Balancing battleship armour, guns, and speed

How should a battleship balance very heavy armour against its guns and speed?

A useful design sits between protection, firepower, and speed; piling on armour consumes weight that could support speed or other capabilities.

Battleship design is framed as a compromise between protection, firepower, and speed. Armour that becomes thicker than the ship's gun calibre signals how heavily protection is consuming the design's available weight. The game-design rule of thumb used here keeps armour roughly an inch below main-gun calibre while pushing for useful speed, with later battleships becoming faster than early dreadnoughts. The example shows why maximising one battleship quality constrains the others.