A correlation between uncompensated (UC) antiferromagnetic (AF) spins and exchange bias (EB) strength was investigated for Mn74Ir 26/Co100-xFex bilayers. The EB strength had a maximum at x=25 at. %, and the x-ray magnetic circular dichroism of Mn, representing the UC-AF spins, changed systematically in sign and magnitude with respect to x. A linear correlation was found between the EB strength and the root mean square magnitude of the UC-Mn spins. The hidden parameter connecting these two quantities might be exchange coupling energy at the heterointerface, which varies as a function of the ferromagnetic layer composition.