Data collection for natural language (NL) understanding tasks has increasingly included human explanations alongside data points, allowing past works to introduce models that both perform a task and generate NL explanations for their outputs. Yet to date, model-generated explanations have been evaluated on the basis of surface-level similarities to human explanations, both through automatic metrics like BLEU and human evaluations. We argue that these evaluations are insufficient, since they fail to indicate whether explanations support actual model behavior (faithfulness), rather than simply match what a human would say (plausibility). In this work, we address the problem of evaluating explanations from the the model simulatability perspective. Our contributions are as follows: (1) We introduce a leakage-adjusted simulatability (LAS) metric for evaluating NL explanations, which measures how well explanations help an observer predict a model’s output, while controlling for how explanations can directly leak the output. We use a model as a proxy for a human observer, and validate this choice with two human subject experiments. (2) Using the CoS-E and e-SNLI datasets, we evaluate two existing generative graphical models and two new approaches; one rationalizing method we introduce achieves roughly human-level LAS scores. (3) Lastly, we frame explanation generation as a multi-agent game and optimize explanations for simulatability while penalizing label leakage, which can improve LAS scores.