In this paper, we propose Bayesian hierarchical frameworks for predicting the potential for a tropical storm or cyclone to cause damage, and the amount of damage it can cause. Our study is restricted to the Atlantic basin, but conceptually it can be extended to any tropical cyclone basin. We provide Bayesian predictive models at two different temporal scales. First, we develop a predictive model for an entire season, that forecasts the number of storm events that will take place, the probability of each storm causing some amount of damage, and the monetized value of damages it will cause. Then, we consider specific characteristics of individual cyclones, like the minimum central pressure and maximum wind speed, to predict the monetized value of the damage it will cause.