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The Pernicious Effect of Using Statistics for Long Return Period Events

by Michel Bruneau, MCEER Deputy Director

The statistical probability of an earthquake occurring in a given place or time is often used to make critical decisions in hazard mitigation. This anecdote is presented so readers can consider the potential impact of relying solely on statistics to implement policy.

Counting brothers, sisters, children, parents, grandparents, uncles, aunts and cousins, there are 50 members in my family. Tallying old and young, their average age is also 50. Interestingly, it just so happens that over the past 50 years, only one aunt was ever involved in a car accident. It was a terrible head-on collision, and she acknowledges that, without a doubt, the safety belt she wore on that day saved her life. Her doctor agrees, as does most of my family, although honestly, for reasons unknown to me, a few among them still refuse to this day to buckle-up when they drive.

Statistically speaking, it remains that in my immediate region (i.e., my family), a head-on collision is a rather low-probability event. In any given year, there is a one in 2,500 chance that one of us will be involved in such a car crash. Simply, for 50 members in my family having only one accident in 50 years, this equals 1 woman/man-year with an accident out of 2,500 woman/man-years. In other words, a 3% probability of this happening to me in 75 years. No wonder I have never witnessed a car crash.

My uncle is a mechanical engineer who works for one of the big auto manufacturers. Typically, he designs and tests seat belt systems. I brought my mathematical assessment that car crashes are rare events to his attention. I went as far as to suggest that, given that I would live at best 100 years, it might be wise and more economical to design belts to resist smaller loads. Statistically speaking, over 100 years, the accident in which I am more likely to be involved will probably be a minor fender bender. In that perspective, it might be sufficient for my purposes to use a belt designed to resist only 1/3 of the design loads that would otherwise be considered based on a 2,500 year return period.

Without blinking, he replied: "Hey, it's only your life! But if you are going to carry other passengers, they may not be aware that riding in your car carries a higher risk of death. Should they die in your car during a crash, you can bet lawyers will find guys like me to testify that it is possible to design a seat belt to resist the 2,500 return-period car crash, and that seat-belts ought to be designed that way."

Damn lawyers! Ah, forget them. I still thought it was unreasonable to expect me to spend money on a seat belt when I could use that money for other purposes. Particularly since my car has infinite needs for repairs and maintenance (getting new tires is currently on the list as an example of some badly deferred maintenance). Why should I not be allowed to drive half a car if half a car is all I can afford? What's a 0.0004 chance that I'll be involved in a car crash this year? Insignificant! Hence, thanks to statistics, it was possible to make the problem nearly disappear in my mind.

Until last week, when a drunk driver rammed me head-on. Although I had buckled-up, more by habit than by intent, my wife did not. Statistics will not bring her back, and that, my friend, is the pernicious effect of statistics.

Editor's Note: The analogy to a car accident is a fictional account included only to illustrate the author's point of view.


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