The power threshold (PThresh) to access the H-mode in tokamaks remains a subject of active research, because up to now no theoretical relation has proved to be general enough to reliably interpret the L–H transition. Over the last few decades, much effort has therefore been devoted to deriving empirical scalings, assuming 'a priori' a power-law model structure. In this paper, an empirical scaling of PThresh without any a priori assumption about the model structure, i.e. about the functional form, is derived. Symbolic regression via genetic programming is applied to the latest version multi-machine International Tokamak Physics Activity International Global Power Threshold Data Base of validated ITER-like discharges. The derived model structure of the scaling for the global database is not in a power law form and includes a term that indicates saturation of PThresh with the strength of the toroidal field, plasma density and elongation. Furthermore, the single machine analysis of the database for the most representative machines of the international fusion scientific program demonstrates that the model structures are similar but the model parameters are different. The better extrapolation capability of the identified model structures with the proposed methodology is verified with a specific analysis of JET data at two different current regimes. The PThresh values extrapolated to ITER using the derived empirical model structures are a factor of two lower than those of traditional scaling laws and are predicted with a significantly better confidence.