Averages unreliable for predictions, author says

The problem with averages, says Sam L. Savage, is that “plans based on average assumptions are wrong on average.”

This is the thesis of his new book, “The Flaw of Averages” (John Wiley & Sons Inc., $22.95). He argues that this flaw helped to mask the subprime-mortgage crisis and contributed to General Motors Corp.’s bankruptcy, among countless other disasters.

It is the flaw of averages that causes businessmen, engineers, generals and others to underestimate risk in the face of uncertainty.

To make his point immediately clear, Mr. Savage, whose father was a highly acclaimed statistician at the University of Chicago and author of “The Foundations of Statistics,” cites the apocryphal example of the statistician who drowned while wading across a river that was, on average, only three feet deep.

“In everyday life,” said Mr. Savage, “the flaw of averages ensures that plans based on average customer demand, average completion time, average interest rate and other uncertainties are below projection, behind schedule and beyond budget.”

When people use a single number, usually a historical average, to predict the future, they invite systematic errors and generate unintended consequences, mostly negative, argues Mr. Savage, who received his doctorate in 1973 in the application of computers to operations research.

The subject of his dissertation was “computational complexity.” Today he is a consulting professor of management science and engineering at Stanford University and a fellow of the Judge Business School at the University of Cambridge.

Virtually no institution, profession or household can avoid the consequences of the flaw of averages, asserts Mr. Savage, who has helped to devise a solution that has recently been made possible in part by the exponential increase in computer power.

Terri Dial quickly grasped the concept of the flaw of averages years ago.

“Consider a drunk staggering down the middle of a busy highway,” Mr. Savage told a group of Wells Fargo bank executives in 1995. “And assume that his average position is the center line. Then the state of the drunk at his average position is alive, but on average he’s dead.”

Ms. Dial, who began her Wells Fargo career as a teller in the 1970s, immediately exclaimed, “That’s the reason we always blow the budget on our incentive plan!”

Since the number of checking accounts sold by employees averaged 200 per year, the bank decided to give $1,000 bonuses to workers who performed above average, Ms. Dial explained by way of a simple example. The bonus of the average employee would be zero. So zero must be the average bonus, right? Wrong.

Roughly half the employees will exceed the average, so the average bonus will be about $500, much higher than Wells Fargo projected.

On a grander scale, Mr. Savage argues, the flaw of averages caused the subprime-mortgage debacle, which precipitated a worldwide crisis that threatened to bring down the global financial system.

The housing bubble relentlessly inflated during the first half of this decade, and subprime mortgages flourished across the country, especially in bubble areas. In those regions, such as California and Florida, middle-income families with decent credit histories could not qualify for prime mortgages given the prices of the houses they were buying and the down payments they were offering.

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