Tier list & power ladder

A band is one rung of the power ladder: a whole number from 0 to 30 carried by every fighter. It is not a description of them — it is the input. Hand the game a band and it works out that character's health and damage from it, by formula, with no per-fighter tuning anywhere.

It goes in three steps:

• The band becomes a rating: rating = 2 ^ band. So each band doubles the rating — band 10 rates 1,024, band 20 rates 1.05M.
• Damage is multiplied by rating ^ 0.5 — the square root of the rating.
• Health is multiplied by rating ^ 0.5 as well: the same exponent.

Taking the square root is what makes the ladder usable. Doubling the rating only multiplies damage by 1.41, so in plain terms:

• One band up ≈ 1.41× the damage and 1.41× the health.
• Two bands up = exactly double both.
• Ten bands up = ×32 both.

And because damage and health take the same exponent, they grow together. A band-30 fight does not end faster than a band-0 one — it lasts about as long, with far bigger numbers floating over it. The band decides who wins when two fighters are mismatched, not how quickly anybody dies.

The tier letter adds nothing. It is a reading of the band and nothing else: Z 30 / X 24-29 / S 20-23 / A 16-19 / B 12-15 / C 8-11 / D 4-7 / F 0-3. Band 0 is special only in that it means “unscaled” — the stats the model shipped with.