The Law of Large Numbers

What The Law of Large Numbers means

The law of large numbers says that the average of many independent observations settles toward the true rate as the observations pile up, while the average of a few can land almost anywhere. That is the whole statement. Owning it changes how we read every figure that arrives with a story attached. We stop treating a number as a value and start treating it as a value and a count, because without the count the value cannot be read. We expect the most extreme results we ever meet to come from the smallest groups, and we check the group before we admire the result. Before, a perfect score felt like proof. After, a perfect score from three cases is the cheapest kind of number there is, and a slightly worse score from thousands is the one that will still be true tomorrow.

The Law of Large Numbers examples: where it shows up

• At work: a new hire closes three of their first four deals and is called a natural; a year on they sit at the team average, like most people who start with a lucky run.
• With money: a fund that beat the market for two years is sold on that record, when two years of returns is a sample in which luck alone produces plenty of winners.
• In the news: the places with the highest and the lowest rates of a disease are both small towns, because one case moves a small town's rate a long way.

Where it sits

Open to walk. See where The Law of Large Numbers sits on the sky →

Nearest on the sky

• Bayes' Theorem
• The Equal-Odds Rule
• Ergodicity
• Gambler's Fallacy
• Kelly Criterion
• Recency Bias

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