which surfaces the associated Teichmüller space is hyperbolic. The relationship between the pants graph and Teichmüller space has been used to study volumes of 3-manifolds [@Brock-WPtoPants; @Brock-WPtrans]. In particular, it has been used to relate volumes of the convex core of a hyperbolic 3-manifold to the distance of two points in Teichmüller space. It has also related the volume of a hyperbolic 3-manifold arising from a psuedo-Anosov element in the mapping class group to the translation length of the psuedo-Anosov element as applied to the pants graph. Both of these relations have constants which depend on the surface; this paper is the start of effectivising those constants. Notice Aougab, Taylor, and Webb have some effective bounds on the quasi-isometry bounds, however even these still depend on the surface in a way that is unknown [@ATW].

Let $S_{g,p}$ be a surface with genus $g$ and $p$ punctures. We define the complexity of a surface to be $\xi(S_{g,p}) =3g + p - 3 $. Brock and Farb have shown that the pants graph is hyperbolic if and only if the complexity of the surface is less than or equal to $2$ [@BF]. Brock and Masur showed that in a few cases the 