The pilot reported that, during the preflight inspection, he observed no discrepancies and noted that the oil level was "inside the lower bound of normal oil capacity." He reported that en route, the oil pressure "was in the 30s [pounds per square inch] and trending downward" but still within the normal engine oil pressure limits. He decided to divert to a nearby airport as a precaution. The pilot reported that, while maneuvering to the alternate airport, the engine instruments appeared normal. However, during left base for the runway, he observed "a few seconds of white smoke" coming from the engine over the left wing. He reduced power, added flaps, and noticed that the airplane's approach speed was too fast. He decided he would not attempt a go-around due to the smoke and shut the engine off "thinking of the possibility of an engine fire." Subsequently, the airplane bounced during the initial touchdown and landed near the runway's halfway point. The pilot applied brakes, but the airplane overran the runway into a dirt field, and the nose landing gear collapsed. The airplane sustained substantial damage to the fuselage. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.