Playing the odds

In the Frontpage article on a series of terrible murders, the author, Stephen Webster of the racist American Renaissance, says this:

    Of one thing we can be certain: If whites had done something this horrible to blacks, it would be universally assumed the crime was motivated by racial hatred. From the outset, police and prosecutors would have investigated the friends, habits, reading matter, and life history of each defendant. If either had ever uttered the word "nigger," had a drink with a Klansman, or owned a copy of American Renaissance, this would be discovered and brandished as proof of racial hatred. In the Carr case, there appears to have been no investigation at all. Instead of searching for possible racial animus, the authorities have simply declared there was none.

Gee, y'know, this sure sounds reasonable, doesn't it? I mean, if a man kills eight black people, I know I'd go looking for racist motives. So if a man kills eight white people, shouldn't I do the same?

This is a great parlor game. We call it "false equivalence," and we'll show you how to refute it in the comfort of your own home.

Let's pretend that you've been given Ed McMahon's job with Publisher's Clearinghouse. However, due to recent market downturns, several positions have been consolidated, so that you not only deliver the check, but you also will randomly select eight winners. Also, the sweepstakes is limited to the environs of Wichita, Kansas, to save on advertising and media costs.

After a few weeks of junk mail, unsolicited phone calls, and door-to-door salesmanship (oh, yeah, we didn't tell you that you had to sell the magazines as well, did we?), you've distributed contest forms to all 545,220 residents. In addition, 42,060 have bought magazine subscriptions from you, even though you assured them that buying a subscription doesn't change the odds of their winning.

The big day comes, and the entire populace turns out to see who wins. Reaching into a giant wire tumbler, you pick out the first name ...

Okay, let's review. There are 545,220 people in the sweepstakes. 42,060 bought magazine subscriptions; that's 7.7% of the population. Roughly speaking, the odds are 1:13 that anyone you randomly select will have subscribed to a magazine (actually 1:12.96, if you're following along with a calculator, but close enough for demonstrative purposes. We're also going to ignore the fact that one person leaves the potential-winner population, since they can't win twice, but the skew is miniscule).

So you draw out the first name, and it turns out to be a woman who ordered 12 months of Martha Stewart's Prison Living. You give her a brand new KitchenAid and a gift certificate to TGI Friday's, and everyone applauds. At this point, as we mentioned, the odds are 1:13 that you would have selected 1 subscriber.

Moving on, you draw the next name, who is a man who bought not only Details, but Maxim, Playboy, and The American Prospect. Now, the chance of drawing another subscriber is still 1:13, but the odds of drawing a subscriber twice in a row are (1:13 * 1:13) 1:169. Much less likely, but luckily all the statisticians moved out of Kansas after creationism became an academic subject, so no one's done the math yet.

Next name, same game. Probability: (1:13 * 1:13 * 1:13) 1:2197. The natives are getting restless.

And so it goes, through all eight names. When the last name is called, you're sweating, because even the dullest person in the crowd has figured out that someone fixed the game. Maybe ... even ... you.

Final probability that eight randomly chosen names would all be subscribers (1:13 * 1:13 * 1:13 * 1:13 * 1:13 * 1:13 * 1:13 * 1:13) = 1:815730721. You can't even represent that as a percentage without using scientific notation (1.25423789814898e-07 %, in case you were wondering).

You won't be surprised to find out that the black population of Wichita was 42,060 in the 2000 census. Thus, if a serial killer were to randomly choose eight victims, and all were black, then the chances of him not deliberately choosing them by race or some other race-correlated criteria (for example, a mugger might choose primarily white victims because he believes that whites will, as a class, have more money on them then blacks) is infintesimal.

Now, in this case, there were actually three attacks involving eight people, so the probabilities would be 1:2197, as mentioned above. So, if all the victims were black, and assuming that any group of people will be ethnically homogenous, then if the killer selected completely randomly he would have a 0.045% chance of getting all black victims.

If we reverse the victims' ethnicities, the chance of randomly choosing a non-black victim from the population is a bit over 92%, which means that the chance of choosing eight random white victims is 54%, give or take. Given the three-choice assumption made above, there would be an 83% chance that a completely random selection would result in all white victims.

Police use these sorts of odds all the time to determine what kinds of patterns exist in criminal behavior. Since they have limited time and resources, it's not fruitful to look for a racial motive in the absence of any evidence* when totally random selection offers an 83% chance of the racial composition of the victims.

Horowitz has always been incautious when it comes to his allies, freely choosing from the most extreme fringes as well as from more mainstream venues. But his new associates, who deplore the "restrained coverage" of media outlets like The Wichita Eagle while speaking highly of such Internet sites as NewNation.org ("For a white minority in a colored world") and JeffsArchives.com ("Reporting on the Jewish war against Gentiles and the resulting destruction of White Western civilization") are further beyond the pale than any with whom he's dealt. The results of such a devil's deal will be dismal indeed.