Between-individual variation in phenotypes within a population is the basis of evolution. However, evolutionary and behavioural ecologists have mainly focused on estimating between-individual variance in mean trait and neglected variation in within-individual variance, or predictability of a trait. In fact, an important assumption of mixed-effects models used to estimate between-individual variance in mean traits is that within-individual residual variance (predictability) is identical across individuals. Individual heterogeneity in the predictability of behaviours is a potentially important effect but rarely estimated and accounted for. We used 11,389 measures of docility behaviour from 1,576 yellow-bellied marmots (Marmota flaviventris) to estimate between-individual variation in both mean docility and its predictability. We then implemented a double hierarchical animal model to decompose the variances of both mean trait and predictability into their environmental and genetic components. We found that individuals differed both in their docility and in their predictability of docility with a negative phenotypic covariance. We also found significant genetic variance for both mean docility and its predictability but no genetic covariance between the two. This analysis is one of the first to estimate the genetic basis of both mean trait and within-individual variance in a wild population. Our results indicate that equal within-individual variance should not be assumed. We demonstrate the evolutionary importance of the variation in the predictability of docility, and illustrate potential bias in models ignoring variation in predictability. We conclude that the variability in the predictability of a trait should not be ignored, and present a coherent approach for its quantification.