A probabilistic description of the quasi-static response of offshore structures to random wave loading has been developed recently in terms of the cross-covariance statistics of the mean-zero and Gaussian distributed particle kinematics at an array of locations beneath the water surface. Implementation of this model was initially restricted by the computational requirements associated with evaluation of certain high order expectations. However, approximations for these expectations have now been developed which enable some relaxation in these restrictions. The procedure employed makes use of standard properties of mean-zero Gaussian random variables and, in particular, application of Price's theorem. The paper presents, for the first time, the complete description of the expected value analysis upon which the model is based.