The pilot reported that, while flying over the destination airport, the airplane's engine lost power. He initiated a glide, applied mixture full rich, and restarted the engine, but during the approach the engine lost power again. He checked the fuel gauges and the right gauge read between ¼ and ½ tank, and he switched to the left fuel tank which he knew was full. The engine restarted briefly, but then lost power. He added that, he "must not have put the selector in the [correct] position because [he] had plenty of fuel in the left tank." During the forced landing, the airplane landed off of the runway, rolled for about 20 to 25 ft., the left main landing gear collapsed, and the airplane came to rest on its nose. The airplane sustained substantial damage to the left wing. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.