Abstract: Several puzzles and issues in quantum gravity are related to the question of what type of high-energy information is actually available to low-energy observers. In this talk I will try to argue that the best description available to a low-energy observer is probably of a statistical nature. Such a statistical description naturally connects to e.g. the eigenstate thermalization hypothesis, and wormholes and the apparent lack of factorization. I will describe this statistical picture and the evidence we have for it, and what we could possibly learn from it. Partially based on work in progress.