Short for Badge Weighted Seeding, BWS is a tournament-minded seeding method intended to more accurately seed players and enforce rank restrictions based on the player's tournament badges.
In short, BWS artificially "ranks up" players based on the amount of badges they have.
In terms of how much a player ranks up per badge, each badge is worth more than the one before it.
More specifically, the formula is as follows:

	rank^(0.9937^(badges^2))

The formula caps at rank 1. That is, a player can't go past rank 1.00 BWS (even if you were rank 2 it'd take like 30 badges to actually get rank 1.00 BWS).
Remember, BWS is not intended to reflect solo play skill. Read the first bullet point again.

Thanks to DigitalHypno for letting us use this system, check out his work here : https://osu.ppy.sh/users/4384207