We present information value, a measure which quantifies the predictability of an utterance relative to a set of plausible alternatives. We introduce a method to obtain interpretable estimates of information value using neural text generators, and exploit their psychometric predictive power to investigate the dimensions of predictability that drive human comprehension behaviour. Information value is a stronger predictor of utterance acceptability in written and spoken dialogue than aggregates of token-level surprisal and it is complementary to surprisal for predicting eye-tracked reading times.