Successful science needs deviant ideas that may challenge established norms. The last decade saw an unprecedented science-engineering project, with strict rules on preregistration, statistical testing, result-independent guaranteed publication, replication, and openness badging being enforced by psychological journals. These normative methodologies seek to prevent failure (negative deviance) rather than promote success (positive deviance), and run counter to the historical development of successful science. By narrowly focusing on research data, while avoiding theoretical bias, they are inadequate for tackling, often intractable, scientific problems. Instead, unconventional, exceptional, and even initially implausible hypotheses should be fostered. A novel connection is drawn between positive deviance and the unplanned, haphazard evolution of successful science. Hypotheses compete for the highest fitness while probing an ever-changing, infinitely wide, empirical and theoretical landscape. The winner constitutes the positive deviant, but always remains subject to future competition. Losing negative deviants, which may share characteristics with winners, become irrelevant, sometimes long after their inception, and eventually sink into oblivion. Normative methodologies aim to curb negative deviants at their source, but also cut off positive deviants and may freeze successful science. More room for deviance and a theory primacy are advocated, allowing research to generate discovery and innovation in psychological science.