The potential benefits of seasonal streamflow forecasts for the hydropower sector have been evaluated for several basins across the world, but with contrasting conclusions on expected hydropower production and economic gains. This raises the prospect of a complex relationship between reservoir characteristics, forecast skill and value. Here, we unfold the nature of this relationship by studying time series of simulated power production for 735 headwater dams worldwide. The time series are generated by running a detailed dam model over the period 1958-2000 with three operating schemes: basic control rules, perfect forecast-informed, and realistic forecast-informed. The realistic forecasts are issued by bespoke models, based on lagged global and local hydroclimatic variables, predicting seasonal monthly dam inflows. Results show that most dams (94%) could benefit from perfect forecasts. Yet, the benefits for each dam vary greatly and are primarily controlled by the time to fill and the ratio between reservoir depth and hydraulic head. When realistic forecasts are adopted, 25% of dams demonstrate improvements with respect to basic control rules. In this case, the likelihood of observing improvements is controlled not only by design characteristics but also by forecast skill. We conclude our analysis by identifying two groups of dams of particular interest: dams that fall in regions expressing strong forecast accuracy and have the potential to reap benefits from forecast-informed operations, and dams with strong potential to benefit from forecast-informed operations but lack forecast accuracy. Overall, these results represent a first qualitative step towards informing site-specific hydropower studies.