A minimal model for the evolution of the global dynamical state of the magnetotail during the substorm has been developed, involving only three simple rules and one free parameter D-the period between substorms under constant solar wind driving. The model is driven with a power input derived from solar wind observations from the Wind spacecraft between 1995 and 1998, to derive a sequence of simulated substorm onsets. For values of D between 2.6 h and 2.9 h, the probability distribution of waiting times between successive simulated substorm onsets is not significantly different to an empirical distribution derived from energetic particle observations at geostationary orbit in 1982-3. Similar results are obtained using solar wind data from the ACE spacecraft between 1998 and 2002. Thus, we argue that the minimal substorm model provides a useful statistical and physical description of the timing of substorm onsets and possibly other substorm properties.