Field Evidence on the Law of Small Numbers

Abstract

The law of small numbers is the fallacious belief that even small samples should closely resemble the parent distribution from which the sample is drawn. It is expressed through two opposite behaviors; the hot hand fallacy and the gambler’s fallacy. Both have been demonstrated to exist in many dierent settings in previous research. Little empirical attention, however, has been given to study the link between the biases. The new data set acquired for this study allows a considerably more thorough analysis than seen in earlier studies. The results confirm earlier findings that hot hand- and gambler’s fallacy behavior is prevalent among Lotto players; although it appears to be concentrated within a relatively small group. For the first time in field data this study shows evidence indicating that the two biases are not mutually exclusive, but depend on the time-horizon in the way predicted by recent behavioral theory. Further, I find that biased players gamble more, and there are weak indications that women and the elderly are more often biased.