Damped-driven systems are ubiquitous in science, however, the damping and driving mechanisms are often quite convoluted. This paper presents an experimental and theoretical investigation of a fluidic droplet on a vertically vibrating fluid bath as a damped-driven system. We study a fluidic droplet in an annular cavity with the fluid bath forced above the Faraday wave threshold. We model the droplet as a kinematic point particle in air and as inelastic collisions during impact with the bath. In both experiments and the model, the droplet is observed to chaotically change velocity with a Gaussian distribution. Finally, the statistical distributions from experiments and theory are analyzed. Incredibly, this simple deterministic interaction of damping and driving of the droplet leads to more complex Brownian-like and Levy-like behavior.