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Due to the comprehensive nature of this paper, it has been updated and split into two separate papers: "A Framework For Benchmarking Class-out-of-distribution Detection And Its Application To ImageNet" and "What Can We Learn From The Selective Prediction And Uncertainty Estimation Performance Of 523 Imagenet Classifiers". We recommend reading them instead. Deep neural networks must be equipped with an uncertainty estimation mechanism when deployed for risk-sensitive tasks. This paper studies the relationship between deep architectures and their training regimes with their corresponding selective prediction and uncertainty estimation performance. We consider both in-distribution uncertainties and class-out-of-distribution ones. Moreover, we consider some of the most popular estimation performance metrics previously proposed including AUROC, ECE, AURC, and coverage for selective accuracy constraint. We present a novel and comprehensive study of selective prediction and the uncertainty estimation performance of 484 existing pretrained deep ImageNet classifiers that are available at popular repositories. We identify numerous and previously unknown factors that affect uncertainty estimation and examine the relationships between the different metrics. We find that distillation-based training regimes consistently yield better uncertainty estimations than other training schemes such as vanilla training, pretraining on a larger dataset and adversarial training. We also provide strong empirical evidence showing that ViT is by far the most superior architecture in terms of uncertainty estimation performance, judging by any aspect, in both in-distribution and class-out-of-distribution scenarios.