A classic example of the Flaw of Averages involves the Statistician who drowned crossing a river that was on average 3 ft. deep.

Desperately casting around for a topic to write about today, I was grateful to see a link to an interview in the San Jose Mercury News with Stanford professor Sam L. Savage about his book, The Flaw of Averages (great title!). I’ve not read the book yet, but the review has certainly piqued my interest:

How does General Motors, Sam L. Savage wonders, explain the pathetic performance of its crystal ball? When Americans started driving hybrids, GM was still pushing Hummers. Executives at the giant carmaker — fully aware of union contracts, presumably prepared for rising gasoline prices and economic uncertainty — drove straight into the ditch of bankruptcy.

“Probability management” is often mismanaged by business leaders, says Savage, a consulting professor of management science and engineering at Stanford University and a fellow at the Judge Business School at the University of Cambridge. Savage, who has performed probability studies for Royal Dutch Shell, set out to right statistical wrongs in his book “The Flaw of Averages.”

The Information Age has transformed statistics into a vital field of study, yet Savage says many habits and practices have been slow to change from the “steam era statistics” of the Industrial Age.

Written for a business audience, “The Flaw of Averages” leavens the math with levity, even the occasional cartoon.

Well alright then. Working with business executives and their measures for so many years, I continue to be amazed at how easily decisions are made on the basis of numbers with little consideration for the risks and consequences of those decisions. I’ve been meaning to write at some length about the need for the discipline of risk management in change programs, but before doing so, we all need to take a deep breath and consider the magnitude of our collective innumeracy.

The topic has been covered before. I just pulled Innumeracy: Mathematical Illiteracy and its Consequencesby John Allen Paulos from my bookshelf, and thumbing through it, I remember how much I appreciated the book, but that is wasn’t the easiest read. From the back cover description:

Why do even well-educated people understand so little about mathematics? And what are the costs of our innumeracy? John Allen Paulos, in his celebrated bestseller first published in 1988, argues that our inability to deal rationally with very large numbers and the probabilities associated with them results in misinformed governmental policies, confused personal decisions, and an increased susceptibility to pseudoscience of all kinds. Innumeracy lets us know what we’re missing, and how we can do something about it.

Sprinkling his discussion of numbers and probabilities with quirky stories and anecdotes, Paulos ranges freely over many aspects of modern life, from contested elections to sports stats, from stock scams and newspaper psychics to diet and medical claims, sex discrimination, insurance, lotteries, and drug testing. Readers of Innumeracy will be rewarded with scores of astonishing facts, a fistful of powerful ideas, and, most important, a clearer, more quantitative way of looking at their world.

SinceI found that Innumeracy was not especially accessible, I haven’t yet found occasion to use examples from it. Perhaps The Flaw of Averages will be better. It looks promising. From the interview with Savage:

Q. What are the most common ways people foolishly apply the law of averages? Is it the faith placed in “average returns” on retirement portfolio?

A. Plenty of people have been caught off base by the Flaw of Averages in investing, but here is an example that is closer to home. Imagine that both you and your wife are right on time for appointments, on average.

When you go somewhere together, however, you will be late, on average. Why? If we model being early or late for each of you by flipping a coin (heads is early, tails is late), then the only way you will not be late as a couple, is if neither of you is late. This is like flipping two heads in a row, or one chance in four. Now expand this to a big industrial project with thousands of tasks, and you can imagine the implications.

We don’t have to imagine the implications – we live with them every day. More to come (soon, I hope), on the topics of innumeracy and strategic risk management.