Saccades quite systematically undershoot a peripheral visual target by about 10% of its eccentricity while becoming more variable, mainly in amplitude, as the target becomes more peripheral. This undershoot phenomenon has been interpreted as the strategic adjustment of saccadic gain downstream of the superior colliculus (SC), where saccades are programmed. Here, we investigated whether the eccentricity-related increase in saccades’ hypometria and imprecision might not instead result from overrepresentation of space closer to the fovea in the SC and visual-cortical areas. To test this Magnification-factor (MF) hypothesis, we analyzed four parametric eye-movement data sets, collected while humans made saccades to single eccentric stimuli. We first established that the undershoot phenomenon generalizes to ordinary saccade amplitudes (0.5–15 degrees) and directions (0–90 degrees) and that landing-position distributions become not only increasingly elongated but also more skewed toward the fovea as target eccentricity increases. Moreover, we confirmed the MF hypothesis by showing (a) that the linear eccentricity-related increase in undershoot error and negative skewness canceled out when landing positions were log-scaled according to the MF in monkeys’ SC and (b) that the spread, proportional to eccentricity outside an extended, 5-degree, foveal region, became circular and invariant in size in SC space. Yet the eccentricity-related increase in variability, slower near the fovea, yielded progressively larger and more elongated clusters toward foveal and vertical-meridian SC representations. What causes this latter, unexpected, pattern remains undetermined. Nevertheless, our findings clearly suggest that the undershoot phenomenon, and related variability, originate in, or upstream of, the SC, rather than reflecting downstream, adaptive, strategies.