  Athreya, Bufetov, Eskin and Mirzakhani have shown the number of mapping class
group lattice points intersecting a closed ball of radius $R$ in
Teichm\"{u}ller space is asymptotic to $e^{hR}$, where $h$ is the dimension of
the Teichm\"{u}ller space. We show for any pseudo-Anosov mapping class $f$,
there exists a power $n$, such that the number of lattice points of the $f^n$
conjugacy class intersecting a closed ball of radius $R$ is coarsely asymptotic
to $e^{\frac{h}{2}R}$.
