The “Texas sharpshooter” fallacy

This is a common misuse of statistical information illustrated by a gunslinger taking a quick shot at the side of a barn. He then draws a bullseye target round the bullet hole and claims to be a sharpshooter. If the target had been drawn before he fired the shot then random factors would be extremely unlikely to result in a bullseye hit. However by drawing the target afterwards, he has turned a highly improbable event into a near certainty. All he has to do is hit the barn.

Comparison table, Texas sharpshooter and the Shirley McKie fingerprint match.

The Texas sharpshooter paints the bullseye around the bullet hole AFTER firing the shot.	The prosecuting authorities develop a theory (that Shirley McKie was in the murder house) AFTER a fingerprint match is found.
The Texas sharpshooter offers only two explanations for the target hit. Either he is indeed a sharpshooter (he hit the target due to his skill) or a near impossible coincidence has happened (he is not skilful and the bullet hit the target by chance).	Fingerprint experts offer only two explanations for print Y7. Either the print is McKie’s or a near impossible coincidence has happened (despite many points of similarity the apparent fingerprint match is by chance).
The Texas sharpshooter thinks that a significant non-random event has occurred (he hit the bullseye using skill). In fact a non-significant random event happened (he hit the barn somewhere).	The jury in the perjury trial is led to believe that a significant non-random event has occurred (Shirley McKie made fingerprint Y7). But perhaps a non-significant random event happened (somewhere in the world at some point in time there was a large number of similarities between two fingerprints).

If only one suspect was in the area of a murder at the time, and there is one fingerprint on the murder weapon then the target is painted before firing the shot. “If the fingerprints match then we will have found the culprit”

In a traditional criminal investigation there will be a number of suspects and a number of fingerprints. The target is still painted before firing the shot. “If any of the crime scene fingerprints match any of the suspects then we will have found the culprit”. This is a wider target than the first case so it will be a little easier to hit it by chance, rather than skill. Hitting by chance represents an erroneous match due to random factors (bad luck) rather than a match with the real culprit.

Almost any fingerprint test carried out in Scotland could have led to a McKie type accusation. But why limit ourselves to Scotland? A McKie type inquiry could have happened in Amsterdam in 1990 or could happen in Los Angeles in 2020 - as long as the authorities are prepared to pursue a disputed fingerprint all the way to a perjury trial, and the accused maintains innocence. We have not painted any target before we shoot so we cannot use the normal low probability of error as the proof of guilt.

Stephen Horn

26 June 2006