MD-type calculations required to sample energy gap fluctuations in the condensed phase to construct cumulant spectra are computationally expensive compared to calculations on simple model systems (generally requiring the computation of tens of thousands vertical excitation energies along the trajectories). Additionally, computing reliable third order cumulant corrections requires significantly more data than second order cumulant spectra, as two-time correlation functions of the energy gap have to be converged. Thus, there is merit in being able to predict the overall stability of the third order cumulant approximation based on statistics of energy gap fluctuations alone, which can be computed cheaply from preliminary data sets. If the skew and excess kurtosis of energy gap fluctuations of a molecule fall into a region of low confidence in Fig. , it can be concluded that expending the extra computational cost to construct third order cumulant corrections is unlikely to yield improved spectra. In other systems, specifically those with moderate positive skew in the energy gap fluctuations, we expect a prefactor-conditioned MD-based third order cumulant approach to yield improved lineshapes, both by removing unphysical negative spectral features and by improving the underlying vibronic fine-structure of the transition.