Small aquatic insects that jump on water using drag force as the dominant force can be modelled using an elastic hoop. Unlike elastic hoops jumping on land, jumps on water are far more sensitive to the initial conditions as it is difficult to get a thin hoop to float perfectly upright on water with hydrophobic coating applied. We show that the efficiency of the hoops as a proportion of its translational kinetic energy to its elastic strain energy, depends on a single dimensionless parameter, regardless of the other properties of the hoops. With known initial conditions, our theoretical model allows us to predict with high accuracy, the efficiency of a hoop. Other geometrical forms could be applied to our model to obtain the optimal efficiency to deepen our understanding of drag dominated jumps on water.