  A Teichmuller lattice is the orbit of a point in Teichmuller space under the
action of the mapping class group. We show that the proportion of lattice
points in a ball of radius r which are not pseudo-Anosov tends to zero as r
tends to infinity. In fact, we show that if R is a subset of the mapping class
group, whose elements have an upper bound on their translation length on the
complex of curves, then proportion of lattice points in the ball of radius r
which lie in R tends to zero as r tends to infinity.
