In this paper we determine the probability of substorm onset as a function of open magnetic flux in the magnetosphere by comparing the occurrence distribution of open flux observed at all times with that observed at the time of substorm onset. The open magnetic flux is measured in 12735 auroral images of the ionospheric polar cap from the IMAGE WIC detector. The probability of substorm onset is found to be negligible for fluxes below ~0.3 GWb, increases almost linearly until ~0.9 GWb, and is undefined above this. We also demonstrate that those substorms which show a clear particle injection signature at geosynchronous orbit, as measured by the LANL spacecraft, occur, on average, with higher values of open flux than those showing no activity. We discuss these results in the context of various hypotheses for substorm onset.