Recently, Defant and Propp defined the degree of noninvertibility of a function between two finite nonempty sets by . We obtain an exact formula for the expected degree of noninvertibility of the composition of functions for every . Subsequently, we use the expected value to quantify a strengthening of a sort of a submultiplicativity property of the degree of noninvertibility. Finally, we generalize an equivalent formulation of the degree of noninvertibility and obtain a combinatorial identity involving the Stirling numbers of the first and second kind.