Finite-length, numerical simulations of Gaussian seasare widely used in the wave energy sector. The most commonmethod consists of adding up harmonic sinusoidal components,with random phases and deterministic amplitudes derived fromthe target wave spectrum [deterministic amplitude scheme (DAS)].In another approach, the component amplitudes are chosen ran-domly with a variance depending on the spectrum [random am-plitude scheme (RAS)]. It is now generally accepted that onlythe latter method reproduces the true statistical properties of aGaussian sea. Compared to previous works, this study clarifies theexact nature of the “statistical properties” that should be repre-sented in the simulation process. Further analysis is carried outto address unanswered questions highlighted in the existing lit-erature, especially with respect to the statistical relationships be-tween discrete successive simulation points, and the probabilitylaw governing the average power estimator of a wave energy con-verter (WEC) simulated with the generated wave time series. It isshown that RAS exactly reflects how the WEC performance, con-sidered over a finite duration, varies with respect to its long-termaverage, whereas DAS has the advantage of providing accurateestimates of the long-term average values using fewer, or shorter,simulations; in particular, it is demonstrated that only one simu-lation is sufficient when the WEC model is linear. Furthermore,it is shown why alternative methods, based on nonharmonic su-perposition of sinusoids, are not recommended. The effects of thesimulation method (RAS or DAS) upon the statistics of individualoscillations in the time domain are also explored experimentally.Finally, a table is provided that gives recommendations, dependingon the objective of the simulations.