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Athreya, Bufetov, Eskin and Mirzakhani have shown the number of mapping classgroup lattice points intersecting a closed ball of radius $R$ inTeichm\"{u}ller space is asymptotic to $e^{hR}$, where $h$ is the dimension ofthe Teichm\"{u}ller space. In contrast we show the number of Dehn twist latticepoints intersecting a closed ball of radius $R$ is coarsely asymptotic to$e^{\frac{h}{2}R}$. Moreover, we show the number multi-twist lattice pointsintersecting a closed ball of radius $R$ grows coarsely at least at the rate of$R \cdot e^{\frac{h}{2}R}$.

Growth Rate Of Dehn Twist Lattice Points In Teichm\"{u}ller Space