Most criminological theories are not truly scientific, since they do not yield exact quantitative predictions of criminal career features, such as the prevalence and frequency of offending at different ages. This Element aims to make progress towards more scientific criminological theories. A simple theory is described, based on measures of the probability of reoffending and the frequency of offending. Three offender categories are identified: high risk/high rate, high risk/low rate, and low risk/low rate. It is demonstrated that this theory accurately predicts key criminal career features in three datasets: in England the Offenders Index (national data), the Cambridge Study in Delinquent Development (CSDD) and in America the Pittsburgh Youth Study (PYS). The theory is then extended in the CSDD and PYS by identifying early risk factors that predict the three categories. Criminological theorists are encouraged to replicate and build on our research to develop scientific theories that yield quantitative predictions.