Camera-based eye trackers are the mainstay of eye movement research and countless practical applications of eye tracking. Recently, a significant impact of changes in pupil size on gaze position as measured by camera-based eye trackers has been reported. In an attempt to improve the understanding of the magnitude and population-wise distribution of the pupil-size dependent shift in reported gaze position, we present the first collection of binocular pupil drift measurements recorded from 39 subjects. The pupil-size dependent shift varied greatly between subjects (from 0.3 to 5.2 deg of deviation, mean 2.6 deg), but also between the eyes of individual subjects (0.1 to 3.0 deg difference, mean difference 1.0 deg). We observed a wide range of drift direction, mostly downward and nasal. We demonstrate two methods to partially compensate the pupil-based shift using separate calibrations in pupil-constricted and pupil-dilated conditions, and evaluate an improved method of compensation based on individual look-up-tables, achieving up to 74% of compensation.