  If $A$ is a finite group (or a finite ring) and $\omega$ is a word map (or a
polynomial map), we define the quantity $|\omega(A)|/|A|$ as the image ratio of
$\omega$ on $A$ and will be denoted by $\mu(\omega,A)$. In this article, we
investigate the set $\mathrm{R}(\omega)=\{\mu(\omega,A) : A \text{ is a finite
group}\}$, and also consider the case of rings. Specifically, we demonstrate
the existence of word maps (and polynomial maps) whose set of image ratios is
dense in $[0,1]$ for both groups (and rings).
