Weather at New Orleans was below landing minima, so the flight was diverted to Baton Rouge. Weather at Baton Rouge was a ceiling 300 feet overcast, visibility 1,5 miles in light rain and fog, wind 360deg/5 knots. Runway 13 ILS minima were 300 feet ceiling and 3/4 mile visibility, weather was below circling minima, however. The approach was continued and the plane touched down fast 2500 feet past threshold. Approaching the end of the runway, the pilot attempted to ground loop, but the plane just turned 20deg and slid off the runway. PROBABLE CAUSE: “Failure of the captain to execute a go-around during a landing overshoot under existing unfavourable wind and adverse runway conditions. Ineffective braking caused by hydroplaning.”