LETTER:Law of large numbers says it all
October 22, 2002
In the wake of the sniper in Maryland, people are turning toward science for an answer to the problem. While ballistics are an excellent tool, there is a law of large numbers that comes into play when one tries to compare one bullet to the 200 million legally owned guns in the US.
For example; let’s say ballistics testing is 99.9% accurate. There are 13,000 homicides committed using guns in the US per year. We’ll assume for generosity that every homicide was committed by a unique gun. We’ll also assume that every gun in existence that is legally owned is registered, properly documented and tested, and no illegally owned or unregistered guns are ever used to commit murder. That means 12,987 guns that were actually used to commit a homicide will be flagged as such, and 199,987 guns will be incorrectly flagged as being used to commit a homicide.
So, what is the probability that any given gun flagged as being used to commit a homocide actually did? About 6.1%. Which means if you drag people in who are flagged as owning a “homicidal gun,” and want to have a 90% chance of actually questioning the right person you’ll have to drag in 37 people per homicide (ignoring multiple matches to the same person).
Multiply that by the 13,000 homicides per year, and you’ll question 481,000 people.
Now, how practical is this? Remember, you still don’t know who did it — only that odds are that you’ve questioned them. Could it generate leads? Yes. So could Ms. Cleo. Companies that make top-end ballistics equipment agree that the technology has not been developed to make a ballistics database useful. According to them, equipment on both ends of the testing must be at least 100 times more accurate (99.999%) before the numbers get reasonable.
David Klipec
Senior
Computer Engineering