Understanding the macroscopic statistical properties of a physical system can provide vital clues to its microscopic characteristics.  I will show that Einstein gravity at long distances contains statistical information about quantum spacetime.  For example, certain wormhole spacetimes encode statistics of quantum black hole microstates, precisely matching predictions of random matrix theory.  The connection between statistics and spacetime provides a gravitational manifestation of semiclassical quantum chaos.  I will also discuss the role of random matrix theory in quantum cosmology and establish a duality between a statistical ensemble and de Sitter quantum gravity.  This duality provides the first solvable model of de Sitter holography and helps build a framework for quantum cosmology.