Cancer, probability, normality and theodicy – part 1

I have posted recently about the lotteries that you will likely lose and the lotteries you have already won. In this post I want to talk about the math of a lottery you might win, but really do not want to. And understanding the math here is to get to a closer understanding of probability and fate in nature.

Every year in the U. S. state of Florida, an average of fourteen out of every 100,000 people in the state are diagnosed with one particular form of cancer, involving the kidney. If you are one of this small number who gets this diagnosis, or that of a different form of cancer, this is a major life crisis, bound to generate one of those Big Questions like “Why me?”

What makes this number of fourteen even more curious is that this diagnosis rate has not varied by more than plus or minus one person out of 100,000 in any of the last ten years reported by the Centers for Disease Control. [1] Both the rate and the range vary by how you slice the demographics further, say by age, gender, or location, but similar patterns emerge in all locations and groupings. While sometimes we discover factors that gradually “move the odds” of the “How many?” over time (such as less smoking or better early diagnosis), the question of “Who?” still looks closer to the math of a lottery than some identifiable cause-effect. And it is that contention that is both mathematically interesting to some (well, me anyway) and existentially disturbing to many.

Even in more common cancers, the diagnosis rate from year to year runs within a narrow band. One common form of cancer shows in Iowa statistics to be diagnosed in a ten-year average of about 123 per 100,000 people. This particular rate has varied only plus or minus eight from that average in the last ten years, and usually runs much closer to that average. But while not as small as your chance of winning the lottery, even this common form of cancer still holds pretty low odds of happening (a little more than one person in 1000) as compared to many other of life’s challenges.

And contrary to common opinion, heavy smokers are more likely to die of something other than lung cancer, even though their probability for contracting it is much higher than with non-smokers. Multiply a small probability by several times and it is still relatively small. [2] That’s not a defense of smoking; you will still likely die earlier than the non-smoker, but rather there is a long list of other causes aggravated by smoking.

So, we are looking at life-changing events, each with a very small probability of happening to you in any given year, but persistently happening to someone, a real-life demonstration of Poisson’s Law of Large Numbers. One reason for the consistent, though small, average and the narrow variation comes down to a common misunderstanding of what normality means. We are all familiar with the “bell-shaped curve” that represents a “normal probability distribution,” but what you are actually seeing when you see one of these in nature, like a bell curve showing varying cancer rates in different demographics, is less understood.

Try for a moment to visualize an odd single six-sided die that has six dots on one side, but the other five sides are blank. Now imagine, for a moment, what kind of results you would get if you roll this die one hundred times, counting up the dots. In Part Two of this series of posts, you will be able to use a computer simulation to “virtually” roll this die, with its very skewed probability pattern, hundreds of times, and see an interesting statistical effect, called the Central Limit Theorem, at work.

Let’s take another unlikely event. In every large city there is a particular traffic intersection with heavy traffic and regular accidents. The chance of any one driver being in an accident there is very small. Yet, in many of these cities, the total aggregate number of accidents at that particular intersection will likely be very close to the same every year, within, like our cancer statistics, a very narrow range that approaches a bell curve in shape. And a fairly-consistent, though smaller, percentage of those crashes will involve a tragic fatality. What is happening here?

I will explore this counter-intuitive idea in Part Three of this series of posts, but we can say here that these accidents comprise many different causes, each with a very low “lottery probability” of occurring, and they are effectively getting “averaged out.” There is likewise something similar happening with the cancer statistics, and just about anything else affected by our genetic makeup, including how tall you are.

Recognize that all of this math is “in the aggregate,” the quantitative land in which lottery directors and insurance actuaries live. However, are YOU, specifically, a random event like the lottery winner if you are diagnosed with a particular form of cancer? This is where theological “God language” again enters the picture: “Why me, specifically?” In Part Four of this series, I will look at some of the most common eastern and western religious answers posited to that question.

Part Two of this series is now posted.


  1. Similar relationships and tight ranges exist for most reported forms of cancer, varying by the state and demographic group selected. See the Centers for Disease Control site, where you can download the most recent data, with 2014 the most current year at this writing. Note that the death rates from cancer are different, and have been declining, which is covered in Part Three.
  2. Wanjek, Christopher. “Smoking’s Many Myths Examined.” LiveScience, 18 Nov. 2008.

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