I can verify that from what I know (Bosch fuel injection) that 14.7:1 is "optimum" for complete burning and is a good comprimise between fuel economy and power.
But obviously that is not what is desired here. As you get closer to 12:1 power climbs a little bit but fuel economy drops like a rock. As you get closer to 17:1 fuel economy climbs a little bit but power drops like a rock. If you can visualize that graph. Any further than roughly those points and both power and economy drop quickly.
Too rich and you get unburned hydrocarbons out of the exhaust and very little oxygen. Too lean and you get oxides of nitrogen and some oxygen left over. At 14.7:1 what little unburned hydrocarbons and oxides of nitrogen you get left over are in a fairly stoichiometrically balanced amount such that a catalytic converter can catalyze a reaction using them to produce carbon dioxide and water. This is why we try for this mixture in automotive applications, when everything is right, the exhuast is quite clean.
In a performance application where the EPA is not a concern (for example at the drag strip) you would be trying for somewhere around 12:1, most power and it keeps things running cool.
Disclaimer is that this is from what I know about modern engine management systems in cars and trucks, but I can't believe it wouldn't apply in small 2 cycle engines...