Small Engines (Lawn Mowers, etc.): Rough running LX-188, rocket scientist, engine fire

Question
The other day my engine started running rough, so, I changed the spark plugs.  The left plug had lots of carbon but the right looked perfect.  The plugs made a big difference but it still seems to be running rich.  If the carburetor was the problem, shouldn't both plugs show carbon build up?  The mower is at least 10 years old but has been perfect except for a couple of belt replacements.
The engine is a Kawasaki FD501V 17 horse engine.  What else should I check?  

Answer
One of the things that makes this machine run so satin-smooth is that the plugs fire at 15 and 30 degrees.  Most engine fire at 180 and 360.  This causes "rebound" intake.  It's a long tale to explain and unless you are a rocket scientist you wouldn't be able to understand any way,  Not to mention I'm not sure I can explain under about 1000 words.  I would be talking out of my ass the whole 1000 words because I'm not sure I get it either.

Black powdery plugs always means rich. Always!  1 plug worse than the other is normal in this engine.  I think its the left side that is always the worst.

Clean the carb and tank and the black plug will go away.