Pick a date, like 1/1/12 and give everyone 1200 base rating starting from that date and calculate rating starting from then.
"Just make formula and rate everyone by current stats."
This would be incredibly hard to do and doesn't make sense. Someone playing support at a high rating level might not have the greatest KDA, gpm, exp per minute, etc. but is still playing at a high level. You have to start everyone out at the same base rating.
I think it'd be nice simply to be able to track progress -- Am I getting better? I wouldn't want the data publicly available, because people will use it to bitch. But a simple percentile or normal distribution with "you are here" after you've logged in would be cool.
Difficult to base on role... Were you playing a carry tide, a farming support tide, or a ward bitch tide?
Honestly, Elo based on win/loss and average rating of the two teams would get you most of the way there.
Honestly I just want to know if I'm playing what tier I'm in at the moment based on the last 5-ish games I've played. It's annoying to start up Dota and search for your name etc.
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You guys have a great interface for stats and are generally very accurate. Wouldn't it be great if you implemented your own rating system using the stats you've gotten from Valve servers?