  The results of the probabilistic analysis of the direct numerical simulations
of irregular unidirectional deep-water waves are discussed. It is shown that an
occurrence of large-amplitude soliton-like groups represents an extraordinary
case, which is able to increase noticeably the probability of high waves even
in moderately rough sea conditions. The ensemble of wave realizations should be
large enough to take these rare events into account. Hence we provide a
striking example when long-living coherent structures make the water wave
statistics extreme.
