  Recently, Defant and Propp [2020] defined the degree of noninvertibility of a
function $f\colon X\to Y$ between two finite nonempty sets by
$\text{deg}(f)=\frac{1}{|X|}\sum_{x\in X}|f^{-1}(f(x))|$. We obtain an exact
formula for the expected degree of noninvertibility of the composition of $t$
functions for every $t\in \mathbb{N}$. An equivalent formulation for the
definition of the degree of noninvertibility is then the starting point for a
generalization yielding a seemingly new combinatorial identity involving the
Stirling transform of the signed Stirling numbers of the first kind.
