The behaviour of the turbulence in magnetic fusion plasmas is discussed in the framework of dimensional analysis. Three main dimensionless parameters are identified, which directly affect the adiabatic response of the plasma and hence control the electron response. They were originally introduced by Scott (1997 Plasma Phys. Control. Fusion39 1635) and Rogers and Drake (1997 Phys. Rev. Lett.79 229), and represent the effect of the electromagnetic induction, collisions and electron inertia. The dimensionless parameters are then evaluated at different radial positions in four existing divertor machines (ALCATOR C-MOD, ASDEX-Upgrade, JET and MAST) and in three future experiments (MAST-Upgrade, ITER and DEMO). Clear multi-machine trends, suggesting a quasi-universal behaviour of the plasma, are identified and discussed. Exploiting this quasi-universality, useful insight into the physics of the machines is obtained without complex calculations or expensive numerical simulations. In particular, the trends show a clear separation of the plasma in four distinct regions: core, edge, scrape-off layer and divertor, each of them characterized by a different set of parameters which, in turn, lead to significant variation of the dominant physical mechanisms across the machine.