It's a neat subject that will result in hours of discussion. Many areas are not well understood.
The FMC/QRH V1 speed is determined by the performance engineers (at least at Boeing) using an arbitrary V1/Vr. If the takeoff were to be calculated from the AFM you would see that for every takeoff there are two V1 figures, one for continuing and one for stopping. If you are doing the calculation the long way you would then select the figure that suits you for that particular takeoff. In other words, you select the V1/Vr. (Not that airlines would be happy allowing their pilots to use their judgement in such matters. Keep it simple for simple people.) Whenever you have excess runway the split can be very large, but in practical terms the highest V1 is equal to Vr and the lowest would be about 80%.
For a four engine airplane the engine failure case is not limiting. The limiting condition is for all engines, since the factor applied to the all engine takeoff is a reduction of 15%, while the engine failure case is not factored. A twin is not so lucky.
When reducing the V1 for a Wet runway, it is more correct to apply the speed correction to the Maximum V1 (the speed applicable to a takeoff at maximum takeoff weight for the runway length and conditions). Thus the actual V1 may not be reduced at all.
And if the Wet V1 is used, a continuing takeoff will result in a reduction of screen height (height at end of TOD) to as low as 10 feet. Now another question: if the screen height reduction is allowed on a wet runway, is it also allowed on a dry runway?