We examined the neurophysiological underpinnings of individual differences in the ability to maintain up-to-date representations of the positions of moving objects. In two experiments similar to the multiple object tracking (MOT) task, we asked observers to monitor continuously one or several targets as they moved unpredictably for a semi-random period. After all objects disappeared, observers were immediately prompted to report the perceived final position of one queried target. Precision of these position reports declined with attentional load, and reports tended to best resemble positions occupied by the queried target between 0 and 30 ms in the past. Measurement of event-related potentials showed a contralateral delay activity over occipital scalp, maximal in the right hemisphere. The peak power-spectral frequency of observers’ eyes-closed resting occipital alpha oscillations reliably predicted performance, such that lower-frequency alpha was associated with superior spatial localisation. Slower resting alpha might be associated with a cognitive style that depends less on memory-related processing and instead emphasises attention to changing stimuli.