Definition
The Texas sharpshooter fallacy is a thinking trap where you go looking, after the fact, for a rule or cause in random data that happens to be clumped together. It happens when you pick out a few good-looking results from a huge scatter that has no intent or rule behind it, and give them special meaning.
The fake marksman who paints the target afterward
Picture the wooden wall of a country barn, shot up at random. Hundreds of bullets are stuck in the wall every which way, but in one spot three or four holes sit close together and catch your eye.
Now a shooter walks up, paints a red target around that cluster of holes, and brags, "I hit the bullseye every single time!" You'd call him a fraud, right? He didn't pick a goal first and then shoot. He just laid a target over the spot where the results happened to clump.
In daily life, we often fall into the same trap as this fake sharpshooter. From a huge scatter of information, we pick out a few clues we like, say "See, I knew I was right," and paint our own target after the fact.
Random data still makes accidental clumps
If you flip a coin 100 times, heads and tails won't take neat turns. Even with no tricks at all, it's very common to get a streak of 5 or 6 heads in a row. In pure chance, specific data bunching up in one place is a perfectly natural property of probability.
But the human brain dislikes meaningless chaos. It has an instinct to find order and rules no matter what. That's how people connected randomly scattered stars into constellations and attached plausible myths to them.
The same illusion shows up in modern data analysis. Compare thousands of machine logs against environmental conditions without a plan, and pure coincidence will produce a fake clump, such as "parts broke down more often on certain days of the week." Firmly believing that this is the real cause of a machine defect is exactly the sharpshooter fallacy.
To be more precise: the hypothesis has to come first
For science and sound data analysis to work, you have to follow a strict order, like a detective. Just as you must hang the target on the wall first before you can test your shooting, you must declare the hypothesis you want to test before you collect the data.
Suppose you look through a huge pile of data that has already been collected and happen to spot an interesting pattern. That's not a proven fact. It's only a "candidate for a new hypothesis." To show the pattern isn't mere chance, you need to run the experiment again, using other data collected independently under entirely new conditions.
In the big-data era, when information is everywhere, bizarre coincidences are seen far more often. The most important thing is to resist the temptation to move the target to fit the conclusion you want to believe, and to look at the wider context of the whole dataset.
Common misconceptions
If you spot a striking pattern in the data, it must be a meaningful cause-and-effect link.
Even purely random data can form convincing-looking clumps by chance. Until you set a hypothesis in advance and confirm it with new data, you may just be mistaking coincidence for a pattern.
Where you meet it
Out of many cities, one neighborhood happens to get a burst of lightning strikes in a certain year, and someone declares that a special magnetic field flows through the area.
Someone picks words out of a huge prophecy text that match historical events which have already happened, strings them together, and claims it was an amazingly accurate prediction.
In one sentence
Don't give meaning after the fact to results that happened to clump together. Set a hypothesis first, then test the whole dataset fairly.