Sudden stratospheric warmings (SSWs) are major disruptions of the polar vortex that can strongly affect winter weather. However, predicting how often they will occur in the future is challenging, as full climate models are costly to run and the triggers of SSWs are not fully understood. We developed a simplified one-dimensional model of the winter stratosphere that captures key dynamics while being fast to run. Using 42 years of atmospheric data, the model reproduces the observed seasonal behavior of winds and wave activity. By running 1000 years of simulations with realistic variability, we show how changes in wind strength, wave forcing, or nonlinearity can affect the likelihood of SSWs. Despite its simplicity, this model offers valuable insight into the factors that control SSW frequency and helps bridge the gap between theory and complex climate models.