The Kazhdan Lusztig map gives a correspondence between conjugacy classes of Weyl groups and nilpotent orbits. So, let $w$ be a conjugacy class and $N$ be the nilpotent orbit it gets mapped to under the KL map. My question is

Is there a simple relationship between $n(w)$ and and $dim(N)$ ?

($n(w)$ is the number of elements in the conjugacy class and $dim(N)$ is the complex dimension of the nilpotent orbit).

The Kazhdan Lusztig map gives a correspondence between conjugacy classes of Weyl groups and nilpotent orbits. So, let $w$ be a conjugacy class and $N$ be the nilpotent orbit it gets mapped to under the KL map. My question is

Is there a simple relationship between $n(w)$ and $dim(N)$ ? (alternatively, is this data obtainable from the combinatorial information contained in the KL polynomials ?).

Notation : $n(w)$ is the number of elements in the conjugacy class and $dim(N)$ is the complex dimension of the nilpotent orbit.