The Flaw of Extremes
Did you know that localities whose residents have the largest average earlobe size tend to be small towns? More amazingly, if this seeming bit of trivia were more widely understood, it could save millions of dollars per year. To explain why, I will start with a problem familiar to anyone who has worked in a large organization: bottom-up budgeting.
Consider a firm in which each of ten divisional vice presidents submits a budget to the CEO. The VPs are not completely certain of their cash requirements, but suppose for argument’s sake that each is 95 percent confident of requiring between $800,000 and $1.2 million with an average of $1 million. Further, their needs are not interrelated. If any one of them requires more or less than average, it won’t affect the needs of the others.
If each VP requests the average requirement of $1 million, then the CEO can add the ten estimates together to arrive at the correct average of $10 million. The Strong Form of the Flaw of Averages does not apply because summing is a straight line calculation.
But what kind of VP submits a budget that has a 50 percent chance of being blown? Instead of submitting their averages, the VPs will probably provide numbers they are pretty sure they won’t exceed—let’s say 90 percent sure. This is the widely practiced budgeting technique known as sandbagging.
Assuming the uncertainties are bell-shaped and based on the preceding ranges of uncertainty, then the cash required ...