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The proton light yield of liquid scintillators is an important property in the context of their use in large-scale neutrino experiments, with direct implications for neutrino-proton scattering measurements and the discrimination of fast neutrons from inverse beta-decay coincidence signals. This work presents the first measurement of the proton light yield of a water-based liquid scintillator (WbLS) formulated from 5% linear alkyl benzene (LAB), at energies below 20 MeV, as well as a measurement of the proton light yield of a pure LAB + 2 g/L 2,5-diphenyloxazole (PPO) mixture (LABPPO). The measurements were performed using a double time-of-flight method and a pulsed neutron beam from the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. The proton light yields were measured relative to that of a 477 keV electron. The relative proton light yield of WbLS was approximately 3.8% lower than that of LABPPO, itself exhibiting a relative proton light yield $15-20\%$ higher than previous measurements of an analogous anoxic sample. The observed quenching is not compatible with the Birks model for either material, but is well described with the addition of Chou's bimolecular quenching term., Comment: 14 pages, 11 figures