Due to the flexibility in adapting to different fitness landscapes, self-adaptive evolutionary algorithms (SA-EAs) have been gaining popularity in the recent past. In this paper, we postulate the properties that SA-EA operators should have for successful applications. Specifically, population mean and variance of a number of SA-EA operators, such as various real-parameter crossover operators and self-adaptive evolution strategies, are calculated for this purpose. In every case, simulation results re shown to verify the theoretical calculations. The postulations and population variance calculations explain why self-adaptive GAs and ESs have shown similar performance in the past and also suggest appropriate strategy parameter values which mus...