Recent work has identified potential multi-year predictability in soil moisture (Chikamoto et al. in Clim Dyn 45(7–8):2213–2235, 2015). Whether this long-term predictability translates into an extended predictability of runoff still remains an open question. To address this question we develop a physically-based zero-dimensional stochastical dynamical model. The model extends previous work of Dolgonosov and Korchagin (Water Resour 34(6):624–634, 2007) by including a runoff-generating soil moisture threshold. We consider several assumptions on the input rainfall noise. We analyze the applicability of analytical solutions for the stationary probability density functions (pdfs) and for waiting times for runoff under different assumptions. Our results suggest that knowing soil moisture provides important information on the waiting time for runoff. In addition, we fit the simple model to daily NCEP1 reanalysis output on a near-global scale, and analyze fitted model performance. Over many tropical regions, the model reproduces the simulated runoff in NCEP1 reasonably well. More detailed analysis over a single gridpoint illustrates that the model, despite its simplicity, is able to capture some key features of the runoff time series and pdfs of a more complex model. Our model exhibits runoff predictability of up to two months in advance. Our results suggest that there is an optimal predictability “window” in the transition zone between runoff-generating and dry conditions. Our model can serve as a “null hypothesis” model reference against more complex models for runoff predictability.