Despite years of research, the origin of ocean rogue waves is still disputed. Some early theories suggested that simple linear random interference of many elementary waves suffices to explain the heavy tail in the wave height distribution. Recently nonlinear explanations (Peregrine solitons, Akhmediev breathers etc.) received increasing popularity. We now confirm that the rogue wave phenomenon can be nearly completely explained by linear interference of a finite and variable number of elementary waves. More importantly, we show a method that allows reconstruction of this number, i.e., the phase space dimension, from recorded time series of the surface elevation. In most cases, the phase space dimension will lie below 10, and rogue waves cannot form as a matter of principle. However, rare situations exist where this number is substantially higher, and rogue wave formation seems virtually unavoidable. Nonlinearities play a minor role only, e.g., for explaining the much smaller probability of rogue holes. Finally, a forecast of ocean rogue waves seems possible, both from measured time series as well as from meteorological prediction.