  Dynamical four-point susceptibilities measure the extent of spatial
correlations in the dynamics of glass forming systems. We show how these
susceptibilities depend on the length scales that necessarily form part of
their definition. The behaviour of these susceptibilities is estimated by means
of an analysis in terms of renewal processes within the context of dynamic
facilitation. The analytic results are confirmed by numerical simulations of an
atomistic model glass-former, and of two kinetically constrained models. Hence
we argue that the scenario predicted by the dynamic facilitation approach is
generic.
