Self-supervised learning (SSL) is a machine learning approach where the data itself provides supervision, eliminating the need for external labels. The model is forced to learn about the data's inherent structure or context by solving a pretext task. With SSL, models can learn from abundant and cheap unlabeled data, significantly reducing the cost of training models where labels are expensive or inaccessible. In Computer Vision, SSL is widely used as pre-training followed by a downstream task, such as supervised transfer, few-shot learning on smaller labeled data sets, and/or unsupervised clustering. Unfortunately, it is infeasible to evaluate SSL methods on all possible downstream tasks and objectively measure the quality of the learned representation. Instead, SSL methods are evaluated using in-domain evaluation protocols, such as fine-tuning, linear probing, and k-nearest neighbors (kNN). However, it is not well understood how well these evaluation protocols estimate the representation quality of a pre-trained model for different downstream tasks under different conditions, such as dataset, metric, and model architecture. In this work, we study how classification-based evaluation protocols for SSL correlate and how well they predict downstream performance on different dataset types. Our study includes eleven common image datasets and 26 models that were pre-trained with different SSL methods or have different model backbones. We find that in-domain linear/kNN probing protocols are, on average, the best general predictors for out-of-domain performance. We further investigate the importance of batch normalization for the various protocols and evaluate how robust correlations are for different kinds of dataset domain shifts. In addition, we challenge assumptions about the relationship between discriminative and generative self-supervised methods, finding that most of their performance differences can be explained by changes to model backbones.