Law of (Truly) Large Numbers

The Law of Truly Large Numbers states that with a large enough sample, any outrageous thing is likely to happen. Given millions of events, million-to-one coincidences occur daily. This is not the standard Law of Large Numbers (which says averages stabilise); it's the observation that extreme events become expected when the number of opportunities is vast. For founders, the model is a calibration tool: "miraculous" customer stories, freak failures, and viral outliers aren't necessarily signal — they may be the statistically inevitable consequence of operating at scale. Don't over-index on extreme anecdotes when the denominator is large.

When you see an extreme event, ask: what's the denominator? At scale, million-to-one events happen. Don't build strategy around anecdotes when the sample is huge — look at rates, not raw counts. Use this to resist narrative fallacy: the "amazing" customer story or the "terrifying" failure may be statistically inevitable, not a sign that something is right or wrong. Signal lives in rate changes, not in individual extremes.

The Law of Truly Large Numbers: with enough observations, extreme events are statistically inevitable. Don't over-react to individual outliers at scale — track rates, not anecdotes. The question isn't whether extreme events happen, but whether the rate has changed.