Randomized A/B tests in educational software are not run in a vacuum: often, reams of historical data are available alongside the data from a randomized trial. This paper proposes a method to use this historical data--often highdimensional and longitudinal--to improve causal estimates from A/B tests. The method proceeds in two steps: first, fit a machine learning model to the historical data predicting students' outcomes as a function of their covariates. Then, use that model to predict the outcomes of the randomized students in the A/B test. Finally, use design-based methods to estimate the treatment effect in the A/B test, using prediction errors in place of outcomes. This method retains all of the advantages of design-based inference, while, under certain conditions, yielding more precise estimators. This paper will give a theoretical condition under which the method improves statistical precision, and demonstrates it using a deep learning algorithm to help estimate effects in a set of experiments run inside ASSISTments. [For the full proceedings, see ED593090.]