The below combines the six tables listed under "Research Upgrades by Facility" found on the main research page. This version is sortable and useful to use with the search function (Ctrl+F).
Also available sorted by Effect.
Research Upgrades: Sortable Table  

F  RP  For  Name  Type  Base  Effect  Requirement 
S  1  FR  Enchanting  P (BU)  MP (This game)  Increase the production of Enchanted Fields based on mana produced.
Formula: round(0.75 * x^0.6)% where x is your Mana Produced (This Game) stat.  
S  10  AN  Channeling  P (BNU)  BU  Increase the production of all other buildings by 110% per Heaven's Domain you own.  2000 Heaven's Domain 
S  30  Any  Vacuumancy  MM MR  Time (This Game)  Increase maximum mana and mana regeneration rate based on time spent in this game.
Formula: Max Mana:floor(45 * x),  Have 4000 Max Mana 
S  50  GB  Conjuration  Spell  B  Each time you cast a spell you also cast free Tax Collections based on the amount of Goblin Banks you own. Also increases offline spell cast amount multiplicatively by 150%.
Formula: floor(x /650) where x is the number of Goblin Banks you own.  Have 6000 mana (as Fairy) 
S  105  Any  Mysticism  MR  Research  Increase mana regeneration based on the amount of research made.
Formula: floor(x^0.5) where x is number of researches made.  600 Researches 
S  135  Any  Augmentation  P (BU)  MM  Increase the production of Unique Buildings based on maximum mana.
Formula: round(2 * x^0.8)% where x is your maximum mana.  5000 Unique Buildings (as Fairy) 
S  150  Any  Pyromancy  P (B)  MR  Increase the production of the two highest building tiers based on your mana regeneration.
Formula: round(4 * x^1.3)% where x is your Mana per Second stat.  Research D10, A105 
S  175  Elf  Empowered Luck  P (B)  Click (Elven Luck)  Increase production of all buildings by 36,000% for 20 seconds each time you trigger Elven Luck and increase the chance to trigger it by an additional 24%.  Research D1, S135 
S  180  FR  Incantation  MR  A  Increase mana regeneration based on the number of assistants you own.
Formula: floor(13 * x^0.6) / 10 where x is the number of assistants you have.  Research S1, S105 
S  200  Any  Cryomancy  P (B)  M (Current)  Increase the production of all buildings based on your current mana (the less mana, the better bonus).
Formula: round((100  x)^1.75)% where x is percentage of current missing mana.(at 0 mana x is 100).  Research S50, A55 
S  215  Any  Projection  P (Spell)  Spell  Increase Spiritual Surge effect based on the amount of active spells.
Formula: 15 *((15 * x) ^Y) where x is active spells and y is ascension. (does not include Spiritual Surge)  300 Spiritual Surge (Total), Research S10, S175 
S  225  UD  Necromancy  P (A)  BU  Increase the production of assistants based on the amount of Necropolises you own.
Formula: round(5 * x^0.75)% where x is the number of Necropolises you own.  Research D175, S200 
S  250  Any  Aeromancy  P (BU)  MP (This game)  Increase the production of Unique Buildings based on mana produced in this game.
Formula: round(0.5 * x^0.58)% where x is your Mana Produced (This Game) stat.  Research
D225, A150 
S  251  FC  Assimilation  P (BU)  Time (Other Faction Playtime)  Increase the production of Sunken Cities based on time spent affiliated with factions different than the Faceless.
Formula: round(0.3 * x^0.7)% where x is total time spent as nonFaceless factions.  Play as Faceless 
S  270  Any  Runecarving  P (B)  MM  Increase the production of all buildings based on your bonus from Gems.
Formula: round(1.15 * x^0.75)% where x is your gem bonus.  500,000 clicks (This game) 
S  300  TT  Chain Lightning  P (B)  Spell Casts (This Game)  While Lightning Strike is active, all nontarget buildings have their production increased based on the amount of Lightning Strikes cast in this game.
Formula: 250 * (x / 20)^0.9% where x is your Lightning Strikes Active Time (This Game) stat.  25 Brainwaves (Total) 
S  305  Any  Mesmerization  P (B)  P (Offline)  Increase the production of all buildings by a fraction of your offline production bonus.
Formula: 2.5 * log(1+x)^2.5 where x is your preAscension offline multiplier.  5 days as Faceless (Total across all R) 
S  330  Any  Reverberation  P (B)  Spell  Increase the production of all buildings based on the number of active spells you have. You must have at least 3 active spells to generate a bonus.
Formula: 375 * 2^x% where x is the number of spells currently active.  Research
A200, D225 
S  375  FC  Illusion  A  Spell Time (This Cast)  Brainwave also provides progressively more assistants over its duration.
Formula: Floor(1.15 * (x + y) ^ 2) where x is brainwave runtime in minutes and y is headstart in minutes.  Research
S330, S305 
S  400  Any  Capacity  MM  Spell Casts (Highest)  Increase maximum mana based on the highest amount of spells cast in a single game.
Formula: floor(35* x^0.35) where x is your Spell Cast (Max) stat.  Research S215, W275 
S  435  DW  Spellbinding  P (Offline)  Spell  Passively grants the effects of Call to Arms while offline.  4h Combo Strike Cast Time (This game) 
S  460  Any  Focus  P (B)  Spell Casts (Faction This Game)  Increase the production of all buildings based on the amount of times you cast your faction spell in the game.
Formula: 15 * x^0.8% where x is Faction Spells' Cast This Game (Vanilla + Prestige spell count).  25000 spell casts (This game) 
S  500  Any  Heirlooms  MM  Artifact  Increases maximum mana based on the number of owned artifacts.
Formula: 100 * x^1.1 where x is artifacts.  40 Artifacts (as Drow) 
S  545  Any  Hiearchy  P (B)  MP (This game)  Increase the production of buildings based on mana produced in this game, depending on their tiers. Gives better bonuses for lower tiers.
Formula: (0.1 * x^0.45 * T^2)% where x is Mana Produced (This Game) stat, and T is the building tier, starting at 11 for Farms and decreasing to 1 for Halls of Legends.  10 M (1_{E}7) mana produced (this game) 
S  590  FR DN  Trickery  P (B Neutral)  MM  Increase the production of Neutral buildings based on maximum mana.
Formula: 0.5 * x^1.05% where x is Maximum Mana.  200 Dwarf Exchanges as Dwarf/Fairy, Research
S105, S375 
S  1275  Any  Sequence  Reduc (Spell)  Reduce spell cost for higher spell tiers.
Reduces cost multiplier by 0.5; with no other reductions applying, the multiplier will be 1.5 instead of 2.  60,000 Spells cast  
S  1450  DG  Spellstorm  P (BU)  Spell  Increase the production of Unique Buildings based on the amount of active spells.
Formula: 50 * x^1.5% where x is number of active spells, counting tiers.  Research
S435, C1325 
S  1500  FC DG  Psionics  P (BU)  A  Increase the production of Unique Buildings based on the amount of assistants you own.
Formula: 8.5 * x^0.85% where x is the amount of assistants.  1000 Base Assistants as Faceless/Dragon Research
S545, E1325 
S  2875  M  Scholarship  P (BNU)  U  Increase the production of NonUnique buildings by 40% per Unique building you own.  11000 Merc Unique Buildings 
S  3200  Any  Manipulation  MR  Spells  Each active spell increases mana regen by an additional 8% (Share Benefits tiers also count). Also increases offline spell cast amount by multiplicatively by 1200%.  1e9 Tax collection casts
Research 
C  1  Elf  Dummy Targets  P (BU)  FC (This game)  Increase Elven Training Grounds production based on the amount of Faction Coins you found.
Formula: round(1.3 * ln^3(1+ x))% where x is your Faction Coins Gained (This Game) stat.  
C  10  FR  Cultivation  P (B)  BU  Increases production of Blacksmith and Inn by 60% per Enchanted field that you have.  2500 Farms 
C  25  AN  Light Condenser  MR  Spell Casts (This Game)  Increase mana regeneration based on the amount of spells cast.
Formula: floor(10 * x^0.3) / 10 where x is your Spells Cast (This Game) stat.  12,000 Spells casts (Total) 
C  50  DM  Refining  P (BU)  FC (This game)  Increase the production of Infernal Realms based on the amount of Demon Coins you found in this Game.
Formula: round(0.8 * ln^3(1 + x))% where x is your Demon Coins Gained (This Game) stat.  1 B (1_{E}9)Faction Coins (as Elf) 
C  80  Vanilla  Apprenticeship  P (B Neutral)  B (Good+Evil)  Increase the production of Neutral buildings based on the amount of Good and Evil buildings.
Formula: round(x^0.8)% where x is the number of Good and Evil Buildings you own.  16,000 Good and Evil buildings 
C  105  Any  Woodcraft  FC%  BU  Increase the chance to find Faction Coins based on the amount of Unique Buildings you own.
Formula: floor(1.5 * x^1.05)% where x is the number of Unique Buildings you own.  25,000 clicks (This Game) 
C  120  Any  Socketing  P (Click)  Gem  Increase clicking reward based on the amount of gems you own.
Formula: round(20 * log(1 + x))% where x is your current number of gems.  200,000 clicks (This Game) 
C  135  Any  Reinforcing  P (B)  Click (Total)  Increase the production of all buildings based on your total number of clicks.
Formula: (ln(1 + x))^2.75% where x is your Treasure Clicks (Total) stat.  250,000 clicks (This Game, as Elf) 
C  150  Any  Tinkering  P (B)  Research  Increase the production of all buildings based on the amount of research made.
Formula: round(125 * x^0.38)% where x is number of researches made.  Research E10, C135 
C  175  GB  Gemcutting  P (Gem)  B  Increase the production bonus from gems based on the number of buildings you own.
Formula: floor(x / 2000)% where x is your Buildings Owned (This Game) stat.  Research C50, C120 
C  200  Any  Journeymen  P (BU)  Time (Faction Playtime)  Increase the production of Unique Buildings based on total time spent as that faction.
Formula: round(0.125 * x^0.7)% where x is your Time Spent as that faction stat.  Research C80, E50 
C  225  Elf  Automatons  P (Spell)  BU  Each Elven Training Grounds counts as 200 buildings for Call to Arms purposes.  Research C1, A120 
C  250  Any  Magnetism  FC%  Time (Offline Total)  Increase the chance to find Faction Coins by a multiplicative 50%. Increase the chance to find faction coins based on total time spent offline. (in minutes) Formula: 2.5 * x ^{0.75} where x is your Time Spent Offline (Total) stat in minutes.  Research C150, W225 
C  251  TT  Architecture  P (BU)  B  Increase the production of Olympian Halls based on the amount of buildings you own.
Formula: round(0.5 * x^0.8)% where x is your Buildings Owned (This Game) stat.  Play as Titan 
C  300  DD  Weighting  P (Spell)  MM  IWhile Grand Balance hits Stone Pillars, increase its production by 3.09%. Also increase the production of every Grand Balance target based on maximum mana. Formula: round(0.12*ln(1+x))^2)^y) where x is your maximum mana and y is spell tier.  650 Lightning Strikes 
C  305  Any  Golemcraft  A  Time (Offline Total)  Gain assistants based on your total time spent offline (in hours).
Formula: floor(2 * x^0.5) where x is your Time Spent Offline (Total) stat.  5 days as Titans (Total across all R) 
C  330  Any  Overload  P (Click)  Research  Increase clicking reward based on the amount of research made.
Formula: round(145 * x^0.38)% where x is researches made.  Research A250, W225 
C  340  Any  Gem Duster  P (Gem)  Ruby  Increase production from gems based on the amount of Rubies you collected. (Multiplicative)
Formula: 10 * x% where x is your Rubies Gained (All Time) stat.  800 Gem Grinders,
Research 
C  375  TT  Lightning Rod  Spell  Olympian Halls are always hit by Lightning Strike in addition to the primary target. Olympian Halls can no longer be a primary target.  Research S300, C330  
C  400  Any  Gravitation  FC%  FC (This game)  Increase the chance to find Faction Coins based on the amount of Faction Coins found in this game.
Formula: floor(3.5 * ln^3(x + 1)) where x is your Faction Coins Gained (This Game) stat. Also increases Faction Coin find chance by a multiplicative 175%.  Research C250, C300 
C  405  DN  Metallurgy  P (BU)  P (BU)  Increase the production of Dwarven Forges based on the amount of Dwarven Forges you own.
Formula: 45 * x^0.825% where x is the number of Dwarven Forges you own.  Secrets of the Underworld upgrade (as Dwarf) 
C  460  Any  Distribution  P (BNU)  Click (This Game)  Increase the production of nonunique buildings based on the amount of clicks you made in this game. (including assistant clicks)
Formula: 35 * x^0.5% where x is your Treasure Clicks (This Game) stat.  1 M (1_{E}6) Clicks (This Game) 
C  500  Any  Minecrafting  P (Gem)  Ex  Increase the production bonus of gems based on the amount of Excavations you made.
Formula: 3 * x^0.35% where x is the amount of Excavations you made.  3250 Excavations as Dwarf 
C  520  DN  Blacksmithing  P (Spell) + FC% (Spell)  BU  Increase clicking reward for Diamond Pickaxe based on the amount of Dwarven Forges you own. Also increase Faction Coin find chance bonus of Diamond Pickaxe based on the amount of Dwarven Forges you own. {{FormulanakedTClicking Reward: 2.5 * x^0.3%  Research C135, C405 
C  590  Elf DN  Alloys  P (Click)  FC%  Increase clicking reward based on your chance to find Faction Coins, (if your FC chance is 10k%, this will be 10k%). Autoclicks the treasure 10 times per second.  200 Dwarf Exchanges as Dwarf/Elf, Research
A105, C520 
C  1300  DG  Scintillation  P (Gem)  MM  Increases production bonus from gems based on maximum mana.
Formula: 2 * x^0.4% where x is where x is maximum mana.  30,000 max mana 
C  1325  Any  Plasmation  A  MP (This game)  Gain assistants based on mana produced in this game.
Formula: floor(1.25 * ln(1 + x)^2) where x is mana produced (this game).  50 M (5_{E}7) mana produced (this game) 
C  1500  TT DG  Gargantuaness  P (B)  Time Spent  Increase production for all buildings based on total time spent as Neutral.
Formula: (1.5 * x)^0.7% where x is your Neutral time (this R) stat in minutes.  2,500 Royal Exchanges as Titan/Dragon, Research
E460, D1275 
C  3000  M  Customizing  P (B)  Artifact  Increase the production of all buildings based on the amount of artifacts you own.
Formula: 1.65 * x^1.65 where x is artifacts.  9,000 Excavations (as Mercenary) 
C  3100  Any  Engineering  MM  Clicks  Increase maximum mana based on the total amount of clicks made that Reincarnation.
Formula: 7.5 * log10^2.15(1 + x) where x is your Clicks (this R) stat.  15d Mercenary time spent 
D  1  AN  Blessing  P (BU)  Spell Time (Total)  Increase the production of Heaven's Domains based on total time spent with at least one active spell.
Formula: round(2 * x^0.8)% where x is total time spent with at least one active spell.  
D  10  DM  Inflame  P (BNU)  BU  Increase the production of all other buildings by 110% per Infernal Realm you own.  2000 Infernal Realms 
D  25  UD  Cursing  P  P (Offline)  Increase the production of all buildings based on your offline production bonus.
Formula: 2.75 * log(1 + x)^2.75 where x is your offline production bonus.  Play 8 hours Offline (This Game, as Undead) 
D  50  Elf  Hallowing  FC%  B  Increase your chance to find Faction Coins based on the amount of Elven Training Grounds you own.
Formula: floor(5 * x^0.85)% where x is the number of Elven Training Grounds you own.  15,000 Good Buildings (as Angel) 
D  55  Any  Transfixion  P (Click)  Spell Casts (This Game)  Increase clicking reward based on spell cast in this game.
Formula: round(3.5 * x^0.8)% where x is your Spells Cast (This Game) stat.  Produce 3 M (3_{E}6) Mana (This Game) 
D  135  Any  Illumination  MR  Gem  Increases mana regeneration based on the amount of gems you own.
Formula: floor(1.25 * ln(1 + x)) / 10 where x is amount of gems you own.  250 m/s Mana Regen (as Angel) 
D  150  Any  Retribution  FC%  Research  Increase the chance to find Faction Coins based on the amount of research made.
Formula: floor(0.05 * x^1.25 where x is the amount of research made.  Research W120, D55 
D  175  AN  Resurrection  A  Spell Time (This Game)  You gain additional assistants based on God's Hands activity time.
Formula: floor(0.45 * (0.15 * x)^0.6) where x is God's Hands' Active Time (This Game).  Research D1, A55 
D  200  Any  Transcendence  Reduc (Spell) +Spell Time  Decrease the cost of all spells by 20% and increase their duration by 20%.  Research
D175, D135  
D  205  Good  Communion  Spell Time  Increase Holy Light duration by 110 seconds.  777 Holy Lights (Total), Research C175, D135  
D  225  FR  Weather Control  P (BU)  MM  Increase the production of Enchanted Fields based on maximum mana.
Formula: floor(2.25 * x^0.8)% where x is your maximum mana.  Research C25, S30 
D  245  Any  Soulrending  P (Spell)  R#  Reincarnations count twice for Spiritual Surge.  500 Spiritual Surge (Total), Research A175, S225 
D  250  Any  Demonology  A  FC (This game)  Gain assistants based on the amount of Faction Coins found in this game.
Formula: floor(ln^1.3(1 + x)) where x is your Faction Coins Gained (This Game) stat.  Research D200, S150 
D  260  FC  Mutation  P (BNU)  BU  Increase the production of all other buildings by 95% per Sunken Cities you own.  3000 Sunken Cities 
D  275  DD  Meditation  MR  M  Increase mana regeneration based on your current mana. Also increases offline spell cast amount by multiplicatively by 300%. Formula: 0.5 * (100  x)% where x is percent of max mana.  10,000 Mana (as Druid) 
D  290  Any  Transubstantiation  MR  Artifact  Each artifact you discover increases mana regeneration by 1.5 m/s.
Formula: floor(1.5 * x)) where x is the number of artifacts found.  Rough Stone Artifact 
D  320  Any  Deliverance  P (A)  MR  Increase assistants production based on mana regeneration.
Formula: round(20 * x^0.85)% where x is your Mana per Second stat.  350 m/s Mana Regen 
D  330  Any  Eternity  Spell Time (Faction)  Double the duration of all faction spells.  Research E275 & D320  
D  350  TT  Descent  A  BU  Gain assistants based on the amount of Olympian Halls you own.
Formula: floor(x^0.5) where x is the number of Olympian Halls you own.  Research W250, W330 (as Titan) 
D  400  Any  Miracle  P (Brandom)  Increase the Production of a random building by x250. Target changes every 2 minutes. While offline, increase the production of all buildings by x75.  Research D205, D290  
D  435  DN  Devotion  P (B Good)  Spell Casts (This Game)  Increase the production of Good buildings based on spells cast this game. Formula: 2.5 * x^0.85% where x is your Spells Cast (This Game) stat.  4h Diamond Pickaxe Cast Time (This Game) 
D  480  Any  Mercy  P (B)  Time (Each Alignment Playtime)  Increase the production of all buildings based on the difference in time spent with the three alignments. A smaller difference produces an higher bonus. Formula: 100000 * (tmin / tmax)^{1.5}% where tmin and tmax are the shortest and longest Time Spent Being Alignment (Total) Stat.  12h Time Spent as each Good, Evil and Neutral alignment, (1d12 in total) 
D  525  GF  Purity  Spell  Spell Casts (Faction This Game)  Increase Holy Light multiplier based on the amount of times you cast your faction spell in this game.
Formula: 300 * x^0.3% where x is your Faction Spells' Cast This Game (Vanilla + Prestige spell count) stat.  1d, 12h Good Time Spent, Research D205, D435 (as any good faction) 
D  560  DW  Ritualism  MR  Trophy  Increase mana regeneration based on the amount of trophies you unlocked.
Formula: floor(0.7x) / 10 where x is the amount of Trophies Unlocked.  Research S225 and S500 (as Drow) 
D  590  AN DN  Dispelling  P (BU)  MR  Increase production of Unique buildings based on mana regeneration.
Formula: 2.5 * x^1.25% where x is your Mana per Second stat.  200 Dwarf Exchanges as Dwarf/Angel, Research W320, A480 
D  1125  DG  Oblation  P (BU)  FC%  Increase the production of Wyrm's Den based on Faction Coin find chance.
Formula: 1.5 * x^0.55% where x is the Faction Coin find chance (in percentage).  Buy Wyrm's Den. 
D  1275  Any  Solemnity  P (B)  B  Increase the production of each building by 0.3% per building of the same type.  100,000 Total Buildings. 
D  1375  Any  Sanctification  P (BU)  B (NU)  Increase the production of Unique Buildings based on the amount of NonUnique buildings you own.
Formula: 2.5 x^0.55% where x is the number of NonUnique buildings you own.  1 day Good Time spent (Total) 
D  2775  M  Intervention  P (BU)  Time spent  Increase the production of Unique Buildings based on time spent with Mercenaries.
Formula: 0.1 * x^0.7 where x is time spent with Mercenary.  Secrets of the Warriors upgrade 
D  3350  Any  Vampirism  P (Offline)  Reincarnations  Increase offline production based on the amount of Reincarnations you made.
Formula: 1.7 * x^1.7 where x is Reincarnation count.  1 Sp (1_{E}24) Offline Bonus Research D2775, W3150 
E  1  GB  Coinage  P (BU)  B  Increase the production of Goblin Banks based on the amount of buildings you own.
Formula: round(0.8 * x^0.8))% where x is your Buildings Owned (This Game) stat.  
E  10  UD  Recycling  P (BNU)  BU  Increase the production of all other buildings by 95% per Undercity you own.  2,000 Undercities 
E  25  Elf  Commerce  A  RE  Gain assistants based on the amount of Royal Exchanges you purchased.
Formula: floor((1 + 6x)^0.5  1) where x is your Royal Exchanges Made stat.  100 M (1_{E}8) Faction Coins 
E  30  Any  Diplomacy  FC% RE  Time (this game)  Increases Faction Coin find chance and Royal Exchange bonus based on time spent in this game.
Formula: Faction Coin Chance: floor(10 * x)%  1000 Exchanges 
E  50  FR  Bartering  Reduc (BU)  Reduce Enchanted Field cost multiplier.
Reduces cost multiplier by 0.035; with no other reductions applying, the multiplier will be 1.115 instead of 1.15.  1,000 Exchanges (as Goblin)  
E  80  Vanilla  Common Business  P (B Good+Evil)  B (Neutral)  Increase the production of Good and Evil buildings based on the amount of neutral buildings.
Formula: round((1.75 * x)^0.8)% where x is the number of neutral buildings you own.  9,000 Neutral Buildings 
E  135  Any  Bribing  Reduc (BU)  Reduce the building cost multiplier for Unique Buildings.
Reduces cost multiplier by 0.02; with no other reductions applying, the multiplier will be 1.13 instead of 1.15.  28,000 Total Buildings (as Goblin)  
E  145  Any  Royal Demand  P (Spell) + FC  Increase Tax Collection reward by 30 seconds of production.  5000 Tax Collections (Total), Research C10, C105  
E  150  Any  Investment  P (B)  Coin  Increase the production of all buildings based on the amount of gold you own.
Formula: round( (ln(1 + x))^1.25)% where x is the amount of gold you own.  Research E135, E25 
E  200  Any  Acquisition  P (B)  Trophy  Increase the production of all buildings based on your percentage of trophies unlocked.
Formula: round(0.0003 * (100 * x)^3.35) where x is trophiesunlocked / trophiesmax.  Research E150, E80 
E  225  GB  Forgery  P (B Evil)  BU  Increase the production of Evil Buildings based on the amount of Goblin Banks you own.
Formula: round(10 * x^0.85)% where x is the number of Goblin Banks you own.  Research E1, A50 
E  230  DM  Coercion  P (BU)  Time (Evil Playtime)  Increase the production of Infernal Realms based on total time spent being Evil.
Formula: round(0.2 * x^0.7)% where x is your Time Spent Being Evil (Total) stat.  Research W50, E30 
E  250  Any  Trade Routes  MR  RE  Increase mana regeneration based on the amount of Royal Exchanges you purchased.
Formula: floor(10 * x^0.55) / 10 where x is your Royal Exchanges Made stat.  Research E225, E145 
E  260  DD  Sifting  P (BNU)  BU  Increase the production of all other buildings based on the amount of Stone Pillars you own.
Formula: (100 * x) where x is the number of Stone Pillars you own.  3,000 Stonehenge Circles 
E  275  TT  Offering  MR  RE  Increase mana regeneration based on your Royal Exchange Bonus.
Formula: floor(0.9 * x^0.95) where x is your Royal Exchange Bonus.  1,250 Royal Exchanges (as Titans) 
E  290  Any  Surveyorship  Reduc (Ex)  Reduce Excavation cost multiplier.
Reduces cost multiplier by 0.025; with no other reductions applying, the multiplier will be 1.175 instead of 1.2.  7 Artifacts  
E  320  Any  Smuggling  P (Gem)  Gem (Made this Game)  Increase production bonus from gems based on the gems you have in your abdication treasury.
Formula: floor(0.45 * log(1+ x))% where x is the amount of gems you will gain upon abdication.  Have 2x Gems in Abdication Treasury 
E  330  Any  Collection  P (B)  Artifact  Increase the production of all buildings based on the amount of artifacts you found.
Formula: round(50 * x^1.1)% where x is the amount of artifacts found.  Research E200, E225a 
E  350  FC  Repurpose  P (B)  R#  Increase the production of all buildings based on the amount of Reincarnations you made.
Formula: round(2.5 * x^2.25)% where x is the amount of times you reincarnated.  Research C200, A330 (as Faceless) 
E  400  Any  Conversion  P (Gem)  RE  Increase production bonus from Gems based on your Royal Exchange bonus. Formula: floor(x^0.95)% where x is your Royal Exchange Bonus.  Research A250, E350 
E  410  DN  Marketing  P (BNU)  P (BU)  Increase the production of all other buildings by 85% per Dwarven Forge you own.  5000 Blacksmiths 
E  460  Any  Inflation  RE  FC (This game)  Increase Royal Exchange bonus based on the amount of Faction Coins found in this game.
Formula: floor(3.5 * log(1 + x))% where x is your Faction Coins Gained (This Game) stat.  100 B (1_{E}11) Faction Coins 
E  480  Any  Undercutting  P (BNU)  Spell Casts (Total)  Increase the production of nonunique buildings based on total spells cast. Formula: 0.65 * x^0.65% where x is your Spells Cast (Total) stat.  15,000 Max Mana 
E  495  DW  Jewellery  P (Gem)  BU  Increase the production bonus from gems based on the amount of Spider Sanctuaries you own.
Formula: (1.2 * x^0.8 / 20)% where x is the number of Spider Sanctuaries you own.  12,000 Unique Buildings (as Dwarf) 
E  590  GB DW  Slavery  A  B (Evil)  Gain additional assistants based on the amount of Evil buildings you own. Formula: floor((x / 300)^1.05) where x is the number of Evil Buildings you own.  200 Drow Exchanges as Drow/Goblin, Research C225, E480 
E  1225  DG  Hoarding  Reduc  RE  Reduce Ascension 1 penalty for Royal Exchanges.
Formula: ((((((bonus per RE as %)^0.2(if E1225)) * #REs)/100)+1)^0.1(if not E1225).  1 T (1_{E}12) Faction Coins 
E  1325  Any  Intimidation  Reduc  RE  Reduce Royal Exchange cost modifier.
Reduces cost multiplier by 0.025; with no other reductions applying, the multiplier will be 1.075 instead of 1.1.  18,000 Unique Buildings 
E  1425  Neutral  Rarity  P (Spell)  Artifact  Increase Gem Grinder bonus based on the amount of artifacts you found.
Formula: 1.75 * x^1.75) where x is the amount of artifacts you found.  30d Time Spent (Alltime), 10d with each Titan, Druid, and Faceless. Research A54, C1300 
E  3250  M  Estates  B (U)  Alignment  Gives you all the Unique Buildings of your alignment. Can only be used as Mercenary.  45,000 Unique Buildings Research E1225, A2950 
E  3300  M  Hirelings  A  Coins  Gives assistants based on the gold you have.
Formula: 2 * \log_{10}(x + 1) additive where x is gold you have.  Research E1325, A2950 
A  1  UD  Plague  P (BU)  A  Each assistant increases the production of Undercities by 8% per assistant you own.  
A  10  GB  Transmutation  P (BNU)  BU  Increase the production of all other buildings by 85% per Goblin Bank you own.  2250 Goblin Banks 
A  25  DM  Deflagration  Reduc (Spell)
+ P (Spell)  Reduces Hellfire Blast duration by 16 seconds, reduces its mana cost by 200 and multiplies its effect by x7.  666 Hellfire Blast Casts (Total)  
A  30  FR  Delayed Reaction  Spell Time +
P (Spell)  B  Increases duration of Fairy Chanting based on the amount of Enchanted Fields, Inns, Blacksmiths and progressively increases spell bonus.
Formula:  750 Fairy Chanting Casts (Total) 
A  50  AN  Gliding  MR  BU  Heaven's Domains further increase your mana regeneration rate.
Formula: 1.45 * x^0.45 where x is the number of Heaven's Domains you own.  120 m/s Mana Regen (as Undead) 
A  55  Any  Refraction  P (Offline)  Spell Casts (Total)  Improve offline production based on spells cast.
Formula: round(3 * x^0.85)% where x is your Spells Cast (Total) stat.  25000 spell casts (This Game) 
A  105  Any  Fusion  P (B)  FC (This game)  Increases the production of buildings based on the amount of Faction Coins found this game.
Formula: round(0.7 * ln^3(1 + x))% where x is your Faction Coins Gained (This Game) stat.  2750 Blacksmiths 
A  120  Any  Vivification  A  MM  Gain assistants based on max mana.
Formula: floor(x / 15)^0.825) where x is your maximum mana.  Have 6500 Max Mana 
A  135  Any  Decay  P (B)  Time (Total)  Increase the production on all buildings based on total time spent.
Formula: round(c * x^{0.7})% where x is your Playtime (Total) in seconds stat and c is 0.03(2^{0.7}), which is approximately 0.049.  1 Day Total Play Time (as Undead) 
A  150  Any  Explosives  P (B)  MP (This game) + Spell  Whenever you cast a spell, increase the production of your most productive building based on the amount of mana produced in this game for 20 seconds. If another spell is cast while this effect is active, it is restored to full duration.
Formula: round(0.7 * x^0.6)% where x is your Mana Produced (This Game) stat.  Research A25, A30 
A  175  UD  Soulweaving  P (B)  R#  Increase the production of all buildings based on the amount of times you Reincarnated.
Formula: round(2.5 * x^2.25)% where x is the amount of times you reincarnated.  Research D25, C135 
A  200  Any  Corrosion  P (Click)  Time (This game)  Increase clicking reward based on time spent in this game.
Formula: round(c * x^0.75)%, where x is your Playtime (Total) in seconds stat and c is 0.07(2^0.75), which is approximately 0.118.  Research A1, A135 
A  250  Any  Philosopher's Stone  P (Gem)  Research  Increase production bonus from gems based on the amount of research made. Formula: floor(x^0.9 / 25)% where x is the amount of research made.  Research A10, S175 
A  251  DD  Infusion  P (BU)  MP (This game)  Increase the production of Stonehenge Circles based on mana produced in this game.
Formula: round(0.75 * x^0.6)% where x is your Mana Produced (This Game) stat.  Play as Druid 
A  270  Any  Synthesis  MR  FC (This game)  Increase mana regeneration based on the amount of Faction Coins found in this game.
Formula: floor(10 * ln(1 + x)) / 10 where x is your Faction Coins Gained (This Game) stat.  20 B (2_{E}10) Faction Coins (This game) 
A  300  FC  Creeping  MR  MP (This game)  Increase mana regeneration based on mana produced in this game.
Formula: floor(30 * ln^1.2(1 + x)) / 10 where x is your Mana Produced (This Game) stat.  Produce 5 M (5_{E}6) mana (This game, as Druid) 
A  305  Any  Engraving  FC%  Spell Casts (This game)  Increase your chance to find Faction Coins based on the amount of spells cast in this game. Also increase Faction Coin find chance by a multiplicative 100%. Formula: floor(3.5 * logE(1+x)^3.5)% where x is your Spells Cast (This Game) stat., or approximately Formula: floor((ln(x) + 0.69)^2.75)% where x is your Spells Cast (This Game) stat.  5 days as Druids (Total across all R) 
A  330  Any  Adaptation  P (B)  Time (Other Faction Playtime)  Increase the production of all buildings based on time spent playing as other factions.
Formula: round(0.05 * x^0.7)% where x is time spent as other factions.  Research D260, D275 
A  375  DD  Transfusion  A  MP (This game)  Gain assistants based on mana produced this game.
Formula: floor(4.5 * ln(1 + x)) where x is your Mana Produced (This Game) stat.  Research A251, A305 
A  400  Any  Bloodspring  Bloodline  You get your faction's Bloodline effect for free. Bloodstream counts time spent with both factions.
NOTE: Does not work with two Bloodlines of the same type and unavailable as Mercenaries.  Research S251, A375  
A  410  DW  Poisons  P (BNU)  BU  Increase the production of all other buildings by 95% per Spider Sanctuaries you own.  4,000 Spider Sanctuaries 
A  480  Any  Waste  P (Offline)  RE  Increase offline production based on the amount of Royal Exchanges you purchased.
Formula: 120 * x^0.85% where x is your Royal Exchanges Made stat.  2,000 Royal Exchanges 
A  495  DN  Elixirs  P (A)  Research  Increase assistants production based on the amount of research made.
Formula: 120 * x^0.42% where x is the Amount of Researches made.  500 Base Assistants (as Drow) 
A  545  Any  Mineralogy  P (B)  Ruby  Increase the production of all buildings based on the amount of Rubies you own.
Formula: 10 * x^1.05% where x is your Rubies Gained (All Time) stat.  700 Trophies 
A  590  UD DW  Hexing  P (B)  MP (This game) + Time (Offline This Game)  Increase the production of all buildings based on mana produced and the percentage of offline time spent in this game.
Formula: 0.045 * x^0.45 * P% where x is your Mana Produced (This Game) stat and P is the percentage of your Time Spent Offline for this game.  200 Drow Exchanges as Drow/Undead, Research D25, A410 
A  1200  DG  Melting  P (B)  BU  Increase the production of all other buildings by 0.35% per Iron Strongholds.  5000 Iron Stronghold, Any Neutral Dragon 
A  1325  Any  Calefaction  MR  Ex  Increase mana regen based on the amount of excavations made.
Formula: floor(0.02 * x) where x is current excavations.  5500 Excavations 
A  1500  DD DG  Sublimation  MM  BU  Increase maximum mana based on the amount of Unique Buildings you own.
Formula: 8 * x^0.8 where x is the number of Unique Buildings you own.  6h Grand Balance Cast Time (this game) as Druid/Dragon, Research D590, A1325 
A  2950  M  Combination  Bloodline  Select an additional Bloodline. You also gain the base effect of its respective Lineage.  All 12 Lineages level at 15  
A  3400  Any  Chemistry  FC  Lineage  Increases Faction Coin find chance based on the total amount of Lineage levels you have. Also increases Faction Coin find chance by a multiplicative 350%. Formula: 3 * x^2.25 where x is total Lineage levels..  1 No (1_{E}30) Faction coins, Research C3000, S3200 
W  1  DM  Assault  P (BU)  Spell Casts (This game)  Increase the production of Infernal Realms based on the amount of Hellfire Blasts cast in this game.
Formula: round(70 * x^0.55)% where x is Hellfire Blasts Cast (This Game).  
W  10  Elf  Dueling  P (BNU)  BU  Increase the production of all other buildings by 90% per Elven Training Grounds you own.  2000 Warrior Barracks 
W  25  GB  War Funds  P (B)  Spell Casts (This game)  Increase the production of all buildings based on the amount of Tax Collections cast in this game.
Formula: round(5 * x^0.6)% where x is Tax Collections Cast (This Game).  1 Tqag (1_{E}132) Coins Gained (This Game, as Goblin) 
W  50  UD  Exertion  FC/s  BU  Increase Faction Coin find chance based on the amount of Undercities you own.
Formula: (floor(6.5x^0.65))% where x is the number of Undercities you own.  2d Evil Play Time (Total, as Demon) 
W  120  Any  Betrayal  P (BNU)  A  Increase the production of nonunique buildings based on the amount of assistants you own.
Formula: round(1.5 * x^1.5)% where x is the amount of assistants you own.  250 base assistants 
W  135  Any  Rampage  MM  Trophy  Increase maximum mana based on the number of trophies you have unlocked.
Formula: floor(1.25x) where x is the amount of trophies unlocked.  580 Trophies (as Demon) 
W  150  Any  Invasion  P (B)  A  Increase the production of all buildings based on the amount of assistants you own.
Formula: round(32 * x^0.75)% where x is the amount of assistants you own.  Research W25, W135 
W  175  DM  Overwhelm  A  Spell Casts (Total Evil)  You gain assistants based on total amount of evil spells cast.
Formula: floor(0.75 * x^0.6) where x is the amount of evil spells cast..  Research W1, W150 
W  180  Any  Formation  P (Spell)  B  Each building counts 15 times for Call to Arms purposes.  1000 Call to Arms (Total) Research W10, W50 
W  200  Any  Crusade  A  Time (Good Playtime)  Gain assistants based on total time spent as Good.
Formula: floor(0.065 * x^0.5) where x is your Time Spent Being Good (Total) stat.  Research D50, W180 
W  205  Evil  Berserking  MR  A + Spell  While Blood Frenzy is active, increase mana regeneration based on the amount of assistants you own.
Formula: floor(0.25 * x^0.9) / 10 where x is your Assistants stat.  850 Blood Frenzy (Total), Research W135, D150 
W  225  AN  Critical Strike  P (BU)  Spell Time (This Game)  Holy Light empowers Heaven’s Domains based on Holy Light activity time in this game.
Formula: 5 * x^0.65% where x is Holy Light Active Time (This Game) in seconds.  Research W10, D55 
W  250  Any  Swarming  A  Trophy  Gain assistants based on the amount of trophies you unlocked.
Formula: floor(x / 8) where x is the amount of trophies unlocked.  Research W175, W205 
W  260  TT  Athletics  P (BNU)  BU  Increase the production of all other buildings by 100% per Olympian Hall you own.  3000 Olympian Halls 
W  275  FC  Domination  FC/s  A (Highest)  Gain additional Faction Coins per second based on the highest amount of assistants you had in a single game. Also a 50% multiplicative Faction Coin find chance. Formula: floor(125 * x^0.75) where x is your Assistants (Max) stat.  300 Base Assistants (as Faceless) 
W  290  Any  Entrench  P (BU)  Ex  Increase the production of Unique buildings based on the amount of Excavations you made.
Formula: round(15 * x^0.8)% where x is the amount of excavations made.  2000 Excavations 
W  320  Any  Shattering  P (Click)  Ex  Increase your clicking reward based on the amount of Excavations you made.
Formula: round(10 * x^0.75)% where x is the amount of excavations made.  2650 Excavations 
W  330  Any  Heroism  P (Click)  Trophy  Increase your click reward based on the amount of trophies you unlocked.
Formula: round(2.5 * x)% where x is the amount of trophies unlocked.  Research W200, W260 
W  350  DD  Survival  P (BNU)  P (BU)  Increase the production of all other buildings based on the production of your Stonehenge Circles.
Formula: 75 * (log10(1+x))^1.3) where x is the production of your Stonehenge Circles.  Research A300, A270 (As Druid) 
W  400  Any  Siege  B  Each building in the three highest building tiers count as 2 buildings for all purposes. (All purposes in the build. Does not work for Trophies.)  Research C251, W290  
W  405  DW  Ambush  P (BU)  P (Offline)  Increase the production of Spider Sanctuaries based on Offline Bonus.
Formula: 3.25 * log(1+x)^3.25 where x is Offline Production Bonus.  Secrets of the Underworld upgrade (as Drow) 
W  520  DW  Stalking  A  Spell Time (This Game)  Gain 1 additional assistant for every 100 seconds of Combo Strike activity time. (This Game)  Research W50, W405 (as Drow) 
W  525  Evil  Bloodlust  P (Spell)  Spell Casts (Faction This Game)  Increase Blood Frenzy multiplier additionally based on the amount of times you cast faction spell in this game.
Formula: 300 * floor(x^0.3)% where x is Faction Spells' Cast This Game (Vanilla + Prestige spell count).  1d, 12h Evil Time Spent (total), Research W205, S460 
W  560  DN  Resilience  P (Click)  Click (This Game)  Increase clicking reward based on the amount of clicks made in this game.
Formula: 5 * x^0.45% where x is your Treasure Clicks (This Game) stat.  Research D330, D480 
W  590  DM DW  Torture  P (A)  Time (Evil Playtime)  Increase assistants production based on total time spent being Evil.
Formula: 8 * x^0.8% where x is your Time Spent Being Evil stat.  200 Drow Exchange (as Drow or Demon), Research D245, W520 
W  1275  Any  Authority  P (BNU)  Trophy  Increase the production of NonUnique Buildings based on the percentage of trophies you unlocked.
Formula: 0.2 * x^2 where x is percent of trophies unlocked.  12h Call to Arms cast time (This game) 
W  1375  Any  Scavenging  FC%  A  Increases Faction coin chance based on the amount of assistants you own. Also increase Faction Coin find chance by a multiplicative 275%. Formula: (2500 * x^0.425) where x is assistants.  7 days spent as Evil (Across all Rs) 
W  1400  DG  Cataclysm  MM  Click (This Game)  Increase maximum mana based on the amount of clicks made in this game.
Formula: floor 25 * log(1+x) ^2.5 where x is your Clicks (this R) stat.  Research W400, A1200 
W  3050  M  Flanking  P (B)  U  Increase the production of building tiers directly above or below Unique Buildings based on the amount of assistants you own.
Formula: 0.15 * x^0.8 where x is assistants.  50,000 Base Assistants, Research W1275, E1325 
W  3150  Any  Upheaval  P (B)  B  Increase the production of all buildings based on their tier, giving the best bonus to the lowest.
Formula: 150 * (12x)^2.15 where x is building tier.  60,000 Farms, Inns, and Blacksmiths 
Abbreviations & References Edit
Factions Abbreviations are the same as in mercenary build templates: DD: Druid; DG: Dragon; DM: Demon;
DN: Dwarf; DW: Drow; FC; Faceless; FR: Fairy; GB: Goblin; UD: Undead; M: Mercenary;
Type & Base Abbreviations : A: Assistant; B: Building; Ex: Excavation; FC Faction Coins;
FC/s: FC Per Second; FC%: FC Find Chance; MM: Max Mana; MP: Mana Produced; MR: Mana Regen;
NU: NonUnique Building; P: Production; RE: Royal Exchange; Reduc: Cost Reduction; U: Unique Building;
Colors : Fairy  Elven  Angel  Goblin  Undead  Demon  Titan  Druid  Faceless  Dwarf  Drow  Dragon  Mercenary  Vanilla Factions  Good Factions  Evil Factions  Neutral Factions
Dotted & underlined abbreviations have cursor tooltips.
Note: The inputs in 'Type' and 'Base' (Based On) columns may appear strange, the inputs are simplified; no plural forms, subjects go from biggest to smallest where 'biggest' is the main subject. (e.g. For everything increasing Production, be it building production [P(B)] or assistant production [P(A)]. The P comes first so it can be sorted first.)
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