Law of large numbers
Big samples converge on the true mean. Small samples lie.
Toss a fair coin 10 times and you might easily get 7 heads. Toss it 10,000 times and you'll be close to 5,000 heads. The law of large numbers is the formal version of this intuition: as sample size grows, the observed mean converges on the true mean.
The bias is what happens at small sample sizes. People draw confident conclusions from a handful of data points, then are surprised when the pattern doesn't hold at scale. "This sales rep has closed 4 of 5 deals, we should hire 50 like them." Maybe. Or maybe 5 deals is too few to know anything.
For operators, the practical version: be very cautious about claims based on small samples. The minimum N for a stable observation depends on the variance of the underlying phenomenon, but most business claims are made on N's at least 10x too small.
Examples in the wild
A/B tests with small sample sizes routinely produce "results" that don't replicate. Companies that don't enforce statistical discipline make wrong product calls regularly.
Fund managers with three years of outperformance often look skilled. Three years is a tiny sample. Many "hot hands" reverse in the next three years.
Anecdotes from a few friends about a product, a doctor, a contractor are weak evidence. The truth shows up only at larger N's.
Law of large numbers is one of the mental models we apply through real cases inside the Pareto MBA — a part-time program for professionals who want to think clearly about business.