Ergotropy—the maximal amount of unitarily extractable work—measures the "charge level" of quantum batteries. We prove that in large many-body batteries ergotropy exhibits a concentration of measure phenomenon. Namely, the ergotropy of such systems is almost constant for almost all states sampled from the Hilbert–Schmidt measure. We establish this by first proving that ergotropy, as a function of the state, is Lipschitz-continuous with respect to the Bures distance, and then applying Levy's measure concentration lemma. Furthermore, we argue that ergotropy can be measured in a non-contradictory way even if the initial state is coherent. We show that, despite the concentration phenomenon, fluctuations of work during ergotropy extraction are significant. Lastly, we consider the situation with the least amount of prior information about the state. This corresponds to the quantum version of the Jeffreys prior distribution—the Bures measure. In this case, there exist no analytical bounds guaranteeing exponential concentration of measure. Nonetheless, we provide numerical evidence that ergotropy, as well as von Neumann entropy, concentrate also in this case.