In the nonparametric analysis of multivariate data, the spherical depth of a point x ∈ \( \mathbb{R}^{\textit{d}} \) with respect to a distribution P on \( \mathbb{R}^{\textit{d}} \) is the probability that a ball, determined by two antipodal points on its boundary that are sampled independently from P, covers x. The greatest advantage of the spherical depth is its fast computation, which is, unlike for many other depth functions, not exponential in the dimension d. That makes the spherical depth amenable for the analysis of high-dimensional, and functional data. We explore the theory and practice of spherical depth when applied to data of high dimensionality. In particular, we point to several difficulties with known results in the literature and revise multiple classical propositions on the behavior of spherical depth.