Many recent studies have confirmed that variability in the stratosphere is a significant source of surface sub‐seasonal prediction skill during Northern Hemisphere winter. It may be beneficial, therefore, to think about times in which there might be windows‐of‐opportunity for skillfull sub‐seasonal predictions based on the initial or predicted state of the stratosphere. In this study, we propose a simple, minimal model that can be used to understand the impact of the stratosphere on tropospheric predictability. Our model purposefully excludes state dependent predictability in either the stratosphere or troposphere or in the coupling between the two. Model parameters are set up to broadly represent current sub‐seasonal prediction systems by comparison with four dynamical models from the Sub‐Seasonal to Seasonal Prediction Project database. The model can reproduce the increases in correlation skill in sub‐sets of forecasts for weak and strong lower stratospheric polar vortex states over neutral states despite the lack of dependence of coupling or predictability on the stratospheric state. We demonstrate why different forecast skill diagnostics can give a very different impression of the relative skill in the three sub‐sets. Forecasts with large stratospheric signals and low amounts of noise are demonstrated to also be windows‐of‐opportunity for skillfull tropospheric forecasts, but we show that these windows can be obscured by the presence of unrelated tropospheric signals. Plain Language Summary For successful forecasts of surface winter conditions between two weeks and one season ahead, the stratosphere has been shown to be a key source of information. Despite many studies examining how well the stratosphere can be predicted in computer‐based forecasting systems, there remains a lack of understanding of which surface forecasts the stratosphere is most important for. This study is an attempt to step back from examining the role of the stratosphere in any particular forecasting system and instead to determine a simple framework that can be used to understand when and how the stratosphere is important. Using our framework we can construct a series of simple experiments that help to understand how important the stratosphere is in the longer range forecasting problem. Our experiments show that forecasts made during periods in which the Arctic stratospheric winds are unusually strong or weak have greater skill, but this does not depend on how unusually weak or strong the stratospheric winds are. The results are particularly important for thinking about the times in which longer range forecasts might be more skillfull than on average, so called windows‐of‐opportunity, and how these depend on the stratosphere. Key Points We propose a model that demonstrates how forecast skill present in the lowermost stratosphere contributes to tropospheric forecast skill The model can explain the greater correlation skill in the troposphere for forecasts during weak or strong vortex events The model shows how tropospheric skill arising from the stratosphere can sometimes be confounded by uncorrelated tropospheric signals