We frequently experience feelings of agency over events we do not objectively influence - so-called 'illusions of control'. These illusions have prompted widespread claims that we can be insensitive to objective relationships between actions and outcomes, and instead rely on grandiose beliefs about our abilities. However, these illusory biases could instead arise if we are highly sensitive to action-outcome correlations, but attribute agency when such correlations emerge simply by chance. We motion-tracked participants while they made agency judgements about a cursor that could be yoked to their actions or follow an independent trajectory. A combination of signal detection analysis, reverse correlation methods and computational modelling indeed demonstrated that 'illusions' of control could emerge solely from sensitivity to spurious action-outcome correlations. Counterintuitively, this suggests that illusions of control could arise because agents have excellent insight into the relationships between actions and outcomes in a world where causal relationships are not perfectly deterministic.