  Currently, quantum scattering calculations cannot be used for quantitative
predictions of molecular scattering observables at ultralow temperatures. This
is a result of two problems: the extreme sensitivity of the scattering
observables to details of potential energy surfaces (PES) for interactions
between the collision partners, and the exceedingly large size of molecular
basis sets required for the numerically exact integration of the
Schr\"{o}dinger equation in the presence of external fields. Here, we suggest a
new statistical approach to address both of the above problems. We show that
ensembles of scattering calculations with different PESs are characterized by
cumulative probability distributions, which are insensitive to the size of the
molecular basis sets and can, therefore, be obtained from calculations with
restricted basis sets. This opens the possibility of making predictions of
experimentally relevant observables for a wide variety of molecular systems,
currently considered out of reach of quantum dynamics theory. We demonstrate
the method by computing the success probability of sympathetic cooling of CaH
and SrOH molecules by Li atoms and SrF molecules by Rb atoms.
