Texas Sharpshooter Fallacy

The image is old. A story about the Dubno Maggid, a rabbi and storyteller who died in 1804, used an arrow version of the same idea. In 1866, the logician John Venn described a related version in The Logic of Chance: a man who chalked a target around a bullet hole already in a barn door and then claimed to have hit the mark on purpose. Venn used it to argue that people judge many real-world patterns the same way — after the fact.

The specifically Texan version of the joke first appears in the statistical literature in a 1977 paper by Seymour Grufferman. There is no clear link to the actual 1st Texas Sharpshooter Battalion from the Civil War; the Texas framing more likely trades on a general stereotype of Texans as tellers of tall, boastful tales. The term reached a much wider audience in 1999, when physician and writer Atul Gawande used it in his New Yorker article "The Cancer-Cluster Myth," applying it specifically to how disease-cluster scares are often investigated.

They are close relatives, not identical. The Texas sharpshooter fallacy is the broad rhetorical move of drawing a conclusion around data found after the fact. The "clustering illusion" is the narrower perceptual tendency to see meaningful clumps in truly random sequences — the thing that makes a cluster look surprising in the first place. "Data dredging," "p-hacking," and "HARKing" (hypothesis after results are known) are the more technical, statistics-specific versions of the same error: running many tests or models until one clears a significance threshold, then reporting that one as if it had been the planned test all along.

Daniel Kahneman and Amos Tversky described a related tendency they called belief in the "law of small numbers" — expecting a small sample to look as orderly as a huge one, so that an ordinary run of luck reads as a signal. Separately, Thomas Gilovich, Robert Vallone, and Amos Tversky's 1985 study of the "hot hand" in basketball found that streak shooters showed no more consecutive hits or misses than a random sequence would predict — the streaks people saw and bet on were well within the range chance alone produces.

With a conventional 5% significance threshold, testing 20 independent comparisons makes at least one false positive likely even if nothing real is happening in any of them — that is simple multiplication, not a special property of any one dataset. Raymond Neutra's calculation, reported by Gawande, shows the same logic at a larger scale: thousands of census tracts, each watched for dozens of cancer types, will reliably produce thousands of "statistically significant" but random elevations somewhere.

Gawande's article points to genuine clusters that were traced to real causes — Legionnaires' disease, Haff disease, and DES (diethylstilbestrol) among them — and to occupational cases like Percivall Pott's 1775 finding that chimney sweeps suffered unusually high rates of scrotal cancer from soot exposure. The common thread in confirmed cases is a plausible mechanism and a very large effect size, such as the roughly sevenfold-thousand excess mesothelioma rate found in Karain, Turkey, linked to erionite mineral fibers. Minnesota's health department, by contrast, investigated more than a thousand reported clusters over several years and found the exercise largely unproductive — most were statistical noise.

No — the underlying math shows up anywhere many comparisons are possible: drug trials that report an effect only in a subgroup discovered after the fact, trading strategies tuned against historical price data until one looks profitable, and even wartime pattern-spotting. A frequently cited example is statistician William Feller's analysis of V-1 and V-2 rocket strikes on London during the Second World War: residents were convinced the strike pattern showed non-random targeting, but the distribution matched what a random (Poisson) process would produce.