Improvements

The formula used to calculate improvements is:

[Perk Value] = [Perk Max] * (1 - exp(-[Amount Invested] / ([Coefficient] * [Land] + 15000)))

The stated maximum below can be exceeded with improvement bonuses such as

Improvement Perks
Affinity
Sylvan only
Perk Max Coefficient
Mana production +40% 6,400
Agriculture
All except Barbarian, Growth, Spirit, Sylvan, Troll
Perk Max Coefficient
Food production +40% 5,600
Bashing
Troll only
Perk Max Coefficient
Defensive power +50% 9,000
Bloom
Sylvan only
Perk Max Coefficient
Food production +40% 4,800
Sapling growth +60% 4,800
Brutality
Beastfolk only
Perk Max Coefficient
Offensive power +50% 9,000
Own casualties +50% 6,000
Enemy casualties +50% 6,000
Building
Troll only
Perk Max Coefficient
Construction costs -60% 5,000
Conduits
All except Barbarian, Growth, Sylvan, Troll
Perk Max Coefficient
Mana production +30% 5,600
Construction
All except Barbarian, Growth, Sylvan, Troll
Perk Max Coefficient
Construction costs -20% 4,800
Defenses
All except Barbarian, Beastfolk, Growth, Sylvan, Troll
Perk Max Coefficient
Defensive power +30% 6,800
Education
All except Barbarian, Growth, Troll
Perk Max Coefficient
Improvement points value from investments +20% 3,000
Espionage
All except Barbarian, Growth, Troll
Perk Max Coefficient
Spy strength +40% 6,000
Spy units housing +30% 4,500
Fighting
Troll only
Perk Max Coefficient
Own offensive casualties -20% 6,000
Own defensive casualties -30% 6,000
Glimmering
Troll only
Perk Max Coefficient
Gold production +50% 7,000
Gryphonry
Snow Elf only
Perk Max Coefficient
Unit limit pairing +100% 10,000
Attrition protection +50% 5,000
Hollowing
Dwarg only
Perk Max Coefficient
Population +20% 4,800
Thunderstone discovery +20% 8,000
Housing
All except Barbarian, Dwarg, Beastfolk, Growth, Sylvan, Troll
Perk Max Coefficient
Population +20% 4,800
Hunting
Troll only
Perk Max Coefficient
Food production +120% 6,500
Leadership
All except Barbarian, Growth
Perk Max Coefficient
Ruler title bonus +40% 1,000
Logging
Afflicted, Ants, Beastfolk, Goblin, Kobold, Reptilians, Simian, Snow Elf, Undead, Yeti only
Perk Max Coefficient
Lumber production +30% 5,600
Markets
All except Barbarian, Beastfolk, Growth, Sylvan, Troll
Perk Max Coefficient
Gold production +20% 4,800
Exchange rate +20% 6,400
Mining
All except Barbarian, Ants, Glimjir, Growth, Icekin, Reptilians, Spirit, Swarm, Sylvan, Troll, Wood Elf
Perk Max Coefficient
Ore production +30% 5,600
Muttering
Troll only
Perk Max Coefficient
Wizard strength +65% 5,500
Mana production +65% 5,500
Sorcery damage suffered -65% 5,500
Nesting
Troll only
Perk Max Coefficient
Population +50% 6,000
Nurture
Sylvan only
Perk Max Coefficient
Land discovered +30% 4,800
Construction costs -40% 4,800
Sapling max storage +20% 4,800
Rage
Sylvan only
Perk Max Coefficient
Offensive power +20% 5,600
Defensive modifiers for target -15% 5,600
Reliquary
Reptilians only
Perk Max Coefficient
Unit limit pairing +40% 6,000
Resilience
Sylvan only
Perk Max Coefficient
Defensive power +30% 7,200
Population growth +40% 4,800
Roaming
Sylvan only
Perk Max Coefficient
Population +20% 4,800
Rock Breaking
Troll only
Perk Max Coefficient
Ore production +50% 5,000
Rooting
Glimjir only
Perk Max Coefficient
Kelp harvesting +30% 5,600
Salvaging
Dark Elf, Dwarg, Gnome, Kobold, Wood Elf only
Perk Max Coefficient
Salvaging +50% 5,000
Science
All except Barbarian, Growth, Troll
Perk Max Coefficient
Advancements costs -30% 6,000
Smashing
Troll only
Perk Max Coefficient
Offensive power +60% 10,000
Sneaking
Troll only
Perk Max Coefficient
Spy strength +100% 5,500
Spy losses -100% 5,500
Tactics
All except Barbarian, Beastfolk, Growth, Sylvan, Troll
Perk Max Coefficient
Offensive power +30% 6,800
Thriving
Simian only
Perk Max Coefficient
Barren housing +800% 6,000
Tissue
Growth only
Perk Max Coefficient
Population +140% 90,000
Food production +140% 90,000
Trampling
Troll only
Perk Max Coefficient
Land discovered +75% 5,000
Tranquillity
Beastfolk only
Perk Max Coefficient
Defensive power +50% 9,000
Own casualties -50% 6,000
Enemy casualties -50% 6,000
Tribalism
Barbarian only
Perk Max Coefficient
Population +360% 12,000
Uprooting
Troll only
Perk Max Coefficient
Lumber production +60% 5,000
Warding
All except Barbarian, Growth, Troll
Perk Max Coefficient
Sorcery damage suffered -40% 5,500
Warfare
All except Barbarian, Growth
Perk Max Coefficient
Prestige gains +25% 3,000
Wizardry
All except Beastfolk, Growth, Sylvan
Perk Max Coefficient
Wizard strength +40% 6,000
Wizard units housing +30% 4,500