Flooding is the most frequent and damaging natural hazard globally. While nature-based solutions can reduce flood risk, they are not part of mainstream risk management. We develop a probabilistic risk analysis framework to quantify these benefits that (1) accounts for frequent small events and rarer large events, (2) can be applied to large basins and data-scarce contexts, and (3) quantifies economic benefits and reduction in people affected. Measuring benefits in terms of avoided losses enables the integration of nature-based solutions in standard cost-benefit analysis of protective infrastructure. Results for the Chindwin River basin in Myanmar highlight the potential consequences of deforestation on long-term flood risk. We find that loss reduction is driven by small but frequent storms, suggesting that current practice relying on large storms may underestimate the benefits of nature-based solutions. By providing average annual losses, the framework helps mainstream nature-based solutions in infrastructure planning or insurance practice.