The trend seems to be favorable; generally the average value approximates the nominal value, but there are distortions at both ends of the range which can be attributed to the influence of the bounds to which the tensor squares are subject, but which would not affect a more random collection of matrices.
In order to have 
in Eq. 25 it is necessary that
, 
, or 
. In the first case
all the column sums will be equal, equal to the eigenvalue, and the
matrix will be stochastic. In the second case the vector 
will be an
eigenvector, the row sums will all be constant, and again the matrix
will be stochastic. The final alternative is more interesting,
requiring the residuals in the column sums to be orthogonal to the
residuals in the eigenvector, for a matrix which is explicitly not
stochastic.