The Friday Fillip: Curious Stability

I usually try for a light, not to say fluffy, topic and tone for these fillips. But today the topic, at least, will be rather more sombre; I’ll keep the tone as light as the subject will allow. Two subjects, really — and two I know very little about: statistics and murder. I’m appealing for help in understanding the former, or at least what I think is an odd feature.

A sad item in yesterday’s Globe and Mail informed us of a deadly shooting in Toronto. What struck me, and not for the first time, was the curious stability in the murder rate: this recent homicide is number 26 in 2012 — which is the same number Toronto had suffered at this time last year.

(Let’s clear some irrelevant stuff out of the way first: sad and bad as these killings are, there are fewer of them in Toronto than there are in most other Canadian cities and, measured by murder rates alone, big cities are safer than small cities.)

My interest here is in the relative stability of murder rates. Now, I recognize that the fact that there were exactly 26 murders at this point in both 2011 and 2012 is something of a fluke; the tallies might have been apart by 2, 3, 6 – but probably not 10. And some of any large variation would have disappeared by year end. But let’s take the focus off one location and look at the country as a whole. Here are the statistics for homicides in Canada for five recent years, courtesy of Statistics Canada:

Let me expand a little on why I find these statistics remarkable. Murder is a very “low probability” event, which is to say that there are relatively few homicides compared to the myriad other events of social significance we might pay attention to. It’s almost (but not quite) of the same order of magnitude as injuries due to lightning strikes. And that’s perhaps an appropriate comparison to help explain my puzzlement. Lightning strikes are natural phenomena resulting from the operation of a (hugely complex) physical system; some regularity might be expected in such a case, as physical systems tend to be resistant to change. But murder is the result of the acts of individuals, each of whom will have individual motivations; some kill out of revenge, some out of rage (which in turn will have different causes), some out of cupidity, and so on. There are about 35 million of us, which embraces a staggering diversity. And yet each year the number of murders winds up within a very few points of the mean. Somehow all of that human variation disappears and we operate as if we were parts of a system, a system that seeks a constant level.

I find that curious.

Now, because my comprehension of statistics is poor indeed, it’s likely I’m fixed on something that you’ll say is spurious or trivial. If so, I’d be glad to learn how that is. How it is that as November comes round, people who have never met either hurry up or slow down to “ensure” that the overall homicide rate comes out very near the average by the end of December.