I’m reading a work of fiction about the Knights Templar, based on the same mythos as Dan Brown’s novels. A throw-away line about the history of the Order’s Masters sparked my mathematical curriosity: “For the sixty-six who’d come before, the average tenure was a mere eighteen years.”
Is this reasonable? Did the author calculate the average tenure or just guess? The Knights Templar got their start in 1119. The story takes place around 2000, maybe 2005. So do sixty-six Masters average eighteen-year tenures over some 885 years?
We can do a quick check: had there been eighty-eight Masters, the average tenure would be about ten years. Had there been forty-four Masters, the average tenure would have been twenty years. Sixty-six falls mid-way between the two, so the average should be around fifteen. Eighteen is not completely unreasonable, but it might be too long.
We can be more exact: divide 885 by 66 and we immediately see that the average should be about 13.5 years. But this calculation is really answering the question “how long would the tenures be if all the Masters had the same tenure?” We might expect some short tenures of a year or two and one or two long tenures of perhaps twenty or thirty years.
Such a distribution, with no values less than zero, a few large values and most values clustering somewhere inbetween, might have a very different average due to the lopsided (skewed) distribution. We can approximate such a distribution with the Poisson distribution. Poisson does not have fractional increments, so we’ll only get whole-year tenures, but it should be good enough to determine if 18 is a reasonable average tenure. Also, Poisson is easier to fit than the more precise beta distribution.
So I fired up Minitab, generated a bunch of random Poisson-distributed values with a mean of 18, and then added them up in groups of sixty-six. The average of these sums was 1224 years; much longer than the 885 years required by the story. Eighteen years is too long.
Playing around with different values for the mean, I find that the “right” average for tenure length should be close to 13.5.
To answer the original question, then: eighteen years isn’t completely unreasonable, but it’s definitly wrong. I have to wonder how the author came up with this. If he just pulled “eighteen” and “sixty-six” out of thin air, then I have to say that he guessed pretty well. Unfortunately, it’s clear that he didn’t bother to do even a simple calculation while sitting in front of his computer typing, where a calculator was readily available.
I know: mathematical accuracy isn’t the point of the story. However, the point of fiction isn’t to create a milieu based on logical falsehoods, but to create a fictional milieu that is believable (i.e. our modern world, if the myths surrounding the Templars were real). The author lets us down through such acts of carelessness or laziness.
This also brings me back to my title. You know you’re a geek when you take a throw-away statement in a work of fiction and perform some statistical analysis to fact-check it.
At least it’s a fun journey.