In the context of the 2018 IEEE Congress of Evolutionary Computation, the Matrix Adaptation Evolution Strategy for constrained optimization turned out to be notably successful in the competition on constrained single objective real-parameter optimization. Across all considered instances the so-called $\epsilon$MAg-ES achieved the second rank. However, it can be considered to be the most successful participant in high dimensions. Unfortunately, the competition result does not provide any information about the modus operandi of a successful algorithm or its suitability for problems of a particular shape. To this end, the present paper is concerned with an extensive empirical analysis of the $\epsilon$MAg-ES working principles that is expected to provide insights about the performance contribution of specific algorithmic components. To avoid rankings with respect to insignificant differences within the algorithm realizations, the paper additionally introduces significance testing into the ranking process.