I'm teaching a course on population genomics using the book Molecular Population Genetics by Matthew W. Hahn. In said book, the first mention of the Watterson Estimator appears in Chapter 3 in the classical form \theta =4N_{e}\mu ( N_e= the effective population size and \mu = per-generation mutation rate of the population).

My students asked how to interpret this equation and, specifically, where does the 4 come from.

I know that this equation is derived from the coalescent and it will become clearer for them once we get to that topic. The coalescent nonetheless comes in chapter 6 and is reserved for a latter class.

Is there an intuitive way to explain \theta =4N_{e}\mu that doesn't require going into the coalescent?