  We define the $Q$-factor in the percolation problem as the quotient of the
size of the
  largest cluster and the average size of all clusters. As the occupation
probability $p$
  is increased, the $Q$-factor for the system size $L$ grows systematically to
its maximum
  value $Q_{max}(L)$ at a specific value $p_{max}(L)$ and then gradually
decays. Our numerical
  study of site percolation problems on the square, triangular and the simple
cubic lattices
  exhibits that the asymptotic values of $p_{max}$ though close, are distinctly
different
  from the corresponding percolation thresholds of these lattices. We have also
shown using
  the scaling analysis that at $p_{max}$ the value of $Q_{max}(L)$ diverges as
$L^d$ ($d$
  denoting the dimension of the lattice) as the system size approaches to their
asymptotic
  limit. We have further extended this idea to the non-equilibrium systems such
as the
  sandpile model of self-organized criticality. Here, the $Q(\rho,L)$-factor is
the quotient
  of the size of the largest avalanche and the cumulative average of the sizes
of all the
  avalanches; $\rho$ being the drop density of the driving mechanism. This
study has been
  prompted by some observations in Sociophysics.
