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Old version of the rating system.

#3
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As a professional chess player, I find the Elo system more appealing. But it's definitely important to calculate and update ratings promptly! Based on Elo, you can create some kind of grading system (in chess, this translates to sports categories and titles like Candidate Master of Sports, Master, and Grandmaster), and perhaps something similar could be implemented for Heroes. The distinction between online and offline play is also valid; even in chess, there's correspondence chess, which is rated separately.
The rating should be based solely on gameplay; achievements outside of the game (such as organizing tournaments, creating reports, preparing arenas, or judging) should contribute to reputation, not the rating itself.
And it's certainly wrong to allow ratings to be bought and sold, as is done on one of the Heroes-related resources.
As for rewards, distinctive badges