  In this paper we investigate the strong lensing statistics in galaxy
clusters. We extract dark matter haloes from the Millennium-XXL simulation,
compute their Einstein radius distribution, and find a very good agreement with
Monte Carlo predictions produced with the MOKA code. The distribution of the
Einstein radii is well described by a log-normal distribution, with a
considerable fraction of the largest systems boosted by different projection
effects. We discuss the importance of substructures and triaxiality in shaping
the size of the critical lines for cluster size haloes. We then model and
interpret the different deviations, accounting for the presence of a Bright
Central Galaxy (BCG) and two different stellar mass density profiles. We
present scaling relations between weak lensing quantities and the size of the
Einstein radii. Finally we discuss how sensible is the distribution of the
Einstein radii on the cosmological parameters {\Omega}_M-{\sigma}_8 finding
that cosmologies with higher {\Omega}_M and {\sigma}_8 possess a large sample
of strong lensing clusters. The Einstein radius distribution may help
distinguish Planck13 and WMAP7 cosmology at 3{\sigma}.
