The amateur-built light sport aircraft sustained substantial damage during a forced landing to a baseball field after a complete loss of engine power while turning from base leg to the final approach for landing. The pilot reported that the two-cycle engine rpm slowed to 3,500 rpm for a few seconds and then stopped. The altitude was about 300 - 400 feet above ground level (agl), and he was unable to make it to the runway. The pilot reported that there was 1/4 tank of fuel in the right tank and less fuel in the left tank. He attempted to land in a baseball field, but was "unable to retain directional control" as the airplane cleared the obstructions to the field. The pilot reported that the left wing "dipped" and the airplane impacted bushes and trees. The inspection of the engine revealed that it did not seize. No deficiencies were found that would have precluded normal engine operation.