If $({\mathscr{X}},{\mathscr{L}})$ is an algebraic ${K^{\circ}}$-model of $(X,L)$ as in 2.1, then we get an associated algebraic metric ${\|\hskip 4.30554pt\|}_{\mathscr{L}}$ on ${L^{\rm an}}$ by using the above construction for the formal ${K^{\circ}}$-model $(\hat{{\mathscr{X}}},\hat{{\mathscr{L}}})$ of $({X^{\rm an}},{L^{\rm an}})$ from Remark 2.3. By construction, every algebraic metric is a formal metric. The converse is also true as shown in [GK14, Proposition 8.13] (as the argument does not use the assumption that $K$ is algebraically closed).