  For a finite group $G$ and a non-negative integer $d$, denote by
$\Omega_d(G)$ the number of functions $G^d\rightarrow G$ that are induced by
substitution into a word with variables among $X_1,\ldots,X_d$. In this note,
we show that nilpotency of $G$ can be characterized through the asymptotic
growth rate of $\Omega_d(G)$ as $d\to\infty$.
