  In particulate soft matter systems the average number of contacts $Z$ of a
particle is an important predictor of the mechanical properties of the system.
Using X-ray tomography, we analyze packings of frictional, oblate ellipsoids of
various aspect ratios $\alpha$, prepared at different global volume fractions
$\phi_g$. We find that $Z$ is a monotonously increasing function of $\phi_g$
for all $\alpha$. We demonstrate that this functional dependence can be
explained by a local analysis where each particle is described by its local
volume fraction $\phi_l$ computed from a Voronoi tessellation. $Z$ can be
expressed as an integral over all values of $\phi_l$: $Z(\phi_g, \alpha, X) =
\int Z_l (\phi_l, \alpha, X) \; P(\phi_l | \phi_g) \; d\phi_l$. The local
contact number function $ Z_l (\phi_l, \alpha, X)$ describes the relevant
physics in term of locally defined variables only, including possible higher
order terms $X$. The conditional probability $P(\phi_l | \phi_g)$ to find a
specific value of $\phi_l$ given a global packing fraction $\phi_g$ is found to
be independent of $\alpha$ and $X$. Our results demonstrate that for frictional
particles a local approach is not only a theoretical requirement but also
feasible.
