We look at the variability of the power produced by the three-float M4 wave energy converter for locations in the North-East Atlantic and North Sea using the NORA10 hindcast data from 1958-2011. The aim is to investigate whether the produced power is also strongly affected by the climate variability (such as the North Atlantic Oscillations) in the winter, just as the ocean wave power resource as observed in previous studies. In this study, we demonstrate the use of proxy indices in combination with the climate indices to reconstruct a historic practical wave power climate from 1665-2005. We also conduct sensitivity studies to assess the changes in the practical wave power variability in response to perturbing the machine size, the power take-off coefficient, the response bandwidth and the power limit of the power take off. We find that the resultant temporal variation is still dominated by the climate variability. However, the overall variability important for power availability and energy supply economics is smaller than that of the ocean wave power resource because of the finite capture bandwidth of the M4 machine. The statistical methodology presented here is also potentially relevant to other wave energy converters in similar locations.