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Faced with an expensive human annotation process, creators of NLP systems increasingly turn to synthetic data generation. While this method shows promise, the extent to which synthetic data can replace human annotation is poorly understood. We investigate the use of synthetic data in Fact Verification (FV) and Evidence-based Question Answering (QA) by incrementally replacing human-generated data with synthetic points on eight diverse datasets. Strikingly, replacing up to 90% of the training data only marginally decreases performance, but replacing the final 10% leads to severe declines. We find that models trained on purely synthetic data can be improved by including as few as 125 human-generated data points. We show that matching the performance gain of a little human data requires an order of magnitude more synthetic data, and then estimate price ratios at which human annotation would be a more cost-effective solution. Our results suggest that even when human annotation at scale is infeasible, there is great value to having a small proportion of the dataset being human-generated.