When Jeff Bezos walks into a bar, the average customer becomes a billionaire. Unfortunately, that fact won’t pay for their next round. Extreme outcomes like Bezos’ net worth are a common characteristic of power law distributions. In a fat-tailed world, averages can mislead.

Watch Your Head, Part 1

Many things in the natural world follow a normal distribution: heights, weights and blood pressure. In a normal distribution, or bell curve, most measures fall around the mean. Move further away from the average in either direction, and occurrences become less likely. For example, the average height of an adult male in the United States is 5 feet, 7 inches. Most guys you know probably fall within six inches average, a relatively tight range. A man one foot above average is tall enough to play in the NBA, where the average height of a player is 6 feet, 7 inches (in shoes).

Source: Guinness Book of World Records, A history of record-breaking giants 100 years after the tallest man ever was born, February 22, 2019.

Watch Your Head, Part 2

While normal distributions are easy to think about, power laws are flabbergasting. Jeff Bezos’ wealth is equivalent to a man eight miles tall. In a power law, a relative change in one quantity results in a proportional relative change in another. For example, doubling the length of a square from three inches to six inches quadruples its area from nine inches squared (3²) to thirty-six inches squared (6²).

Source: Newman, M. E. J. (2005). “Power laws, Pareto distributions and Zipf’s law”. Contemporary Physics. 46 (5): 323–351. arXiv:cond-mat/0412004. Note: Left: histogram of the populations of all US cities with population of 10 000 or more. Right: another histogram of the same data, but plotted on logarithmic scales. The approximate straight-line form of the histogram in the right panel implies that the distribution follows a power law. Data from the 2000 US Census.
Source: Society for Human Resource Management, Resources and Tools: Compensation, April 3, 2021.

The 80/20 Rule

One of the best known power laws is the 80/20 rule. In the late nineteenth century, Italian economist Vilfredo Pareto discovered that roughly 80% of Italy’s land was owned by 20% of its population. Pareto found a similar relationship in other countries and even in his vegetable garden where 20% of the pea pods produced 80% of the peas. Pareto’s finding that a majority of consequences comes from a minority of causes was the basis of the 80/20 rule, also known as the Pareto principle.

Source: Galvani, A., May, R. Dimensions of superspreading. Nature 438, 293–295 (2005). https://doi.org/10.1038/438293a. Note: The figure above shows the 20/XX index, which quantifies the proportion of the transmission (XX%) that results from the most infectious 20% of the population. Confidence intervals are included where available.
Source: Thais Do Rio on Unsplash

Finance at Indeed. Previously finance at Etsy and internet equity research at Deutsche Bank. Find me @kjlabuz.

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store