Self-Supervised Learning (SSL) has become a very active area of Deep Learning research where it is heavily used as a pre-training method for classification and other tasks. However, the rapid pace of advancements in this area comes at a price: training pipelines vary significantly across papers, which presents a potentially crucial confounding factor. Here, we show that, indeed, the choice of hyperparameters and data augmentation strategies can have a dramatic impact on performance. To shed light on these neglected factors and help maximize the power of SSL, we hyperparameterize these components and optimize them with Bayesian optimization, showing improvements across multiple datasets for the SimSiam SSL approach. Realizing the importance of data augmentations for SSL, we also introduce a new automated data augmentation algorithm, GroupAugment, which considers groups of augmentations and optimizes the sampling across groups. In contrast to algorithms designed for supervised learning, GroupAugment achieved consistently high linear evaluation accuracy across all datasets we considered. Overall, our results indicate the underestimated role of data augmentation for SSL.