We propose a new measure of deviations from the expected utility theory. For any positive number e, we give a characterization of the datasets with a rationalization that is within e (in beliefs, utility, or perceived prices) of expected utility theory, under the assumption of risk aversion. The number e can then be used as a measure of how far the data is to the expected utility theory. We apply our methodology to data from three large-scale experiments. Many subjects in these experiments are consistent with utility maximization, but not with expected utility maximization. Our measure of distance to expected utility is correlated with the subjects’ demographic characteristics.