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Making use of the publicly available 1D photoionization hydrodynamics codeATES we set out to investigate the combined effects of planetary gravitationalpotential energy ($\phi_p\equiv GM_p/R_p$) and stellar X-ray and ExtremeUltraviolet (XUV) irradiation ($F_{\rm XUV}$) on the evaporation efficiency($\eta$) of moderately-to-highly irradiated gaseous planets, from sub-Neptunesthrough hot Jupiters. We show that the (known) existence of a thresholdpotential above which energy-limited escape (i.e., $\eta\simeq 1$) isunattainable can be inferred analytically. For $\log \phi_p\gtrsim \log\phi_p^{\rm thr}\approx [12.9-13.2]$ (in cgs units), most of the energyabsorption occurs where the average kinetic energy acquired by the ions throughphoto-electron collisions is insufficient for escape. This causes theevaporation efficiency to plummet with increasing $\phi_p$,. Whether or notplanets with $\phi_p\lesssim \phi_p^{\rm thr}$ exhibit energy-limited outflowsis regulated primarily by the stellar irradiation level. Specifically, forlow-gravity planets, above $F_{\rm XUV}\simeq 10^{4-5}$ erg cm$^{-2}$s$^{-1}$Ly$\alpha$ losses overtake adiabatic and advective cooling and the evaporationefficiency of low-gravity planets drops below the energy-limited approximation,albeit remaining largely independent of $\phi_p$Further, we show that whereas$\eta$ increases as $F_{\rm XUV}$ increases for planets above $\phi^{\rmthr}_p$, the opposite is true for low-gravity planets. This behavior can beunderstood by examining the relative fractional contributions of advective andradiative losses as a function of atmospheric temperature. This novel frameworkenables a reliable, physically motivated prediction of the expected evaporationefficiency for a given planetary system; an analytical approximation of thebest-fitting $\eta$ is given in the appendix.

Irradiation-driven escape of primordial planetary atmospheres II. Evaporation efficiency of sub-Neptunes through hot Jupiters