A dry frictional interface loaded in shear often displays stick–slip. The amplitude of this cycle depends on the probability that a microscopic event nucleates a rupture and on the rate at which microscopic events are triggered. The latter is determined by the distribution of soft spots, P(x), which is the density of microscopic regions that yield if the shear load is increased by some amount x. In minimal models of a frictional interface—that include disorder, inertia and long-range elasticity—we discovered an ‘armouring’ mechanism by which the interface is greatly stabilised after a large slip event: P(x) then vanishes at small argument as P(x)∼xθ (de Geus et al., Proc Natl Acad Sci USA 116(48):23977-23983, 2019. https://doi.org/10.1073/pnas.1906551116). The exponent θ is non-zero only in the presence of inertia (otherwise θ=0). It was found to depend on the statistics of the disorder in the model, a phenomenon that was not explained. Here, we show that a single-particle toy model with inertia and disorder captures the existence of a non-trivial exponent θ>0, which we can analytically relate to the statistics of the disorder.