New statistical theory was developed by the authors in the previous paper, which gives probability density function (p. d. f.) and extreme values of total second order responses of vessels moored in random seas. It assumes the response represented in the form of two term Volterra functional series and is based on the generalized Laguerre polynominal expansion of p. d. f. of which the first term is gamma p. d. f. consisting three parameters. We must compute exciting force and radiation hydrodynamic force in the response transfer function to obtain p. d. f. of the total second order response. In this paper we approached the effect of the second order potential to statistical values, using this theory. The calculation of second order potential in obtaining exciting force transfer function is very complex and takes many time to compute. Therefore, the transfer functions are generally obtained by neglecting this effect. It is investigated whether second order potential is negligible or not in statistical analysis. Furthermore coupled motion of six degrees of freedom (DOF) is discussed. We need coupled hydrodynamic force matrix to solve equations of motion because of coupling effect. Considering each DOF independent, only diagonal terms of hydrodynamic force matrix are necessary, and few tasks are needed for calculating hydrodynamic force. So, we discuss the conditions where the coupling motion effects of a slow drift motion on statistical values are negligible or not, by comparing the computed statistical values with measured ones by model experiments of two typical moorings.