Iterative algorithms for continuous numerical optimization typically need to adapt their step lengths in the course of the search. While some strategies employ fixed schedules, others attempt to adapt dynamically in response to the outcome of trial steps or the history of the search process. Evolutionary algorithms are of the latter kind. A control strategy that is commonly used in evolution strategies is the cumulative step length adaptation approach. This paper presents a theoretical analysis of that adaptation strategy. The analysis includes the practically relevant case of noise interfering in the optimization process. Recommendations are made with respect to choosing appropriate population sizes.