Large and thus statistically powerful A/B tests are increasingly popular in business and policy to evaluate potential innovations. We study how to use scarce experimental resources to screen such innovations by proposing a new framework for optimal experimentation that we call the A/B testing problem. The key insight of the model is that the optimal experimentation strategy depends on whether most gains accrue from typical innovations or from rare and unpredictable large successes that can be detected using tests with small samples. We show that if the tails of the (prior) distribution of true effect sizes is not too fat, the standard approach of using a few high-powered “big” experiments is optimal. However, when this distribution is very fat tailed, a “lean” experimentation strategy consisting of trying more but smaller interventions is preferred. We measure the relevant tail parameter using experiments from Microsoft Bing’s EXP platform and find extremely fat tails. Our theoretical results and empirical analysis suggest that even simple changes to business practices within Bing could dramatically increase innovation productivity.