  In this paper, we derive an asymptotic formula for the number of conjugacy
classes of elements in a class of statistically convex-cocompact actions with
contracting elements. Denote by $\mathcal C(o, n)$ (resp. $\mathcal C'(o, n)$)
the set of (resp. primitive) conjugacy classes of pointed length at most $n$
for a basepoint $o$. The main result is an asymptotic formula as follows:
$$\sharp \mathcal C(o, n) \asymp \sharp \mathcal C'(o, n) \asymp
\frac{\exp(\omega(G)n)}{n}.$$ A similar formula holds for conjugacy classes
using stable length. As a consequence of the formulae, the conjugacy growth
series is transcendental for all non-elementary relatively hyperbolic groups,
graphical small cancellation groups with finite components. As by-product of
the proof, we establish several useful properties for an exponentially generic
set of elements. In particular, it yields a positive answer to a question of J.
Maher that an exponentially generic elements in mapping class groups have their
Teichm\"{u}ller axis contained in the principal stratum.
