This article considers some of the risks and challenges raised by the use of algorithm-assisted decision-making and predictive tools by the public sector. Alongside, it reviews a number of long-standing English administrative law rules designed to regulate the discretionary power of the state. The principles of administrative law are concerned with human decisions involved in the exercise of state power and discretion, thus offering a promising avenue for the regulation of the growing number of algorithm-assisted decisions within the public sector. This article attempts to re-frame key rules for the new algorithmic environment and argues that 'old' law-interpreted for a new context-can help guide lawyers, scientists and public sector practitioners alike when considering the development and deployment of new algorithmic tools. This article is part of a discussion meeting issue 'The growing ubiquity of algorithms in society: implications, impacts and innovations'.