Strong empirical evidence that one machine-learning algorithm A outperforms another one B, ideally calls for multiple trials optimizing the learning pipeline over sources of variation such as data sampling, augmentation, parameter initialization, and hyperparameters choices. This is prohibitively expensive, and corners are cut to reach conclusions. We model the whole benchmarking process and all sources of variation, revealing that variance due to data sampling, parameter initialization and hyperparameter choice impact markedly machine learning benchmark. We analyze the predominant comparison methods used today in the light of this variance. We show a counter-intuitive result that a biased estimator with more source of variation will give better results, closer to the ideal estimator at a 51× reduction in compute cost. Using this we perform a detailed study on the error rate of detecting improvements, on five different deep-learning tasks/architectures. This study leads us to propose recommendations for future performance comparisons.