Non-fullerene acceptors (NFAs) are excellent light harvesters, yet the origin of their high optical extinction is not well understood. In this work, we investigate the absorption strength of NFAs by building a database of time-dependent density functional theory (TDDFT) calculations of similar to 500 pi-conjugated molecules. The calculations are first validated by comparison with experimental measurements in solution and solid state using common fullerene and non-fullerene acceptors. We find that the molar extinction coefficient (epsilon(d,max)) shows reasonable agreement between calculation in vacuum and experiment for molecules in solution, highlighting the effectiveness of TDDFT for predicting optical properties of organic pi-conjugated molecules. We then perform a statistical analysis based on molecular descriptors to identify which features are important in defining the absorption strength. This allows us to identify structural features that are correlated with high absorption strength in NFAs and could be used to guide molecular design: highly absorbing NFAs should possess a planar, linear, and fully conjugated molecular backbone with highly polarisable heteroatoms. We then exploit a random decision forest algorithm to draw predictions for epsilon(d,max) using a computational framework based on extended tight-binding Hamiltonians, which shows reasonable predicting accuracy with lower computational cost than TDDFT. This work provides a general understanding of the relationship between molecular structure and absorption strength in pi-conjugated organic molecules, including NFAs, while introducing predictive machine-learning models of low computational cost.