A small fraction of plasma disruptions at JET lead to a significant horizontal displacement of the vacuum vessel. This can threaten the integrity of the vessel and, in particular, of various vessel attachments such as the main vertical ports and the neutral injector boxes. These events are referred to as Asymmetric Vertical Disruption Events (AVDEs). In this paper we attempt to identify associations between plasma parameters and large asymmetric vessel displacements, by analysis of data from some hundreds of disruptive JET pulses. As far as the pre-disruption parameters are concerned, the amplitude of vessel sideways displacements shows a trend with the boundary safety factor and the poloidal beta. No link has been identified with the plasma triangularity or elongation. With regard to plasma parameters during the disruption, the data show a trend with the amplitude of the instability mode n=1, and a trend with the plasma current quench rate and the minimum value of the boundary safety factor. A reliable short cut to select disruptions with high asymmetric loads and to estimate the effects on the vessel using disruption data has been proposed. Hardly any practical operational space has been found to be wholly safe from triggering such vessel sideways displacements.