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L2 regularization for weights in neural networks is widely used as a standard training trick. However, L2 regularization for gamma, a trainable parameter of batch normalization, remains an undiscussed mystery and is applied in different ways depending on the library and practitioner. In this paper, we study whether L2 regularization for gamma is valid. To explore this issue, we consider two approaches: 1) variance control to make the residual network behave like identity mapping and 2) stable optimization through the improvement of effective learning rate. Through two analyses, we specify the desirable and undesirable gamma to apply L2 regularization and propose four guidelines for managing them. In several experiments, we observed the increase and decrease in performance caused by applying L2 regularization to gamma of four categories, which is consistent with our four guidelines. Our proposed guidelines were validated through various tasks and architectures, including variants of residual networks and transformers.