The observation that people often believe things because many other people believe them is known as the bandwagon effect or the herd effect. The bandwagon effect is partially responsible for the seemingly unstoppable increase in prices at the end of a price bubble. People who fall under the spell of the law of small numbers believe that a small sample closely resembles the population from which it is drawn. The term is taken from the statistical law of large numbers, which shows that a large sample drawn from a population does closely resemble the population from which it is taken. This law is the basis of all polling. A sample of 500 taken randomly from a larger population can give very good estimations for a population of 200 million or more people. In contrast, very small samples do not reveal much about the underlying population. For example, if a trading strategy works four times out of a test of six times, most people would say the strategy is a good one, whereas statistical evidence indicates that there is not enough information to draw that conclusion with any certainty. If a mutual fund manager outperforms the indexes three years in a row, he is considered a hero.
Unfortunately, a few years of performance says very little about what the long-term expectations might be. Belief in the law of small numbers causes people to gain and lose too much confidence too quickly. When combined with the recency effect and outcome bias, it often results in traders abandoning valid approaches just before those approaches start working again.