Broken Wing

How many murderers do you know?

For some reason, on my 5-hour drive home last weekend, I started to wonder if anyone I knew had ever gotten away with murder. Then I figured it wouldn't be that hard to approximate the probability of that being so. So here is what I found out.

First, I had to figure out how many murderers there are. From the Bureau of Justice statistics page, I was able to get the number of murders since 1976. I was also able to find the percentage of homicides cleared by arrest. From these two pieces of information I can figure out how many unsolved murders there are since 1976 - about 160,000.

Now, number of murders is not the same as number of murderers. Some murderers are responsible for multiple deaths (Jeffrey Dahmer - 16, George W. Bush - >100,000). But since the bureau of justice statistics claim that there are fewer homicides with multiple victims than there are homicides with multiple offenders, I think it is reasonable to assume one uncaptured murderer for every unsolved murder. So, that leaves us with 160,000. (Note: I may be thinking of that statistic wrong - it is possible that the BoJ considers a homicide with multiple victims one in which several people are killed at once, like a terrorist explosion, as opposed to a serial killer, who commits multiple homicides with one victim each time. In addition, I'm not really sure what it means for a homicide to have multiple offenders. It's possible that many cases involve more than one person, but only one of those people does the actual killing, and the other is charged with some "conspiracy to commit murder" type crime. Anyways, I'm only interested in people who have actually killed.)

Now that we have an (admittedly rough) estimate of the number of killers on the loose, we need to find out the probability that I know one of them. Given a U.S. population of around 272 million (2002 estimate), and 160,000 uncaught murderers, then the odds that any particular US citizen is a killer on the loose are quite low at 0.000591499868387572.

The easiest way to do the desired calculation is to figure out the probability that none of your acquaintences are killers, and then subtract that value from one to figure out the probability that one or more of your acquaintences are murderers. To that end, the probability that someone isn't a killer is 0.999408500131612. But the odds that neither of two people you know are killers is (0.999408500131612 * 0.999408500131612 = 0.998817350135319). Slightly lower now, isn't it? For each person you know, you multiply this new number by the odds that the new person isn't a killer, so that the number we want is (1 - (0.999408500131612^N)), where "^" is "to the power" and N is the number of people you know. Now the important question: how many people do you know? If you only know 50 people, there is only a 3% chance that you know a killer. But you probably know many more than that, you charismatic devil, you. If you know 500 people, then there is about a 25% chance that you know a murderer. And to get to better than even odds (> 50%) of knowing a killer, your social circle would need to include 1172 people. And if you know 5000 people, then it is a virtual certainty (94%) that you know a killer. 5000 certainly seems like a lot, but remember, Wilt Chamberlain claims he had sex with 20,000 women! According to my numbers, there were probably a few murderers just in the group of people that Wilt the Stilt "knew" in the biblical sense.

Now, I know that there are a lot of rough edges in this analysis, but if you can think of any good reasons why this is complete bullshit, please let me know in the comments section.

Here is my spreadsheet file in Excel and Gnumeric file formats. Posted by mill1991 at May 26, 2005 10:40 AM | TrackBack