Background: The process of β-delayed fission (βDF) provides a versatile tool to study low-energy fission in nuclei far away from the β-stability line, especially for nuclei which do not fission spontaneously. Purpose: The aim of this paper is to investigate systematic trends in βDF partial half-lives. Method: A semi-phenomenological framework was developed to systematically account for the behavior of βDF partial half-lives. Results: The βDF partial half-life appears to exponentially depend on the difference between the Q value for β decay of the parent nucleus and the fission-barrier energy of the daughter (after β decay) product. Such dependence was found to arise naturally from some simple theoretical considerations. Conclusions: This systematic trend was confirmed for experimental βDF partial half-lives spanning over seven orders of magnitude when using fission barriers calculated from either the Thomas-Fermi or the liquid-drop fission model. The same dependence was also observed, although less pronounced, when comparing to fission barriers from the finite-range liquid-drop model or the Thomas-Fermi plus Strutinsky integral method.