# In power law world”average” doesn’t exist

IQ is a fuzzy topic. Extreme values of it fit that old trope about pornography. You know it when you see it. There are some people I meet (including several people on this list) where I just wanna cry foul. Not fair. Too much horsepower in one person. At the opposite end of the brain lottery, there are unfortunate cases of outright impairment. For the bulk of us, we reside somewhere in the middle. If you got tested, depending on how you fared, you either believe those tests are pseudoscience or perfectly calibrated thermometers. While everyday experience hints at its wide range, a precise definition of intelligence and its measurement will remain a bloodless debate.

One thing scientists appear to agree on is that whatever notion of IQ you settle on, it probably follows a bell curve. Let’s say the average IQ is 100. Some lazy googling puts the standard deviation at 15 points.

• Normal distribution math would estimate that 15% of people are more than 1 standard deviation above the mean or an IQ greater than 115. About 5 people in a classroom of 30.
• The odds of having an IQ above 130 is 2.5%. That’s the smartest person in the class.
• The chance of having an IQ of 145 (3 standard devs) is about 1/200. Otherwise known as the smartest person in your HS graduating class. As Gladwell would probably remind you, this is unlikely to have been your valedictorian. No offense to valedictorians (again, many of you on this list).
• Symmetrically, the bell curve implies that 15% of people have IQs that are 1 standard deviation below the mean. In an interview with Tyler Cowen, Jordan Peterson noted that the military has studied this group and found them unable to satisfy basic life tasks and subsequently ineligible for even simple roles.
• Food for thought once you accept that aptitude, even flexibly defined, is not evenly distributed.
•  If our IQ is largely inherited, this seems to imply the need for compassion and aid for swaths of disenfranchised people. There are 5 babies in every hospital nursery (out of 30) who are going to struggle stringing to together chains of tasks which lead to decent lives.
• On the bright side, if we define a genius as a 3 standard deviation IQ, then there are about 6 million geniuses in Africa, most of which are undiscovered. More locally, the Hidden Genius project in Oakland reminds us that the search for hope is far from exhausted.

We are used to seeing bell curves everywhere. Height, test scores, the roll of a pair of dice, shoe size. These quantities are well behaved. No single value from the population is going to have a large impact on the average if your sample size is sufficiently large. Our generic impulse is to estimate quantities according to such a benign distribution.

A less intuitive type of curve is the pareto distribution or power law curve. It shows that the bulk of an outcome can be driven by just a few or even a single observation. If you are an hourly wage earner in an Amazon distribution center and Jeff Bezos walks in the room, the average person in the room’s wealth is now that of a “one-percenter”. This computed average, of course, is meaningless to describe how an actual worker in this room is actually living. Wealth is distributed according to pareto curves, not bell curves.

Recognizing when this distribution is governing a situation as easily as we notice bell curves is an invaluable life skill. Pareto distributions dictate strategies that would seem insane or wasteful to somebody who is incorrectly thinking in bell curves. Taleb calls power law dynamics “extremistan” and bell-curve domains “mediocristan”. When deciding a course of action it is critical to know which world you are operating in. It’s the difference between ownership and hourly wages. Being a partner in a law firm has leverage. If the business grows you make more income as a pro-rata owner but you don’t work more hours. If you are an associate, you sell your time for money. Your average hourly wage is fixed. The grunt’s wage per last hour of work is constant. The owner’s average hourly wage can vary widely based on the total business the firm brings in. Or if the firm is acquired. To speak of the owner’s hourly wage is to misunderstand what drives his income and in turn what strategies will maximize it.

Life should display a #DIV/0! error when you try to apply averages to a power law decision.

It would be nice if there were power law X-ray vision glasses that helped you see when the bell-curve is not in charge. The closest thing I have found is Taylor Pearson’s essay about luck. This has been my go-to article on the 80/20 rule since people I share it with have felt the way the concepts are communicated with specific examples and charts made them stick.

Some of my favorite examples of power laws are city populations and the relative frequency of words we use in the English language.

If you want to dive deeper into power law math using venture capital returns as a case study, investor and professor Jerry Neumann has written a fairly accessible treatment.