The scaling of the single-pulse laser threshold fluence for dielectric breakdown with respect to pulse duration and material band gap energy was investigated in the subpicosecond pulse regime using oxide films (TiO2, Ta2O5, HfO2, Al2O3, and SiO2). A phenomenological model attributes the pulse duration dependence to the interplay of multiphoton ionization, impact ionization, and subpicosecond electron decay out of the conduction band. The observed linear scaling of the breakdown fluence with band gap energy can be explained within the framework of this model by invoking the band gap dependence of the multiphoton absorption coefficient from Keldysh photoionization theory.