Risk Professional - December 2009

bOOK REvIEw
Dos and Don’ts of Dealing

The basic premise of Sam Savage’s The Flaw of Averages is that humans have a tendency to oversimplify things to a single number or average. His general example in the book is someone saying, “Give me a number.”

Any time someone wants to know an estimate of some uncertain variable such as time to completion for a project — or cost or profit or a multitude of other uncertainties — they are usually asking for an average. For example, say a supervisor wants to know how long a specific project will take and a subordinate provides him or her with a range of three to nine months. The supervisor wants a number, so the underling provides the average of six months, and the supervisor then uses “the number.”

Assuming this project has an equal likelihood of being completed in each month (i.e., in any of months three to nine), it has a roughly 57% chance of being finished in six months or less. This may occasionally work for simple problems, but for more complicated problems, the average becomes much less useful as an estimation tool.

Let’s see what happens when we add a little complexity to the problem. One of Savage’s excellent examples was of a computer program with 10 subroutines. The supervisor asks each programmer for an estimate of time to complete each subroutine. Every programmer comes back with an answer of three to nine

months, but the supervisor wants “the number.” So each programmer provides the average of six months, and thus the supervisor estimates a completion time of six months. However, if just one of the programmers takes longer than the average, the whole project takes longer than anticipated, even if the average completion time is six months.

How will the supervisor’s estimate hold up to reality? Let’s assume the chance of each programmer finishing within six months is 50%, and that we need each programmer to finish in six months or less for the project to come in on time. This has the equivalent odds of flipping heads 10 times in a row. The odds of flipping heads are 50%, and we have 10 programmers, so . 5 to the 10th power is .00098% — or less than 1 in 1000. So the odds of completing all the subroutines before six months are just under 1/10th of one percent. Even this number, however, does not account for estimation error by the programmers. Thus, the average is not a great planning tool, and hence we have the “flaw of averages.”

The book is structured in three parts: foundations, applications and probability management. Foundations presents a basic overview of the concepts in the book, which Savage cleverly refers to as “Mindles” (as in handles for the mind). The applications section is fairly self explanatory. It expands readers’ understanding of the concepts by describing how “ Mindles” can be applied to various problems. Lastly, in the prob-