Why Averages Are Misleading

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"The average investor buys high and sells low."

--Ray Dalio

The chairman of Vector Economics, Sam Savage, shares the story of a statistician who drowns while fording a river that he calculates is, on average, three feet deep. "If he were alive to tell the tale, he would expound on the 'flaw of averages,' which simply states that plans based on assumptions about average conditions usually go wrong." 

Mr. Savage, who also lectures at Stanford and Cambridge on risk modeling, says, "This unseen flaw shows up everywhere, distorting accounts, undermining forecasts, and dooming well-considered projects to disappointing results."

A problem with averages

A former client, Brad Hewitt, then CEO of Minneapolis-based Thrivent, first brought the problem of averages to our attention. He recently explained it this way:

"I was a math (statistics) major in college. One part of that coursework was a section on how to tell if someone was lying using statistics. It was eye-opening, and averages were among the best ways to mislead. A professor would say, 'If you put one foot in ice cold water and the other foot in boiling water on average, it would be just right.' 

"Averages  (means, modes, arithmetic, etc) are valuable, but one must look carefully at what they say. Unfortunately, people often have a point of view, and statistics are simply a way to prove their point, not help them gain insight into data," Hewitt concluded.

What specifically should concern us about averages?

The problem with averages is that they can easily obscure the reality of the situation. 

"While averages can provide a simple summary of complex data, they can also distort reality, hiding important variations and nuances with the data," writes Reagan Pannell, CEO of Leanscape. "Averages can be useful for providing a quick snapshot, but they mustn't be the sole metric relied upon for decision-making or understanding a situation," he adds. 

Some examples

Think of baseball batting averages, which Sabermetrics considers a weak performance measure. On-base plus Slugging (OPS) may be a better way to judge a batter's value to their team, but do fans know what that stat means? Do they even care?

Consumers rely on average annual rainfall amounts from their local meteorologists (54 inches in Florida) because they are simple to compute and understand. Yet those averages are only sometimes reliable, failing to account for inconsistent patterns within a year (like hurricane or dry seasons).

Average is a mathematical term, and research suggests it should be so confined. You can't average people (only numbers of people) or concepts or opinions. One person suggested using the word "typical" as an alternative. 

Does that mean the average person is a myth?

This is likely since that definition relies on a single 'average' value and can ignore individual differences and complexities. 

Beware these conditions

Circumstances to avoid:

• Using averages to compare different groups. 
• Applying group behavior to individuals.
• Allowing extreme results to influence averages.
• Fixating on a single number--which is an oversimplified view of reality.  

One way around these pitfalls is to consider probability distributions instead of single numbers. A histogram is a simple way to view a distribution. (linkedin.com/pulse/deceptive-art-using-averages-unveiling-statistical-tricks)

What can we learn?

Consultant Pennell believes we should look beyond averages.

"Consider data distribution, the outliers, and other measures like median and mean. Understanding the range and variance can also provide insights into the spread and inconsistency of data."

Pennell balances the scale:

1. Averages are not inherently bad. They do offer a quick snapshot of data and simplify complex datasets.

2. Use averages as a starting point, but explore other statistical measures.

3. Beware of outliers, as they can significantly skew your average and create a misleading data representation.

4. Tools like AI can provide valuable insights beyond the average, though you should never remove the human mind when analyzing data.

Coin of the realm

Sam Savage, whom we quoted initially, is also the author of The Flaw of Averages. Instead of saying, "Give me a number for my report," he believes every executive should say, "Give me a distribution for my simulation."

If followed, Savage's advice could improve planning and outcomes and establish a more credible standard of leadership. 

Strategist.com

© Bredholt & Co.