Novelty, surprise and transformation of the domain have each been raised – alone or in combination – as accompaniments to value in the determination of creativity. Spirited debate has surrounded the role of each factor and their relationships to each other. This paper suggests a way by which these three notions can be compared and contrasted within a single conceptual framework, by describing each as a kind of unexpectedness. Using this framing we argue that current computational models of novelty, concerned primarily with the originality of an artefact, are insufficiently broad to capture creativity, and that other kinds of expectation – whatever the terminology used to refer to them – should also be considered. We develop a typology of expectations relevant to computational creativity evaluation and, through it describe a series of situations where expectations would be essential to the characterisation of creativity.