We introduce the first application of the lean methodology to machine learning projects. Similar to lean startups and lean manufacturing, we argue that lean machine learning (LeanML) can drastically slash avoidable wastes in commercial machine learning projects, reduce the business risk in investing in machine learning capabilities and, in so doing, further democratize access to machine learning. The lean design pattern we propose in this paper is based on two realizations. First, it is possible to estimate the best performance one may achieve when predicting an outcome $y \in \mathcal{Y}$ using a given set of explanatory variables $x \in \mathcal{X}$, for a wide range of performance metrics, and without training any predictive model. Second, doing so is considerably easier, faster, and cheaper than learning the best predictive model. We derive formulae expressing the best $R^2$, MSE, classification accuracy, and log-likelihood per observation achievable when using $x$ to predict $y$ as a function of the mutual information $I\left(y; x\right)$, and possibly a measure of the variability of $y$ (e.g. its Shannon entropy in the case of classification accuracy, and its variance in the case regression MSE). We illustrate the efficacy of the LeanML design pattern on a wide range of regression and classification problems, synthetic and real-life.