Epidemiology: Everything Turns on One Number Crossing One
If each case produces more than one further case, an outbreak grows; below one, it fades. That threshold is simple — and almost everything else about the subject is context-dependent.
Concept
Power Laws vs. Normal Distributions
Benford's Law: Why So Many Numbers Start With One
Around thirty per cent of numbers in real datasets begin with 1, and only five per cent with 9. People inventing figures don't reproduce that — which is how the pattern became an auditing tool.
The Central Limit Theorem: Why Bell Curves Are Everywhere
One die is flat. Ten dice added together make a bell curve. The shape is a property of adding independent things — which tells you exactly when to expect it and when not to.
The Law of Large Numbers: Small Samples Are Wild
Seven heads in ten flips is unremarkable; seventy thousand in a hundred thousand would be extraordinary. The same probability, different room for chance — with consequences most people miss.
The Pareto Principle: Your Effort and Your Results Are Not the Same Shape
A few pea pods produced most of Pareto's peas. The lopsidedness he kept finding everywhere contradicts a default we apply constantly — treating twenty tasks as twenty roughly equal things.
Bayes' Theorem: The 99% Accurate Test That Is Wrong 91% of the Time
A rare disease, a 99% accurate test, a positive result — and roughly a 9% chance you're ill. The gap comes from one number most people leave out entirely.
Survivorship Bias: The Bullet Holes That Weren't There
Wartime analysts mapped damage on returning bombers and proposed armouring the places full of holes. A statistician pointed out those were the survivable hits — and inverted the entire dataset.
Black Swan Events: The Model Was Never the Problem
Every observed swan was white until Australia. No amount of confirming evidence establishes a universal rule — and the most confident moment is often the one just before the record breaks.
Power Laws: When the Average Describes Nobody
The world's tallest person barely moves a room's average height. The world's wealthiest moves it by a factor of millions. Almost all statistical intuition is built for the first case.
Regression to the Mean: The Jinx That Is Just Arithmetic
Praise a great performance and the next is worse; criticise a bad one and the next improves. A flight instructor learned this lesson over years of observation — and it was never about motivation.
Startups: Most Advice Comes From the People It Worked For
Persistence and bold bets describe the founders who succeeded — and just as many who didn't, and aren't being interviewed. A structural view of these companies is more useful than the folklore.
Venture Capital: The Maths Only Works With Outliers
Most investments return little; one or two return the entire fund. Every practice in the industry that looks strange from outside is a rational response to that distribution.
Markets: A Price Is a Bet, Not a Measurement
A company posts record profits and the share price falls. That stops looking irrational once you see that a price already contains what everyone expected — and moves only on the difference.