The effect of magnetism on the solid solution strengthening (SSS) of CrxCoyNi1?x?y alloys formulated by Varvenne?s and Toda-Caraballo?s (TC?s) models has been investigated comparatively by first-principles. It is found that for a reliable estimation of the model parameters for the paramagnetic (PM) and ferromagnetic (FM) alloys one should adopt the atomic radii and elastic moduli of the constituent metals corresponding to the same magnetic state. Furthermore, we show that Varvenne?s model underestimates the SSS when compared to the experimental data, while TC?s model correctly predicts the SSS of PM CrxCoyNi1?x?y alloys when adopting the PM parameters as inputs. Therefore, the magnetic states should be correctly accounted when estimating the atomic radii and elastic moduli of the constituent elements as input parameters for both models to capture the SSS in complex concentrated alloys properly.