The near-field electromagnetic scattering intensity resonances are redshifted in frequency with respect to their far-field counterparts. We derive simple, approximate, analytical formulas for this shift in the case of a plane wave interacting with a dielectric sphere. Numerical results comparing the approximate formulas to the numerically exact solutions show that the two are in good agreement. We also consider the Rayleigh limit of the formulas to gain more insight into the phenomenon.