Assume maximum health (200) and maximum armor (200). What is the maximum jump increase we can achieve using the rocket launcher (aka. rocket jump) in Quake III Arena?
I'm not sure about jump increase, but the max distance you can rocket jump in Quake 3 Arena is around 280 units in game. Taken from the GtkRadiant Manual (under "Game Physics"):
With normal gravity and without the quad, the maximum rocket jump height is around 280 units (you can sometimes jump a few units higher but this is a safe value for reference). In practice, except for especially tricky jumps, this value should be substantially lower. Test rocket jumps repeatedly before settling on a final height.
The Quake 3 map editor documentation also specifies that the max normal jump height is 45 units (32 for bots).
For reference, the bounding box of the player is 56 units. From the same source:
The player model's actual size is a bounding box 30 units by 30 units square with a height of 56 units. In the game world, eight units roughly equal one foot (30.5 cm). From this, we deduce that the characters are a heroic 7 feet tall (2.13 meters).
This means that in Quake 3, and if my math is right, you can rocket jump a distance of 35 feet (10.668 meters) - five times the player's height, and more than six times the max normal jump height (maybe that's what you meant by "jump increase"?)
Note though that with 200 health and 200 armor you would survive a rocket jump while on quad, and if done on a jump pad... who knows then, only the Quake skybox is the limit.