Spinball and SPP are no good. Never played Sonic Blast so I can't issue judgment there.
My idea for ranking weight:
3D (SA1/2/Heroes):
Time [cat_weight] = 1
Score = 0.7-0.8
Bosses/karts = 0.8
Rings = 0-0.25
2D (1/2/3/K/CD)
Time = 1
Score = 0.4-0.5
S3TA = 0.9
Rings = 0 (or 0.1 if you feel pity)
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What's your basis for those?
Why not split most games in half so you would have a Time/Extra Champ and a Freestyle/Boss/Ring/Score Champ. Because some people are good at time attack and kinda suck at the rest (me >_>) and some people the other way around. That way you can see who's the best Time attacker and the best Score/Ring attacker.
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Firstly, Freestyle doesn't get any weighting, and rightly so. In most cases the ranks are just a duplication of whatever it's replacing (in most cases time).
Second, however, I agree with the rest of what you say. There are people on this site that have concentrated on time, and others who concentrate on score attack. To merge the two into one ranking is hardly fair to those who don't play the game in both disciplines. However, rings are useless ranks, especially in Sonic Heroes where they can be maxed ridiculously easily.
There needs to be separate Time and Score champions, so each gets the recognition they deserve. However overall rankings are downright silly.