The Pareto Distribution: How To Use It To Leave A Mark On The World

Jake - Author/Founder

Jake - Author/Founder

Hi. I'm Jake. I believe you can build a wealthy life through frugal living and index investing.

I like to share helpful books on my blog. These are affiliate links, meaning I get a small commission at no cost to you if you click the link and buy a book. I only link books that I have read and found useful. 

  • In an organization of 10,000 people, about 100  people produce 50% of the organization’s value-added work 1.
  • At the time of writing, the largest 10 businesses make up 23% of the US Stock Market value2.
  • In 2016, the top 1% of US families owned 38.5% of US Wealth3

It’s no wonder that Vilfredo Pareto was curious about inequalities. They have been pervasive across time and cultures.

Many systems generate unequal “Pareto Distributed” outcomes, including financial markets, human competence, and populations of cities.

Even natural systems produce unequal outcomes. The size of lakes, planets, and galaxies are also Pareto-distributed.

The systems that produce these unequal outcomes have very specific characteristics. The characteristics are the same for systems driven by human behavior and systems driven by natural processes.

Understanding Pareto distributed systems will help you operate in non-linear environments.

This can help you add value to the world. And adding value to the world naturally increases your earning capacity. Plus, it laces life with meaning.

Finally, understanding these systems can help you build wealth within our non-linear financial markets via investing.

At the end of the article, I share specific tips that will improve your competence and make you a better investor

Table of Contents

What Is The Pareto Distribution

The Pareto distribution is also known as a power-law distribution or the 80/20- rule. 

In such systems, a small number of “causes” are responsible for most of the “outcomes”.

It looks like this.  

Pareto Distribution Plot: Causes vs. Outcomes

The 80/20 rule advises that 20% of causes produce 80% of outcomes. This 80/20 rule is slick and shows the inequality in cause and effect. 

But this ratio si not always the same. Some systems produce more unequal outcomes than others. 

For example, 5% of causes can be responsible for 99% of outcomes.

I show a  variety of examples of Pareto distributed systems below to show this effect.

Systems With Pareto Distributed Outcomes

Many systems have Pareto distributed outcomes. Here’s what I found, starting with systems related to wealth.

First, I’ll start with stocks. A small number of stocks make hold most of the US market wealth.

At the time of writing, these top 10 companies make up 24% of the value of the US market. For context, there are over 4000 US businesses listed on the US market. 

US Stock Market Share In December 2022 - Pareto Distributed

Similarly, you can see that a small number of countries hold all the wealth.

If you zoom into any specific country, you will see that wealth is Pareto distributed across individuals within that country. Pareto-distribution of wealth repeats at different scales, displaying fractal tendencies. 

Pareto Distributed Wealth Across Countries in 2022

Even in the domain of billionaires, we can see a Pareto distribution, although it’s a bit flatter. Even within the top 1%, a small number of people hold most of the wealth.  

Pareto-distributed outcomes don’t just arise in financial systems. They occur in other human and natural domains as well. 

For example, you can see that most of Canada’s population is concentrated in a small number of cities. 

A larger city attracts more people due to economic output and the scale of the economies. 

As more people are attracted to the city, the population size grows further. This attracts even more people. The cycle repeats. 

Pareto Distribution of City Sizes

I even experience the Pareto distribution on my blog. A small number of blog posts generate most of my traffic. 

A good post will get some traction in Google and will rank better. A better ranking means more traffic, and more traffic means more links back to the post.  

More quality backlinks mean even better Google Rankings, further influencing the cycle. Post traffic is a positive feedback loop, resulting in non-linear exponential growth.  

Blog Traffic Pareto Distribution

Planet mass is also strongly Pareto distributed. A small number of planets hold most of the planetary mass. Jupiter is huge and holds most of the planetary mass in our solar system. 

Planets initially start off as a small collection of dust/rocks. As the collection grows, the gravitational pull increases. The mass (planet) attracts more dust/rocks, further increasing the gravitational pull.

This positive feedback loop of planet growth is a non-linear, exponential process. 

Pareto Distribution of Planet Sizes

 Here is a distribution of lake size by surface area. A small number of lakes hold most of the water

I don’t know exactly how lakes form, but I bet you it involves non-linearities and positive feedback. 

Pareto Distribution Of Lake Sizes

Here are more systems that are Pareto distributed. I’m getting tired of making excel graphs. Here is a list: 

  • Price’s Law states that 50% of the work in an organization is done by the square root of the number of people in that organization. In an organization of 10,000 people, about 100 will do half the work.  
  • A tiny number of authors sell all the books.
  • A small number of songs are responsible for most of human music listening time.
  • A small number of blogs get most of the traffic. 
  • A small number of people in an organization generate most of the personnel problems. 

These are all macro effects, and you may be wondering, how do they apply to me as an individual?

I cover this below, but first, let’s examine the traits of systems that lead to Pareto-distributed outcomes. 

What Leads To Pareto Distributed Outcomes?

Systems that grow exponentially produce Pareto-distributed outcomes. Planets, stocks, wealth, and author popularity fall within this category 

In such systems, small changes in initial conditions balloon to become massive changes later on. With time, effects are magnified.  

Wealth begets more wealth, as money grows exponentially. 

How-Intuition-Thinks-Money-Grows

You can also go in the opposite direction, where debt begets more debt.

A small decision to take out a $10,000 loan or to invest $10,000 shows you how exponential growth amplifies bad decisions as well. 

Compound-Growth-

Example: Small Changes, Big Difference

The power of small decisions in non-linear systems is most evident in investing. Therefore, I must provide an example.

Consider two people, Person A, and Person B, with the same income.

The only difference is that Person A makes lunch every day. Person B buys lunch every day.

Through meal prep, Person A saves an additional $10 per day, or $200/month (20 working days) relative to Person B.

Further, Person A decides to invest this money in stocks, achieving a 10% annual return.

 Monthly InvestmentEnd Wealth, Year 40
Lunch Maker (Person A) $200$1,265,000
Lunch Buyer (Person B) $0$0

A single habit to make lunch at home and investing in a total market index fund gave Person A $1,265,000 in extra wealth over person B.  

In non-linear systems, small decisions result in large inequalities over time. It’s almost time to show how you can operate to benefit from Pareto-distributed environments.

But first, I want to discuss the fractal nature of Pareto distributed systems.

Repetition At Scale: Fractals and Pareto Distributions

Many Pareto distributions are also fractal in nature. This is a fancy way of saying that Pareto distributions repeat at various scales. 

A fractal is a shape or characteristic that generates self-similarity across various scales.

No matter how far you zoom in, you see the same pattern emerge

Shorelines, snowflakes, wealth distribution, and workload distributions have fractal characteristics. Here is a visual example of a famous fractal called the Mandelbrot set.  

You may be thinking, Jake must be on some really good drugs. I assure you this is not the case. Fractal distributions are simply interesting facets of nature.

But how does the concept of fractals apply to Pareto distributed systems?

In an economy, a small number of businesses add most of the economic value. A Pareto distribution. Let’s zoom into one of these organizations.

Once inside, you find another Pareto distribution amongst employees. A small number of people are doing most of the work as per Price’s Law. 

Now, zoom into the specific tasks of one of these hyper-productive employees. A small number of their tasks generate most of their results.

A similar fractal effect occurs when you look at the size distribution of galaxies, stars, planets, and moons based on the non-linear effects of body formation.

This is the end of my curiosity-driven insert on fractals in relation to Pareto distributed systems.

Now let’s transition to see how you can use knowledge of Pareto distribution to your benefit. 

Top 8 Books To Build Wealth

How To Use The Pareto Distribution To Make An Impact On The World

You can exploit the nature of these non-linear systems to provide more value to others. 

By providing value to others, you enhance your sense of purpose and you also increase your earnings capacity (human capital)

First, purpose and meaning critical parts of human well-being.

Second, the capitalist system, when working properly, rewards those who provide value to others. Therefore, making an impact should be financially rewarding. 

Here are 4 main takeaways that you can use to thrive in non-linear,  Pareto distributed systems.  

1. Understand That A Small Number Of Tasks Drive Most Of Your Results

Based on the 80/20 rule (of thumb), 20% of your tasks produce 80% of your outcomes.

Warren Buffet has a system to take advantage of this effect. 

His system enables focus on the right things. First, Buffet lists the top 25 things he needs to do in order of priority. 

Then, Buffett cuts out the bottom 20 tasks completely. He doesn’t work on them at all. Zero. 

Instead, 100% of his focus is allocated to the top 5 tasks. Those top 5 tasks are responsible for nearly all of his outcomes. 

Perhaps this is why they say the A students work for the B students. I suspect some B students are aware of the cause-and-effect relationships between their efforts and outcomes.

Maybe the B students just focus on the right things?

By cutting out the non-essential tasks, you will reduce stress, improve focus and maximize success.  

2. Know That Knowledge Compounds

My perspective on learning completely changed after I read the book How To Take Smart Notes.  

Before reading this book, I looked at learning as the memorization of raw information.

But now I look at learning differently. I view learning as the capacity to connect new information to previously understood topics and concepts.

The stronger your pre-existing foundation of knowledge, the easier it is for you to learn new things.

The more you know, the faster you can learn. Therefore, learning is non-linear. Knowledge grows exponentially. 

You can use this to your advantage by setting a habit of continuously learning. Spending an extra 15 minutes learning every day can result in huge changes over time. 

The compounding effect of learning must be why a small number of people pump out most of the work.

Consistent learning can help you become one of those people if you aren’t already.  

3. Know That Habits Compound

Once you learn a habit, it becomes autonomous. It runs in the background with limited demands on your self-discipline.

That gives room to develop new habits. The new habits layer on top of the old ones and generate a (non-linear) compounding effect.

Hence, why I agree with James Clear when he states that “Habits Are The Compound Growth of self-improvement”. This is a core theme of his book Atomic Habits.

Small changes in habits can have huge effects on long-term outcomes, especially when it relates to sleep, exercise, nutrition, and learning. 

4. See Why Persistence and Self-Discipline Are Critical

A small number of people have all the success in domains that scale, like books, blogs, and companies.

Often, there are low barriers to entry in these scalable domains. Most people fail, and the few who are successful often undergo years of nothingness before the compounding starts to pay off.

This explains why most people quit blogging after 3 months. It can take up to a year for traffic. I’m two years deep and only see 2,000 views per month.  

Those who persist through hardship will be rewarded in the long term. Therefore, persistence and self-discipline are critical to be successful in these scalable systems that undergo exponential growth.

How The Pareto Distribution Can Make You A Better Investor

Stock returns and stock size are both Pareto distributed.

This offers helpful insights to guide investing decisions. For me, the Pareto distributed nature of stock returns is one of the key reasons why I like index investing. 

Skewed Stock Returns

Stock returns are skewed, meaning a small number of stocks are responsible for all of the stock market’s returns.

This study finds that “the top-performing 1.3% of global firms account for the $US 44.7 trillion in global stock market wealth creation from 1990 to 2018”.

You may say, why not just invest in these 1.3% of stocks that are doing well?

Once this 1.3% of stocks explode into large businesses, they rarely continue to beat the market. A new set of stocks takes over to produce the market’s returns.

The best-performing stocks have high churn. To capture these returns, you must detect the company before they undergo explosive growth. This proves difficult due to market efficiency. 

To see the churn in action, you can compare the top 10 Fortune 500 companies in the year 2002 with the top 10 Fortune 500 companies in 2022.

Over the past 10 years, only two businesses held up as the top 10: Walmart and Exxon. The rest were replaced.

My solution to this issue is simple. I hold all stocks in a stock market with a total market index fund. This way, I am guaranteed to capture the returns from the small number of stocks that make up the market’s returns. 

Market Cap Weights Are Pareto Distributed

As an informed investor, it is nice to know that a large fraction of your investment dollars are concentrated in a small number of businesses (stocks). 

The size of stocks (market cap) is Pareto distributed because businesses grow exponentially. 

For example, the US total market index fund VTI holds 4,000 stocks. At the time of writing, the top 10 stocks make up 24% of the index. When you invest $10,000 into VTI, $2,400 is concentrated in the top 10 companies (source). 

And since an index fund is market cap weighted, a small number of businesses make up most of the index.

Even if you invest in mutual funds, it’s likely that most of the invested dollars are concentrated in a small number of stocks within that fund. 

Compound Growth Magnifies The Outcomes Of Today's Actions  

Now you know that small changes in invested amounts cascade into large changes in the end wealth. 

This is why wealth inequality is so much bigger than income inequality. Wealth compounds whereas income grow more linearly.

A moderate earner who lives frugally and invests will have far more wealth than a high earner who spends lavishly. 

Understanding compound growth incentivizes frugal living.  Leasing that BMW car is not just $750/month, it’s $750 that can no longer be invested for growth. This costs you $1.7M over 30 years. 

Knowledge of how money grows will enable you to envision the future cost of today’s spending. 

Conclusion

Understanding Pareto distributed systems can help you leave a mark on the world. 

  • Small daily efforts to improve knowledge and habits will make you a machine in the long run. 
  • A small number of your actions generate most of your outcomes. Focus on these actions. 
  • Wealth scales far faster than income. Small investing decisions have huge effects on end wealth over time. 
  • A tiny number of companies make up most of the stock market’s returns. These companies are hard to find ahead of time. 

I’ll end with a note on fairness. I’m not here to judge if Pareto distributed outcomes are fair or unfair.

All I know is that Pareto distributions are normal in systems that undergo compound growth. 

Understanding Pareto distributed systems can help you gain from these systems, rather than become resentful of those who excel in such systems. 

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