Abstract In a parallel paper mainly focused on the meteorological and oceanographic aspects, the conditions were described for the storm during which the iconic Draupner wave was recorded. Because of increased spatial resolution and improved model physics, the results provided new and previously unrecognized features of the storm, in particular of the wave spectra, features relevant for assessing the wave’s conditions nearby the Draupner platform. Starting from these, and after briefly summarizing the relevant information, the focus of this paper is on the nonlinear analysis of the local situation, with the main purpose of assessing if and how the conditions existed for the possible appearance of very large waves. An intensive analysis of the related probability is carried out, attacking the problem with two different statistical approaches, both briefly described: a completely new one working from the point of view of envelope heights, and a recent, though established, one based on space–time extreme waves. It is remarkable, and certainly supports this line of work, that the two different approaches lead independently to consistent results, supporting the idea, already derived from the meteo-oceanographic hindcast, that the wave conditions were indeed special at the position of the Draupner platform. This is related to a general analysis of high waves showing, also on the basis of 3D (2D space + time) measured wave data at open sea, how, given the severe sea state, the Draupner wave features represent what is expected at certain times and positions as the natural documented temporal evolution of wave groups.