We show that the simultaneous measurement of yields and fluctuations is capable of falsifying and constraining the statistical hadronization model. We show how such a measurement can test for chemical non-equilibrium, and distinguish between a high temperature chemically equilibrated freeze-out from a supercooled freeze-out with an over-saturated phase space. We perform a fit, and show that both yields and fluctuations measured at RHIC 200 GeV can be accounted for within the second scenario, with both the light and strange quark phase space saturated significantly above detailed balance. We point to the simultaneous fit of the K/π fluctuation and the K^*/K^- ratio as evidence that the effect of hadronic re-interactions after freeze-out is small.
