Modern design methods for offshore structures are based on statistical concepts; the economy of the structure is weighed against the calculated risk of operational downtime or structural damage. These methods derive design values for the geometry and strength from a theoretical distribution of extreme values and an accepted risk level by means of statistical techniques. In the present work attention is paid to the nature of the distributions underlying the behaviour of a semi-submersible platform in irregular beam seas. Design aspects considered are the mooring loads, the roll motions and relative wave elevation under the main deck. Applying contemporary concepts for the description of the behaviour of floating structures in irregular waves the work is based on an analysis of the various frequency components in the motion response I and mooring loads. The individual components are considered with special attention to the distribution of extreme values; their overall magnitudes are compared with the results of available theoretical prediction methods. After consideration of the individual components attention is payed to the nature of the distribution of the amplitudes of the total motion response.