Nowadays, an increasing attention is being given to the study of the descriptional complexity on the average case. Although the underlying theory for such a study seems intimidating, one can obtain interesting results in this area without too much effort. In this gentle introduction we take the reader on a journey through the basic analytical tools of that theory, giving some illustrative examples using regular expressions. We finalize with some new asymptotic average case results for several epsilon-NFA constructions, presented in a unified framework.