No. 29 Statistical Fallacies
Texas Sharpshooter
In Turkish: Teksaslı Keskin Nişancı Safsatası
You fired first, then drew the target around the holes.
Look, three holes together! I’m a sharpshooter!
You drew the ring after the holes, Dursun. What about the other ten?
Temel does the same: it happens first, then “I told you so”.
What is it?
Picking out the data points that happen to fall close together from a random scatter and treating them as if they’d been aimed at all along. Things that cluster by chance tell you nothing but that they clustered.
The pattern
- There’s a lot of data, most of it random.
- Pick out the few points that fit each other.
- “Look, a pattern!”
Why it fails
With enough data, chance clusters are unavoidable; fire a hundred shots and some will land side by side. The brain sees the cluster, not the randomness. A dream and a number, a birthday and a lottery, an illness and a street: something always “fits” in hindsight. A target drawn before the shooting means something; one drawn after is just a circle.
How to spot it
- The pattern was found after the data came in; it wasn’t predicted.
- The data that don’t fit were quietly left out.
- The sentence “this can’t be a coincidence”; with enough tries, it can.
What to say
“Did you predict this pattern before seeing the data?” If not, the target was drawn afterwards. Then ask about the leftovers: “How many don’t fit?” A real pattern holds in new data; ask for that: “Predict the next one.”
When it’s not a fallacy
Noticing clusters in data is where science starts; the fallacy isn’t noticing the cluster, it’s counting it as proof. A cluster produces a hypothesis; the hypothesis gets tested on new data. If you hit a target drawn in advance, you’re a sharpshooter.
Examples
- Health“Three people on this street got the same illness, something’s going on.” Out of a thousand streets, one is expected to look like this.
- Work“In the three months sales rose, we’d held the Tuesday meeting.” We held it in the falling months too; nobody looked at those.
- Social media“Collect celebrities’ death dates, they all divide by seven.” Collect enough dates and everything divides by something.
- Football“We win the matches where we wear the maroon kit.” The maroon-kit losses weren’t counted.