  An algebraic method for the reconstruction and potentially prediction of the
solar dipole moment value at sunspot minimum (known to be a good predictor of
the amplitude of the next solar cycle) was suggested in the first paper in this
series. The method sums up the ultimate dipole moment contributions of
individual active regions in a solar cycle: for this, detailed and reliable
input data would in principle be needed for thousands of active regions in a
solar cycle. To reduce the need for detailed input data, here we propose a new
active region descriptor called ARDoR (Active Region Degree of Rogueness). In a
detailed statistical analysis of a large number of activity cycles simulated
with the 2$\times$2D dynamo model we demonstrate that ranking active regions by
decreasing ARDoR, for a good reproduction of the solar dipole moment at the end
of the cycle it is sufficient to consider the top $N$ regions on this list
explicitly, where $N$ is a relatively low number, while for the other regions
the ARDoR value may be set to zero. E.g., with $N=5$ the fraction of cycles
where the dipole moment is reproduced with an error exceeding $\pm$30% is only
12%, significantly reduced with respect to the case $N=0$, i.e. ARDoR set to
zero for all active regions, where this fraction is 26%. This indicates that
stochastic effects on the intercycle variations of solar activity are dominated
by the effect of a low number of large ``rogue'' active regions, rather than
the combined effect of numerous small ARs. The method has a potential for
future use in solar cycle prediction.
