Let $\mathfrak{X}$ be a strongly nondegenerate strictly polystable formal scheme with associated skeleton $\Delta$ and $f\in\mathcal{O}(\mathfrak{X}^{\textup{an}})$ such that $\left\{x\in\mathfrak{X}^{\textup{an}}\;\Big|\;f(x)=0\right\}$ is nowhere dense. Then for any $x\in\Delta$ we have $|f(x)|\neq 0$ and the function $\varphi:\mathfrak{X}^{\textup{an}}\rightarrow\mathbb{R}\cup\{-\infty\}$ given by $\varphi(x):=\log|f(x)|$ is piecewise affine linear and convex on each face of $\Delta$ and satisfies $\varphi\leq\varphi\circ p_{\mathfrak{X}}$.