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## Beware The Flaw of Averages

by | Jul 10, 2020

You’ve probably heard about the statistician who put his head in the oven and his feet in the freezer so that on average he felt comfortable. Or the man who drowned walking across the river that had an average depth of three feet: it was one foot deep in some spots and ten feet deep in others! Knowing that the average depth was three feet was not helpful!

These are simple examples of the concept of the “flaw of averages” which was developed by Stanford economist Sam Savage. The flaw of averages states that “plans based on the assumption that average conditions will occur are usually wrong.”

Here’s a more in-depth description:

In general, the flaw of averages is a set of systematic errors that occurs when people use single numbers (usually averages) to describe uncertain future quantities. For example, if you plan to rob a bank of \$ 10 million and have one chance in 100 of getting away with it, your average take is \$ 100,000. If you described your activity beforehand as “making \$ 100,000,” you would be correct, on average. But this is a terrible characterization of a bank heist! Yet, this very mistake is made all the time in business practice. It helps explain why everything is behind schedule, beyond budget, and below projections, and it was an accessory to the economic catastrophe that culminated in 2008.

Source: Frontiers of Modern Asset Allocation

The flaw of averages can distort our perception of the world and our decision making. As such, it is an important concept to keep in mind, especially during the pandemic as we’re all barraged with statistics about Covid-19. For example, as I wrote earlier this week in the IFOD Relatively Small But Absolutely Big, the Infection Fatality Rate for Covid-19 is about 0.6%. That simple, single average number obscures a more complex underlying reality if you are trying to determine your own risk from dying:

• The fatality rate varies greatly by age – in general the older you are the greater the risk of dying from Covid:
• The infection fatality rate is hugely affected by other health conditions:
• Covid mortality is much higher for minority groups in the U.S.:
• Covid mortality risk might even be affected by blood type.

In sum, the 0.6% infection fatality rate does a very poor job of estimating an individual’s risk of dying from Covid-19. If you are young, healthy and white, the 0.6% figure is probably way too high. If you are elderly, have heart disease and Black, the 0.6% is way too low of a proxy of Covid mortality risk.

Another great example of the flaw of averages is thinking that any particular stock will provide a return that is close to the index average. The vast majority of stocks underperform the index while a relative few greatly outperform. Read more on this concept here: https://www.stlouistrust.com/why-most-stocks-underperform-index/

Yet, we are drawn to the allure of simple averages. Why is that the case? A prior IFOD addressed this: Single Number Simplification Syndrome.

What to do? When you see something that is an average, don’t take it at face value; dig deeper. Realize that most things in life are complex and a simple average often does a poor job of summarizing reality.

1. Hi John — these posts just keep getting more and more interesting and informative.
An add on to the excellent point you are making is the confusion around the use of the term “average” — without specifying whether reference is to the mean, the median or the mode. everyone has pet peeves and this is one of mine (causing eye-rolling by friends and family)
https://www.purplemath.com/modules/meanmode.htm

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