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. Recently, Savage elaborated on his message in an exchange of e-mails with the Mercury News.

Q You take 391 pages to explain, as your subtitle puts it, “Why We Underestimate Risk in the Face of Uncertainty.” What’s the short answer?

A When you plug the average of some uncertainty (future sales, prices, interest rates, etc.) into a spreadsheet you will generally NOT get the average value of the output (profit, cost, return on investment etc.). This has been known by mathematicians for a century as Jensen’s Inequality, and with a name like that, no wonder no one has heard of it.

In 1999 I came up with a better name, the Flaw of Averages, and figured it would be a great book title. But as I began to write, I realized that the Flaw of Averages ensures that everything is behind schedule, beyond budget and below projection. Who wants to read a “feel bad” book without a happy ending? Then, starting in 2005, working with colleagues at Cambridge University and Royal Dutch Shell, a cure for the Flaw of Averages began to emerge. With a happy ending in hand, I had the motivation to finish the book.

Q The Information Age has created a blizzard of data, but search technologies help people navigate the information. What is your impression of society’s adaptation to the Information Age?

A A blizzard is a good analogy. If you focus on the individual snowflakes, you’ll go nuts. It takes statistical thinking to make out what the storm is doing as a whole. For example, although you will never know what all zillion snowflakes in the blizzard are doing, you can learn a lot by sampling 1,000 of them.

Some people are very sophisticated about statistics. Netflix predicts what kinds of movies you like, Google guides you to the Web site you wanted and researchers design vaccines to save us from the next big epidemic — all with statistics.

But most people are still plugging single average numbers into their spreadsheets and are stuck in the 20th century. A central facet of our cure for the Flaw of Averages is a new computer data type that squeezes thousands of numbers instead of just one number into the single cell of a spreadsheet, like a genie into a bottle. It is called the Distribution String, or DIST, and was developed in collaboration with Oracle, SAS Institute and Frontline Systems. It helps you think about your thousand sample snowflakes in terms of a single super snowflake.

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.

Q Have you ever caught yourself making such errors?

A Many times. The first was in 1989, when I was planning a lecture on combined uncertainties and had a clear idea of the result. I then created a very simple simulation in Lotus 1-2-3 with random numbers, which gave the opposite of the answer I expected. I thought to myself: “Whoa! If a management science professor doesn’t get this stuff, how about the rest of the world?” It was like a light bulb going on, which has motivated me ever since.

Q Statistics used to seem like a grim pursuit for creating actuarial tables. Now the Information Age has made it a hot, lucrative field — even “dead sexy,” as one blogger put it. What’s your opinion?

A The theory of probability and statistics is powerful and elegant. But then again, so is the steam locomotive, and they were developed around the same time. Although we no longer teach steam locomotion, most college courses, including many at Stanford, still teach steam-era statistics. Instead of “dead sexy,” I would call it “just plain dead.” Stanford, however, is also a prominent center for computational statistics, which uses the brute force of computers to solve problems, rather than arcane formulas. This leads to a much more visual and interactive approach to statistics that I do find sexy.

Q So do statisticians have surefire pickup lines?

A Although I don’t have a surefire pickup line for a statistician, I can provide a long list of things they could say that would have the opposite effect.

Contact Scott Duke Harris at 408-920-2704.