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A theoretical model is presented that for the first time matches experimental measurements of the pedestal width-height Diallo scaling in the low-aspect-ratio high- β tokamak NSTX. Combining linear gyrokinetics with self-consistent pedestal equilibrium variation, kinetic-ballooning, rather than ideal-ballooning plasma instability, is shown to limit achievable confinement in spherical tokamak pedestals. Simulations are used to find the novel Gyrokinetic Critical Pedestal constraint, which determines the steepest pressure profile a pedestal can sustain subject to gyrokinetic instability. Gyrokinetic width-height scaling expressions for NSTX pedestals with varying density and temperature profiles are obtained. These scalings for STs depart significantly from that of conventional aspect ratio tokamaks.