  We prove a general ergodic-theoretic result concerning the return time
statistic, which, properly understood, sheds some new light on the common sense
phenomenon known as {\it the law of series}. Let \proc be an ergodic process on
finitely many states, with positive entropy. We show that the distribution
function of the normalized waiting time for the first visit to a small cylinder
set $B$ is, for majority of such cylinders and up to epsilon, dominated by the
exponential distribution function $1-e^{-t}$. This fact has the following
interpretation: The occurrences of such a "rare event" $B$ can deviate from
purely random in only one direction -- so that for any length of an
"observation period" of time, the first occurrence of $B$ "attracts" its
further repetitions in this period.
