We extend a chemical evolution model relating galaxy stellar mass and gas-phase oxygen abundance (the mass–metallicity relation) to explicitly consider the mass-dependence of galaxy gas fractions and outflows. Using empirically derived scalings of galaxy mass with halo virial velocity in conjunction with the most recent observations of z∼ 0 total galaxy cold gas fractions and the mass–metallicity relation, we place stringent global constraints on the magnitude and scaling of the efficiency with which star-forming galaxies expel metals. We demonstrate that under the assumptions that metal accretion is negligible and the stellar initial mass function does not vary, efficient outflows are required to reproduce the mass–metallicity relation; without winds, gas-to-stellar mass ratios ≳0.3 dex higher than observed are needed. Moreover, z= 0 gas fractions are low enough that while they have some effect on the magnitude of outflows required, the slope of the gas fraction–stellar mass relation does not strongly affect our conclusions on how the wind efficiencies must scale with galaxy mass. Because theoretical descriptions of the mass loading factor , where is the mass outflow rate and is the star formation rate, are often cast in terms of the depth of the galaxy potential well, which is in turn linked to the host halo virial velocity vvir, we use one of the latest abundance matching analyses to describe outflow efficiencies in terms of vvir rather than stellar mass. Despite systematic uncertainties in the normalization and slope of the mass–metallicity relation, we show that the metal expulsion efficiency ζw≡ (Zw/Zg)ηw (where Zw is the wind metallicitiy and Zg is the interstellar medium metallicity) must be both high and scale steeply with mass. Specifically, we show that ζw≫ 1 and ζw∝v−3vir or steeper. In contrast, momentum- or energy-driven outflow models suggest that ηw should scale as v−1vir or v−2vir, respectively, implying that the Zw–M★ relation should be shallower than the Zg–M★ relation.