To perform a data-driven analysis, we extended the QM7-X database with functional group labels and accurate polarizabilities to explain the physical cause of this phenomenon. Our results demonstrate that the atomic composition has a major role in determining polarizability, while the arrangement of these atoms into chemical functional groups dictates the HOMO-LUMO gap. The physical origin of molecular polarizability was elaborated by studying conceptual models as well as interpreted with the help of a first order linear atomic additive model. Finally, the "freedom of desing" arising from the interaction of HOMO-LUMO gap and polarizability was used on the example of organic photodetectors, demonstrating that the electrochemical properties of such molecules can be freely tailored even with specific requirement on the optical properties. The theoretical insights gained from this work can give the basis for expanding the understanding of the relationship between HOMO-LUMO gap and polarizability by incorporating additional descriptors such as molecular size and electronic mobility. Additionally, the unraveled "freedom of desing" could be applied to the development of new compounds with tailored optical and electronic properties for use in applications such as organic electronics, sensing or energy harvesting.