  In the effective field theory framework the interaction between two heavy
hadrons can be decomposed into a long- and a short-range piece. The long-range
piece corresponds to the one-pion-exchange potential and is relatively
well-known. The short-range piece is given by a series of contact-range
interactions with unknown couplings, which substitute the less well-known
short-range dynamics. While the general structure of the short-range potential
between heavy hadrons is heavily constrained from heavy-quark symmetry, the
couplings are still free parameters. Here we argue that the relative strength
and the sign of these couplings can be estimated from the hypothesis that they
are saturated by the exchange of light mesons, in particular the vector mesons
$\rho$ and $\omega$, i.e. from resonance saturation. However, we propose a
novel saturation procedure that effectively removes form-factor artifacts. From
this we can determine in which spin and isospin configurations the low-energy
constants are most attractive for specific two-heavy-hadron systems. In general
the molecular states with lower isospins and higher spins will be more
attractive and thus more probable candidates to form heavy-hadron molecules.
This pattern is compatible with the interpretation of the $X(3872)$ and
$P_c(4312/4440/4457)$ as molecular states, but it is not applicable to states
with maximum isospin like the $Z_c(3900/4020)$.
