We consider generic translation surfaces of genus $g>0$ with marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order $d$. Given a translation surface, the number of cylinders with waist curve of length at most $L$ grows like $L^2$. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by $L^2$, the limit as $L$ goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points $n$. All necessary background will be given and a connection to combinatorics will be presented. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.