We investigate analytically two questions: (1) how does the coil geometry influence the effect of electric current errors on the induced magnetic field? (2) How does the coil-plasma distance influence our ability to control the pointwise magnetic field error in terms of the average magnetic field error? Regarding (1), we argue that the main geometric quantities of interest are the notion of reach, related to the curvatures of the coil winding surface, and the volume of the region enclosed by the coils. Our main finding is a quantitative formula which shows that the larger the reach (and so the smaller the curvatures) and the smaller the volume of the region enclosed by the coils, the smaller is the influence of the electric current uncertainty on the magnetic field. Regarding (2), we show that the pointwise magnetic field error can be controlled (modulo an explicit constant) by the average square-magnetic field-error times .