Masonry and Architecture increase TC HP by 60% vs Obsidian Arrows Arbalests

Most buildings have 7/8/9/10 pierce armour in Dark/Feudal/Castle/Imperial Age.

TCs have 5/6/7/8 pierce armour in Dark/Feudal/Castle/Imperial Age.

Obsidian Arrows Arbalests (with Bracer and Chemistry) deal 10 pierce damage and 6 standard building damage (and 6 damage to stone defences).

This means that Obsidian Arrows Arbalests do (10 - 8) + 6 = 8 damage to un-upgraded TCs. It would thus take 300 shots to deal 2400 damage.

Masonry and Architecture add a combined 2/2 armour and 21% HP (and 6 building armour (this doesn't protect against standard building damage)).

This means that Obsidian Arrows Arbalests do (10 - 10) + 6 = 6 damage to upgraded TCs. It would thus take 484 shots to deal 2904 damage.

484/300 = 1.6133 i.e. TCs gain 61% HP by upgrading Masonry and Architecture vs Obsidian Arrows Arbalests

This isn't the case for most buildings (since they have more pierce armour than the pierce damage of crossbows/arbs). Most buildings gain a simple 21% HP.

Towers are another case of buildings with below average pierce armour (watch tower/guard tower/keep/bombard tower have 7/8/9/9 pierce armour), thus they gain from masonry/architecture. However, they also take an additional 6 damage based on the fact that they are stone defences.