Scattering prevents light from being focused in turbid media. The effect of scattering can be negated through wavefront shaping techniques when a localized form of feedback is available. Even in the absence of such a localized reporter, wavefront shaping can blindly form a single diffraction-limited focus when the feedback response is nonlinear. We developed and experimentally validated a model that accurately describes the statistics of this blind focusing process. We show that maximizing the nonlinear feedback signal only results in the formation of a focus when a limited number of reporters are contributing to the signal. Using our model, we can calculate the minimal requirements for the number of controlled spatial light modulator segments and the order of nonlinearity to blindly focus light through strongly scattering media.