Building on a survey of previous theories of serendipity and creativity, we advance a model of serendipitous occurrences, and a definition of the serendipity potential of a system. Practitioners can use these theoretical tools to evaluate a computational system's potential for unexpected behaviour that may have a beneficial outcome. In addition to a quantitative rating of serendipity potential -- which is computed in terms of population-based estimates of chance, curiosity, sagacity, and value -- the model also includes qualitative features that can guide development work. We show how the model is used in three case studies of existing and hypothetical systems, in the context of evolutionary computing, automated programming, and (next-generation) recommender systems. From this analysis, we extract recommendations for practitioners working with computational serendipity, and outline future directions for research.
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