Behavioural studies have shown that even after accounting for individual differences in contextual and temporal plasticity, considerable unexplained (residual) variation remains. Recent studies show that individuals differ in the magnitude of residual variation (= their predictability), but hardly any studies exist that assess whether this individual attribute itself is repeatable and potentially subject to selection, and whether predictability is related to aspects of different underlying state variables. Using data on the latency to emerge after disturbance of 100 pill bugs, Armadillidium vulgare, measured 24 times each over time and across contexts, we found substantial among-individual variation in mean boldness (latency) and in their behavioural predictability. Individual mean boldness across weeks was highly consistent over time, as was individual predictability; by contrast, unadjusted repeatability of boldness scores (the familiar ‘intraclass correlation’) and repeatability adjusted for time-related behavioural changes were low to moderate, indicating substantial residual variation. Individual mean boldness was not related to individual predictability, indicating that while selection can potentially act on individual means and individual variances, correlated selection is unlikely, for the traits assessed. Neither boldness nor predictability in boldness was related to mass or to sex, nor did they vary over time concurrent with gains in mass under ad libitum food conditions and in experience with the behavioural assay, indicating they were not clearly related to these potentially important life history and state variables.