Law of small numbers
Wrongly expecting even tiny samples to mirror the whole population.
What it means
The 'law of small numbers' is the mistaken intuition that small samples are highly representative of the population they are drawn from — a misapplication of the genuine law of large numbers, which only guarantees convergence as sample size grows large. Because people expect a handful of observations to reproduce the parent distribution, they read random fluctuation as meaningful signal, over-infer from anecdotes, and trust patterns that rest on far too little data. The mechanism is the representativeness heuristic: a short sequence that 'looks random' or fits a story is treated as informative, while the wide variability inherent in small samples is ignored. A key consequence is that extreme outcomes are far likelier in small samples, so the highest- and lowest-performing schools, hospitals, or regions are disproportionately small ones — a fact routinely misread as evidence that smallness causes excellence. It matters because it leads managers, scientists, and investors to chase noise, abandon sound strategies after a brief unlucky run, and design underpowered studies whose 'findings' will not replicate.
Examples
A manager promotes a sales tactic company-wide after three strong months from one small team, mistaking a short lucky run for a durable edge.
A hospital delivering twelve babies a month is far likelier to record a week of all boys than one delivering two hundred — pure sample size, read as something meaningful.
A parent switches schools because the tiny village primary tops the exam league table; the smallest schools also crowd the bottom of that table, which is the giveaway.
First described in Tversky & Kahneman (1971).