Ultra-low frequency (ULF) waves in the magnetosphere are involved in the energisation and transport of radiation belt particles and are strongly driven by the external solar wind. However, the interdependency of solar wind parameters and the variety of solar wind-magnetosphere coupling processes make it difficult to distinguish the effect of individual processes and to predict magnetospheric wave power using solar wind properties. We examine fifteen years of dayside ground-based measurements at a single representative frequency (2.5 mHz) and a single magnetic latitude (corresponding to L $sim 6.6 RE). We determine the relative contribution to ULF wave power from instantaneous non-derived solar wind parameters, accounting for their interdependencies. The most influential parameters for ground-based ULF wave power are solar wind speed vsw, southward interplanetary magnetic field component Bz <0 and summed power in number density perturbations $delta Np. Together, the subordinate parameters Bz and $delta Np still account for significant amounts of power. We suggest that these three parameters correspond to driving by the Kelvin-Helmholtz instability, formation and/or propagation of flux transfer events and density perturbations from solar wind structures sweeping past the Earth. We anticipate that this new parameter reduction will aid comparisons of ULF generation mechanisms between magnetospheric sectors and will enable more sophisticated empirical models predicting magnetospheric ULF power using external solar wind driving parameters.