Rogue or freak waves sink ships at an alarming rate — estimated at one large ship every few weeks worldwide. It is thought that vulnerable ships (light cargo ships) simply break in two when they plough into a 60 foot wave preceded by a 40 foot hole in the sea, as some sailors that have survived such experiences have called it. Wave refraction due to current eddies (which are ubiquitous in the oceans) has long been suspected to play a role in concentrating wave energy into rogue waves. Existing theories have been based on refraction of plane waves, not the stochastic Gaussian seas one finds in practice. Gaussian seas ruin the dramatic focal caustic concentration of energy, and this fact has discouraged further investigations. Although it was thought that chaos, or the extreme sensitivity to initial conditions displayed by individual ray trajectories would quickly wipe out all significant fluctuations, we show that this is incorrect, and the fluctuations are “structually stable” entities. Significant “lumps” of energy survive the averaging over wave directions and wavelengths. We furthermore demonstrate that the probability of freak waves increases dramatically in the presence of these lumps, even though most parameters, such as the significant wave height, are unchanged. We show here that a single dimensionless parameter determines the potential for freak waves; this is the “freak index” of the current eddies — a typical angular deflection in one focal distance, divided by the initial angular uncertainty of the incoming waveset. If the freak index is greater than 2 or so, truly spectacular enhancements of freak index waves can result, even though the caustics are washed out by the Gaussian nature of the impinging sea.