  Arguments from scale physics, augmented by numerical and analytical
investigations, are used to consider the probability and the detectability of
superoscillations in generic functions. The detectability is defined as the
fraction of the total power in the field that is located at regions of
superoscillations. It is found that the probability for a superoscillation of a
particular scale follows a quadratic power-law decay curve above the scale of
the bounded support of the spectrum. The detectability is found to be even more
severely suppressed, following a fourth-order power-law decay curve above the
scale of the spectrum.
