Let A be a finite group (or a finite algebra), and ω be a word map (resp. polynomial map) on n many generators. We define the quantity |ω(A)|/|A| as the image ratio ofωonA and denote it by μ(ω,A). In this article, we investigate the set R(ω)={μ(ω,A):Ais a finite group}, and study the same for the case of rings. We demonstrate the existence of word maps whose set of image ratios is dense in [0, 1] for groups (and rings).