We consider Adaptively Restrained Langevin dynamics, in which the kinetic energy function vanishes for small velocities. Properly parameterized, this dynamics makes it possible to reduce the computational complexity of updating inter-particle forces, and to accelerate the computation of ergodic averages of molecular simulations... In this paper, we analyze the influence of the method parameters on the total achievable speed-up. In particular, we estimate both the algorithmic speed-up, resulting from incremental force updates, and the influence of the change of the dynamics on the asymptotic variance. This allows us to propose a practical strategy for the parametrization of the method. We validate these theoretical results by representative numerical experiments. (read more)