is definitely possible, because actual.
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### Author:  [@Frylock](https://boards.straightdope.com/u/Frylock)
#### Post date: [November 23, 2013, 1:15am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/6 "2013-11-23T01:15:44Z")
> [@Little\_Nemo](#):
>
> 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.
Makes sense. I think the answer to the question of the OP is, “it depends on the specific numbers.”
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### Author:  [@Frylock](https://boards.straightdope.com/u/Frylock)
#### Post date: [November 23, 2013, 1:21am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/7 "2013-11-23T01:21:28Z")
> [@Frylock](#):
>
> because actual.
Scratch that last bit.
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### Author:  [@Frylock](https://boards.straightdope.com/u/Frylock)
#### Post date: [November 23, 2013, 1:25am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/8 "2013-11-23T01:25:06Z")
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.
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### Author:  [@Strinka](https://boards.straightdope.com/u/Strinka)
#### Post date: [November 23, 2013, 3:36am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/9 "2013-11-23T03:36:37Z")
Here’s an 8-page paper written by Judea Pearl about how Simpson’s Paradox occurs, and how to resolve it.
> **[r414.pdf](https://ftp.cs.ucla.edu/pub/stat_ser/r414.pdf)**
>
> 1109.52 KB
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### Author:  [@Ellen\_Cherry](https://boards.straightdope.com/u/Ellen_Cherry)
#### Post date: [November 23, 2013, 3:53am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/10 "2013-11-23T03:53:36Z")
Pitching over to Game Room, from IMHO.
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### Author:  [@Frylock](https://boards.straightdope.com/u/Frylock)
#### Post date: [November 23, 2013, 2:23pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/11 "2013-11-23T14:23:18Z")
> [@Strinka](#):
>
> Here’s an 8-page paper written by Judea Pearl about how Simpson’s Paradox occurs, and how to resolve it.
>
> [http://ftp.cs.ucla.edu/pub/stat\_ser/r414.pdf](http://ftp.cs.ucla.edu/pub/stat_ser/r414.pdf)
That’s exactly what I was looking for, thanks!
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### Author:  [@Ike\_Witt](https://boards.straightdope.com/u/Ike_Witt)
#### Post date: [November 23, 2013, 7:38pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/12 "2013-11-23T19:38:14Z")
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.
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### Author:  [@crypto](https://boards.straightdope.com/u/crypto)
#### Post date: [November 23, 2013, 9:41pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/13 "2013-11-23T21:41:39Z")
> [@Ike\_Witt](#):
>
> 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.
Ha!
Even stranger, I thought it was going to be about this goofy game on my iPad I’ve started to okay called Tapped Out.
I am embarrassed. D’oh! :smack:
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### Author:  [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)
#### Post date: [November 24, 2013, 1:31am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/14 "2013-11-24T01:31:16Z")
I’ve read the whole thread and haven’t seen any mention of Julius Hibbert or Nick Riviera.
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### Author:  [@dasmoocher](https://boards.straightdope.com/u/dasmoocher)
#### Post date: [November 25, 2013, 5:39am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/15 "2013-11-25T05:39:47Z")
> [@Ike\_Witt](#):
>
> 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.
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### Author:  [@BigT](https://boards.straightdope.com/u/BigT)
#### Post date: [November 25, 2013, 5:42am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/16 "2013-11-25T05:42:33Z")
> [@Frylock](#):
>
> That’s exactly what I was looking for, thanks!
Unfortunately, my brain’s a bit fried by symbolic logic. Could you relate the answer given in that paper to your specific example?
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### Author:  [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)
#### Post date: [November 25, 2013, 6:02pm UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/17 "2013-11-25T18:02:27Z")
BobLibDem presents a real world example of this paradox in another [thread](http://boards.straightdope.com/sdmb/showthread.php?t=708469).
When the Civil Rights Act of 1964 was put up to a vote, these were the results:
## House: Democrats: 152-96 (61-39%) Republicans: 138-34 (80-20%)
Southern Democrats: 7–87 (7–93%)
Southern Republicans: 0–10 (0–100%)
Northern Democrats: 145–9 (94–6%)
Northern Republicans: 138–24 (85–15%)
## Senate: Democrats: 46-21 (69-31%) Republicans: 27-6 (82-18%)
Southern Democrats: 1–20 (5–95%)
Southern Republicans: 0–1 (0–100%)
Northern Democrats: 45–1 (98–2%)
Northern Republicans: 27–5 (84–16%)
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%).
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### Author:  [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)
#### Post date: [November 26, 2013, 3:51am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/18 "2013-11-26T03:51:30Z")
The best known example is the [Berkeley gender bias case](http://en.wikipedia.org/wiki/Simpson's_paradox#Berkeley_gender_bias_case).
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### Author:  [@dasmoocher](https://boards.straightdope.com/u/dasmoocher)
#### Post date: [November 28, 2013, 1:07am UTC](https://boards.straightdope.com/t/simpsons-paradox-so-what-are-you-supposed-to-_do_/674572/19 "2013-11-28T01:07:29Z")
This blog post was recommended by a stats prof in a course I took. Heavy on equations.
[SIMPSON’S PARADOX EXPLAINED](http://normaldeviate.wordpress.com/2013/06/20/simpsons-paradox-explained/)