Open data science and algorithm development competitions offer a unique avenue for rapid discovery of better computational strategies. We highlight three examples in computational biology and bioinformatics research in which the use of competitions has yielded significant performance gains over established algorithms. These include algorithms for antibody clustering, imputing gene expression data, and querying the Connectivity Map (CMap). Performance gains are evaluated quantitatively using realistic, albeit sanitized, data sets. The solutions produced through these competitions are then examined with respect to their utility and the prospects for implementation in the field. We present the decision process and competition design considerations that lead to these successful outcomes as a model for researchers who want to use competitions and non-domain crowds as collaborators to further their research.