We explore the statistical limits on the complexity of data-derived models of magnetic storm phenomena, including magnetic indices, plasmapause evolution, and outer radiation belt dynamics. Specifically, we estimate the limits on the number of free parameters justifiable by application of Occam's razor, or the rule of parsimony. These limits arise from the strong intercorrelation of geomagnetic phenomena, which decimates the effective sample size of independent observations of magnetic storm phenomena. We show that the resulting paucity of distinct magnetic storms over the history of magnetic indices and satellite observations severely limits the justifiable complexity of data-derived models. Our analysis applies to a wide variety of models with a finite number of constant free parameters but not to models with time-varying parameters nor to nearest-neighbors models.