You've (Likely) Been Playing The Game of Life Wrong

Normal distributions cluster data around an average value, but power laws show a different pattern where extreme outliers occur far more frequently than expected.

• Human height follows a normal distribution with a clearly defined average • Income distribution follows a power law with a broad range spanning orders of magnitude • War deaths follow power law distributions

Power laws span several orders of magnitude where some people earn 5, 10, or even 100 times more than others, which would be physically impossible in a normal distribution.

This common phenomenon appears in nature across diverse systems, suggesting an underlying principle that governs how certain systems organize themselves.

Italian engineer Vilfredo Pareto discovered a hidden pattern in how much money people make by analyzing income tax records from Italy, England, France, and other European countries.

When plotted on a log-log scale, income distribution transforms from a broad curve into a straight line with a gradient of negative 1.5, revealing the underlying power law.

The number of people earning an income greater than or equal to X is proportional to one over X to the power of 1.5, and this pattern holds across multiple countries.

Pareto's discovery showed that power law relationships describe income distributions consistently across nations, establishing this as a fundamental economic pattern that persists to this day.

100 coin tosses with $1 payout per heads. Expected payout is $50, demonstrating normal distribution principles where the average remains predictable.

Starting with $1, multiply by 1.1 on heads and 0.9 on tails over 100 tosses. Expected payout is $1, but median payout is only 61 cents, creating a log-normal distribution.

Double payout for each toss until heads appears. Theoretical expected value is infinite because extreme outcomes like a million dollar payout, though unlikely, contribute significantly to the average.

Games one and two have measurable standard deviations, but game three (St. Petersburg paradox) produces a power law with infinite standard deviation, making it fundamentally different from normal distributions.

Power laws lack measurable width with infinite standard deviation. When you average random samples repeatedly, the average keeps growing instead of converging to a stable value.

Extreme outliers occur frequently enough that occasional measurements of whopping big events totally skew the average, like standing in a room with Bill Gates or Elon Musk.

Power laws emerge when two exponentials dance together - an exponential growth in payout combined with exponential decay in probability creates the power law relationship.

• One outlier can dominate the entire average • Systems appear unpredictable due to heavy tail effects • Cannot rely on past averages to predict future outcomes

Small earthquakes are very common, but earthquakes of increasing magnitudes become exponentially rarer.

Destruction is proportional to the energy released, not magnitude. Energy grows exponentially as earthquake magnitude increases.

Combining exponential decay in frequency with exponential increase in energy eliminates magnitude and produces a power law in energy distribution.

The fractal-like patterns appear in veins on leaves, river networks, blood vessels in lungs, and lightning, all describable by power laws.

At low temperatures, magnetic moments align in large domains. Heating causes vibrations that flip moments up and down, breaking alignment and eliminating the net magnetic field.

The critical point occurs at the Curie temperature where the magnet balances between magnetic and nonmagnetic states, revealing fascinating self-similar fractal patterns.

At the critical point, domains exist at all sizes from tens to millions of atoms with no inherent scale, creating fractal patterns and power law distributions.

Local influences chain together like rumors spreading through crowds, expanding the range of influence until at the critical point it becomes effectively infinite, allowing single flips to cascade throughout the material.

Unlike magnets that must be painstakingly tuned, forests naturally drive themselves to criticality through a feedback mechanism where fires burn trees and forests regrow.

• Most fires burn 10 or fewer trees • Less frequently, fires consume fewer than 100 trees • Rarely, massive fires reverberate throughout the entire system

Each fire is caused by a single lightning strike, so large fires are not caused by special events but are magnified versions of small ones driven by the critical state.

The 1988 Yellowstone fire burned 1.4 million acres, 70 times the previous record and 50 times the area of all fires over the previous 15 years combined.

The US Forest Service 1935 10:00 AM policy mandated suppressing every fire by 10:00 AM the next day, which seemed logical but proved extremely risky.

Preventing small fires allowed fuel buildup, creating conditions for catastrophic megafires rather than preventing fires entirely.

• Allow most small fires to burn naturally • Intervene only when necessary • Intentionally create small fires to reduce buildup

After a century of fire suppression, it could take years to return the forest to its natural state through proper fire management practices.

Stresses build up slowly as tectonic plates rub against each other, with most time showing ground movement of just a fraction of a millimeter.

Random movements can trigger powerful chain reactions where stress propagates to the next section of a fault and then the next.

On January 17, 1995, stress near the Nojima fault line cascaded along 40 kilometers of crust, shifting ground by up to two meters and releasing energy equivalent to numerous atomic bombs.

The physical process behind earthquakes produces events ranging across enormous scales, following the exact same mechanism regardless of size.

Per Bak's 1987 thought experiment involved dropping grains of sand on a grid until grains tumble down, creating avalanches of various sizes.

The distribution of avalanche sizes follows a power law, with the same behavior resembling both forest fires and real earthquake energy distributions.

The sandpile naturally tunes itself to the critical state, starting with super tiny avalanches and gradually building complexity until displaying fractal patterns.

Per Bak demonstrated that self-organized criticality is a universal mechanism for generating power laws across different systems, even though real sandpiles don't actually follow this model.

At the critical point, almost none of the physical details about a system matter to how it behaves - different systems exhibit identical universal behavior.

• Some systems require tuning like magnets at Curie temperature • Others self-organize to criticality like forests and earthquakes • Understanding one system reveals how all systems in that class behave

Even the crudest simplest toy models can effectively describe incredibly complex systems because of universality principles.

Power law behavior appears in DNA sequencing, species distribution, mass extinctions, city populations, stock price fluctuations, scientific citations, and war deaths.

Power law systems lull you into false security because you see small events most of the time, making you think you understand how things work.

Insurance companies must charge enough to cover the large rare events, but predicting these extreme events in power law systems is extremely difficult.

The 2018 Paradise, California forest fire became the deadliest and most destructive in state history, exceeding the reserves of insurance company Merced Property & Casualty, which went bust.

Extreme events are much more common than you would think based on normal distribution thinking, requiring fundamentally different planning and preparation strategies.

Between 1985 and 2014, Horsley Bridge invested in 7,000 startups with over half losing money, but the top 6% returned more than 10x and generated 60% of total profit.

Y Combinator calculated that 75% of their returns came from just two out of 280 investments, demonstrating how few outliers carry entire performance.

• Most book titles flop • Bloomsbury's 1997 bet on Harry Potter became a global brand success • Streaming platforms: Netflix top 6% shows account for over 50% of viewing hours

Less than 4% of videos ever reach 10,000 views, but those videos account for over 93% of all views on the platform.

Restaurants and airlines operate under normal distribution principles, needing to fill seats and tables consistently because you cannot squeeze a million passengers onto one plane.

Industries like venture capital, publishing, and streaming rely on rare runaway hits, so the entire game is defined by outliers rather than average performance.

When switching from normal distribution to power law systems, you must act vastly different - from emphasizing consistency to pursuing intelligent risk-taking.

• Normal world: consistency and reliability are important • Power law world: persistence matters more than consistency • Taking riskier bets hoping for one huge payoff becomes rational

Albert-László Barabási discovered that webpage connections follow a power law distribution, with a few sites like Yahoo having thousands of times more connections than most others.

New sites are more likely to link to well-known pages, creating a preferential attachment pattern that generates power laws as the network grows.

Starting with a few nodes and adding new nodes with preference for highly-connected ones produces a power law with gradient negative two, matching real internet data.

Early action provides snowball effects - the more successful or well-known you are, the more likely you are to become more successful, creating runaway effects where few entities dominate.

The number of world wars measured by deaths follows a power law virtually identical to stock market crash distributions.

• War outcomes follow power laws like natural systems • Stock market crashes show identical patterns • Humans are subject to same physical laws despite intelligence and free will

The world operates in a critical state where two identical grains of sand or identical actions can have wildly different effects.

Most things barely move the needle but a few rare events totally dwarf the rest, making the world shaped fundamentally by power laws.

Pursuing areas governed by normal distribution pretty much guarantees average results, while selecting pursuits ruled by power laws requires different strategies.

• In power law worlds, goal is not to avoid risk but to make repeated intelligent bets • Most bets will fail • Only one wild success needs to pay for all the rest

Before making bets, you cannot know which will succeed because the system is maximally unpredictable - your next bet could do nothing, a little, or transform your entire life.

Casper emailed Derek with a research offer after reading about life-changing ideas. After four weeks of silence, received an unexpected freelancer opportunity that launched his Veritasium career.