We need to let go of the Bell Curve

Most human activities as well as many disciplines — from physics and biology to linguistics, finance, and computer science — follow a Pareto distribution instead of a “normal” Gaussian curve. In Pareto distributions, a small change in one variable is associated with a large change in another, because it reflects variables multiplied with each other…

Most human activities, as well as many other disciplines, follow a Pareto distribution rather than a “normal Gaussian curve”. Pareto distributions show that a small change to one variable can be associated with a large change to another. This is because variables are multiplied rather than added together as in the normal distribution. This is sometimes called a “power law.” It is not an obscure intellectual point but has serious practical implications. This error means that our approach to most problems has been suboptimal. What does this all mean for business leaders? This author outlines three practical implications for innovation and risk management as well as people.

I recently had a conversation with one of our senior managers about our company’s new banking division; he told me that only 21% of our cardholders account for 80% of spending. This skewed situation concerned him greatly and he asked me what we could do for our lending portfolio to be more evenly distributed. I’ve had similar conversations with the fundraising manager of a nonprofit I chair: The bulk of the funding comes from some 20 donors, which she tells me is unsustainable. According to her, the organization is on its way to a cliff. These reactions point to a common cognitive error in leadership that is profoundly relevant to both of them.

Most people view the world as largely Gaussian. This means that most things should be distributed according to bell curves. This world would see most cardholders or donors spending or contributing close to the average. The remaining people would spread out symmetrically on either side of the average amount of money. The mode, median, average and mean would all be the same; half of the population would be below the average and the other half would be above it. Variables in this world are independent of each other and have no influence on one another.

Why are we so sceptical? Our brains are wired to seek fairness uplifting , and to be rewarding of inequality .. A Gaussian world with the majority of people clustered around a steady average feels predictable and fair. Symmetry is also a favorite feature of our world, whether it be in art, statistics, faces or art. Our schooling still relies on normal distributions and Newtonian thinking. This breaks down reality into independent variables, cause and effect. This way of seeing the world has permeated many disciplines from medicine and statistics to management .. There are phenomena that do indeed follow Gaussian distributions. For example, take test scores. The test scores (variables) are the result of additive processes (the sum total of each question’s scores).

I learned about many other statistical distributions while studying statistics and probability theory. However, I also believed that the majority of things follow a bell-shaped pattern.

But they don’t.

But they don’t. Let me tell it to you, and why it matters so much.

About 10 years ago, after reading about cognitive biases, I was surprised to find out that most human activities, as well as many disciplines — from physics and biology to linguistics, finance, and computer science — follow a Pareto distribution instead of a “normal” Gaussian curve.

In Pareto distributions (named after economist Vilfredo Pareto, who in the early 20th century observed that 20% of people in Italy owned 80% of the land), a small change in one variable is associated with a large change in another, because it reflects variables multiplied with each other rather than added to each other, as in the normal distribution. This is sometimes called a “power law” and it looks like a hockey stick. There are many observations with low values and few outliers.

Once you begin to look, you will see the pattern almost everywhere you go. Power laws govern everything from the frequency with which we speak, to the severity of hurricanes and earthquakes, to the size of cities and companies, and even the order in which countries win Olympic medals. Social media is no exception — for example, a U.S. study showed that just 25% of the most active Twitter users accounted for 97% of tweets. In our short-term insurance business, Discovery Insure, the worst 30% of drivers account for 60% of serious accidents. Covid-19 also spreads in a Pareto fashion: In two Indian states, 60% of new infections were found to be caused by less than 10% of people carrying the disease — a few “super-spreaders” — whereas another 71% did not infect anyone at all. This transmission pattern has also been observed in other countries. )

Why is Pareto the norm and not the Gaussian distribution “normal”? Even more important, is it getting more so? Because power laws are how interconnected complex systems work, most things follow them. Because our world is increasingly interconnected, power laws are more common. The power law is more prominent the more complex systems are interconnected.

Economies, supply chains and trade have become increasingly intertwined, globalized and global. The interconnection between the many systems we are part of has been exponentially enhanced by information technology and transport. These networks are dynamic and reliant on variables to influence each other. This creates cascading, reinforcing and cascading effects that are nonlinear and multiplicative and less predictable. These systems can even exhibit “black swan” behavior. This is because, unlike Gaussian distributions, Pareto distributions have a variance that measures how dispersed data points are from the mean.

These power laws are not only pervasive but also extremely stubborn. No matter what we do or how much we do it, only a few data points — decisions, people, and other observations — account for the majority of the results. Pareto is often a problem in political systems that are designed to increase income equality. China is an example of a country that, despite having a greater emphasis on income equality than other countries, has a higher GINI coefficient then Germany and the United Kingdom. Such distributions also repeat themselves like Russian dolls, as we see in our health insurance business: The sickest 20% of people generate 79% of health care costs, and the same skewed distribution can be found within that 20% group (with the sickest 20% within that group responsible for nearly 60% of health care costs). You’ll find that the majority of health care costs are borne by a small number of people if you continue to look at the numbers.

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This disconnect between our Gaussian perception and the Pareto reality is not an obscure intellectual point, but instead carries serious practical consequences. This error makes our approach to most problems suboptimal. Malcolm Gladwell, for example, has written about how the typical solutions meant to address homelessness — shelters and soup kitchens — have been ineffective because they’re based on the mistaken assumption that the majority of homeless people follow the average: average number of days without a roof, average cost per person to the public purse, or average reasons for being homeless. Homelessness is a power law on all of these dimensions. Philip Anderson, Nobel laureate physicist, said that we should let go of “average” thinking or focusing only on the mean. This is often misleading in most cases. This is illustrated by the joke that Bill Gates walks into any bar and everyone becomes a millionaire. While tails and outliers are often dismissed as aberrations they actually have the greatest impact, both good and evil. For example, a small viral event can turn into a worldwide coronavirus pandemic or economic disaster.

It can be difficult to accept that we live in a Pareto world, which is inherently unfair, asymmetrical, and unpredictable. However, systemic change in such an environment is easier and more efficient. For a Gaussian world to be able to change the whole system, all components must move. This is tedious, time-consuming and often impossible. A Pareto world on the other hand allows for a shift in the tail to change the whole system, whether it is better or worse.

What does all this mean for business leaders? These are the practical implications of this for people, innovation, and risk management.


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