Sound decision-making relies on accurate prediction for tangible outcomes ranging from military conflict to disease outbreaks. To improve crowdsourced forecasting accuracy, we developed SAGE, a hybrid forecasting system that combines human and machine generated forecasts. The system provides a platform where users can interact with machine models and thus anchor their judgments on an objective benchmark. The system also aggregates human and machine forecasts weighting both for propinquity and based on assessed skill while adjusting for overconfidence. We present results from the Hybrid Forecasting Competition (HFC) - larger than comparable forecasting tournaments - including 1085 users forecasting 398 real-world forecasting problems over eight months. Our main result is that the hybrid system generated more accurate forecasts compared to a human-only baseline which had no machine generated predictions. We found that skilled forecasters who had access to machine-generated forecasts outperformed those who only viewed historical data. We also demonstrated the inclusion of machine-generated forecasts in our aggregation algorithms improved performance, both in terms of accuracy and scalability. This suggests that hybrid forecasting systems, which potentially require fewer human resources, can be a viable approach for maintaining a competitive level of accuracy over a larger number of forecasting questions.