  Let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic
numbers. A rational map $\phi\in K(z)$ of degree at least $2$ is subhyperbolic
if each critical point in the $\mathbb{C}_p$-Julia set of $\phi$ is eventually
periodic. We show that subhyperbolic maps in $K(z)$ exhibit expanding property
with respect to some (singular) metric. As an application, under a mild
assumption, we establish several statistical laws for such maps in $K(z)$ with
compact $\mathbb{C}_p$-Julia sets.
