Recently, self-supervised learning (SSL) has demonstrated strong performance in speaker recognition, even if the pre-training objective is designed for speech recognition. In this paper, we study which factor leads to the success of self-supervised learning on speaker-related tasks, e.g. speaker verification (SV), through a series of carefully designed experiments. Our empirical results on the Voxceleb-1 dataset suggest that the benefit of SSL to SV task is from a combination of mask speech prediction loss, data scale, and model size, while the SSL quantizer has a minor impact. We further employ the integrated gradients attribution method and loss landscape visualization to understand the effectiveness of self-supervised learning for speaker recognition performance.