Based on what it says under Super Jump, it sounds like Jump (Brawling squared) is your horizontal movement rate, up to half of which can be vertical. ( I don't get the point of the note that jumping spends "10 squares per panel mid air" - which makes it sound like you can't exceed 10/turn jumping, so I'm ignoring that for now.) That makes virtually every strong character a great jumper, which isn't that appealing.
I'd suggest making base horizontal jump move equal to Agility with the ability jump half that vertically. Then, I'd convert Super Jump to a 1-4, where your jumping distance is based on the Range chart (Lvl 1 = 5, Lvl 2 = x5, Lvl 3 = x10, lvl 4 = x20), and it also subtracts your vertical jump move from the fall distance when calculating fall damage. That makes the first level a bit inferior to flight (that much fall would be soaked anyway) and progressive levels similar in utility (higher move with a high A and it also comes with some fall protection). It also separates bricks that jump really far (Hulk) from bricks that don't (Thing).
Bouncing is also a bit quirky. I don't like that it has its own damage progression, or that you seem to gain momentum through bouncing (?). It seems like the latter should be jumping ability and the former should give you the same damage bonus you get from Super Movement / Momentum. Bouncing also offers Immune 3 (Slams, Falling, and Knockback damage) which already justifies its cost. I'd change it to:
Bouncing (3, sustained): You are completely immune to Slams, Falling, and Knockback damage. When you fall or slam into a solid surface, you can bounce off that surface as a normal move or with the move value of the prior impact. Attacks get the normal momentum damage modifier.
Thoughts?
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