Honestly, I don't know if ultimate stabilization is a realistic goal or desire. Look at the elite GM`s, they go through serious slumps sometimes. Levon Aronian is just starting to recover from almost a year long slump. Boris Gelfand appears to be in a slump, and these things can last a while. The main thing is to not let it effect your mood. And realize that fluctuations, slumps and periods of excellence are going to cycle through. If you keep your emotional level as cool as possible you'll be doing the best you can.
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When can I expect my realistic rating to stabilize? In some areas I kick others, its obvious I'm out classed.