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Wizards of Odds
by Fred Kilbourne
Yes, it’s possible that you could be brained by a piece of space junk on your way to work. Or trampled by an escaped elephant. Or mauled by a great white. But what are the odds?
WE ACTUARIES DEVOTE OUR LIVES TO PROBING and prodding the quantity QAV, where Q is risk (the probability that an event will occur), A is the cost of that (usually) untoward event, and V allows for the time value of money. This article is about Q.
“I’ve developed a new philosophy... I only dread one day at a time.” This quote from Charlie Brown introduces Risk: A Practical Guide for Deciding What’s Really Safe and What’s Really Dangerous in the World Around You by David Ropeik and George Gray of the Harvard Center for Risk Analysis of the Harvard School of Public Health (Houghton Mifflin Co., 2002). Their book does indeed address dread and fear, but its dedication is to someone who was exemplary at keeping risk in perspective. The goal, of course, is to have your dread be rational, which requires that you take three steps:
The actuary can appreciate the authors’ definition of risk as “the probability that exposure to a hazard will lead to a negative consequence.” Your death or dismemberment, for example. So Risk includes the lifetime odds of the average American meeting his or her demise by reason of a fatal:
“Leventy” is the word that was coined long ago by my brother to denote the number that is one greater than the largest finite number you can come up with. And even leventy is but an infinitesimal portion of the smallest infinity you can imagine.
Consider heart attack versus shark attack. Do you have 1 million times the dread of the former versus the latter? OK, that doesn’t do a very good job of showing risk evaluation bias, because you live in Kansas and vacation in Nebraska.
Well, then, how about this: The average heart attack does more damage to the body than does the average shark attack. And, returning to mortality, are you 455 times more fearful in a car than in a plane, as you should be? (OK, OK, adjust the odds for mileage, or vehicle, or driving style, but the basic point remains.) The basic point is, of course, that risk is best evaluated by substituting facts for appearances and demonstrations for impressions (the motto of the Society of Actuaries).
I recall being surprised but enlightened some years ago, when I was commuting by bicycle and flying a lot, to calculate that my chances of dying in a bike or car or plane accident the following year were each the same—about one in 10,000.
Most of Risk addresses several dozen known risks, from auto accidents to X-ray exposure. For each, the authors examine the hazard, the range of consequences, and what you can do to reduce your risk. Each is also evaluated on a “Risk Meter” on which the probabilities and consequences are graded from low to high. The social and psychological biases, which we must overcome if we’re to “keep risk in perspective,” are evident from a thorough reading of the book.
High-risk hazards, nearly all of which we tend to underestimate, include:
Some hazards require individual comment, but even these with the passage of time are often exposed as conforming to Mark Twain’s comment quoted in Risk (“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”):
One person has died in the United States of mad cow disease, but it was contracted elsewhere, so does that count? But it’s hard not to dread a poorly understood disease that you contract simply by eating, that is caused not by a virus or bacterium but rather by a prion, that may afflict your cat but not your dog, and that eats holes in your brain before it kills you. The risk may be minuscule, but it fairly cries out to be overestimated.
Long odds, such as of contracting mad cow disease, are not only subject to considerable uncertainty (see the differing shark attack estimates above), but they can require access to very large numbers to make your point. An excellent source for this search is the 1997 Scientific American article “The Challenge of Large Numbers” by Richard E. Crandall, which introduces the reader to such colossi as (the numbers in the list are powers of 10, or the number of zeros after the one):
According to Crandall, the fifth Ackermann number “is so large that it could not be written on a universe-size sheet of paper, even using exponential notation.”
And yet even the largest Ackermann number is surpassed by “leventy,” the word coined long ago by my brother (or was it my sister?) to denote the number that is one greater than (literally one-ups) the largest finite number you can come up with. And even leventy, as any mathematician will tell you, is but an infinitesimal portion of the smallest infinity you can imagine.
Back to the merely sublime, other sources have a different view of your mortality prospects. According to “Life: The Odds” by Gregory Baer and other sources in a Feb. 22, 2004, San Diego Union-Tribune article, these are your chances of being killed by:
Not all long odds relate to bad news, of course. There’s also some chance that you will:
And now for my disclaimers and caveats. I do not warrant or certify the numbers in this article, particularly as they apply to you. The data supporting them were taken from sources that have been known to be reliable, but haven’t been audited or checked for accuracy nor even for plausibility. Actual results, especially yours, may vary, for the future is a willful child, put on a straight path by its parents (the past and present) but subject to straying under the wayward influence of its new environment (think anthrax or smallpox).
Finally, it’s as important now as it was 65 years ago to pay careful attention to the wizard behind the curtain, who taught us that: medals can be more useful and less risky than courage; a paper heart can be worn on the chest or on the sleeve and can’t be broken; and you may as well forget the brain and go for the diploma.
FRED KILBOURNE is a consulting actuary with the Kilbourne Co., independent actuarial consultants in San Diego. He is a member of the Contingencies editorial advisory board.
Contingencies (ISSN 1048-9851) is published by the American Academy of Actuaries, 1100 17th St. NW, 7th floor, Washington, DC 20036. The basic annual subscription rate is included in Academy dues. The nonmember rate is $24. Periodicals postage paid at Washington, DC, and at additional mailing offices. BPA circulation audited.
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