Research. It's the fundamental way of advancing in life and in Civ IV, and a necessary part of making your way up the food chain in Civ IV from doormat to winner (whether via space race, diplomacy, conquest, or culture). Unfortunately, it's also the way to figure out how research actually works in Civ IV.
Fortunately for you all, I've done all that. This article came about because I was interested in what the optimal start to the game was. However, upon working out that information, I was startled to discover that the amount of research differed from what my lone city was producing. I dug further in depth into the mechanisms of the game and figured out how research is priced, accumulated, and applied in the game.
This article will explain the ins and outs of how your beakers get put to work to research the technologies that make or break your game of Civ. To learn more, read on....
One important note.
FLOOR means rounding DOWN to the nearest integer AND it has higher precedence than all other operators EXCEPT FOR parentheses. You will see it used a lot in the article.
The basics (of generating beakers)
1) Each city generates a raw amount of commerce via the squares that are being worked and the trade routes in the cities.
2) This commerce is in turn translated into beakers (research), coins (gold), or notes (culture) via the technology and culture sliders. The actual amount of beakers and notes are gained by using the specified slider rate in the following equation:
FLOOR (total commerce * the specified slider rate).
The remainder is then given in gold.
So, yes, you WILL get AT LEAST one gold from each city that has a commerce that is not a multiple of 10, if your science or culture is not 100%.
3) Each city then takes each amount and adds in any additional sources of research, gold, or culture (via shrines, production processes, and specialists, mainly).
4) Each city then multiplies it by whatever modifiers it has depending on what buildings it has built (e.g., beakers are multiplied by 1.25 if it has a library, gold is multiplied by 1.5 if it has a bank, etc.). NOTE: multipliers are ADDITIVE (i.e., if you have a library and university, your beakers will be multiplied by 1.5 (1 + 0.25 + 0.25) NOT 1.5625 (1 * 1.25 * 1.25)).
5) The beaker totals are then added up across the cities and the sum is your base beaker total.
Technology Costs
To calculate the technology cost of a technology:
1) Take the base cost of the technology. (This can be found for each technology in Assets\XML\Technologies\CIV4TechInfo.xml).
2) Take the Difficulty Modifier and add 0.5 * the Number of teammates you have to it. (The difficulty modifier can be found in Assets\XML\GameInfo\CIV4HandicapInfo.xml.)
3) Multiply 1) by 2) and take the FLOOR of the product.
4) Multiply 3) by the Map Modifier and take the FLOOR of the product. (The map modifier can be found in Assets\XML\GameInfo\CIV4WorldInfo.xml.)
5) Multiply 4) by the Speed Modifier and take the FLOOR of the product. This generates the actual cost of the technology. (The speed modifier can be found in Assets\XML\GameInfo\CIV4GameSpeedInfo.xml.)
Thus the formula to calculate a Technology's cost is:
Technology Cost = FLOOR (FLOOR (FLOOR (Base Cost * (Difficulty Modifier + 0.5 * # of teammates)) * Map Modifier) * Speed Modifier)
Applying the Research to the Technology
The amount of beakers applied to the technology cost is dependant upon the number of civilizations which know the tech and the number of requirements you have fulfilled for the technology.
Calculating the Known Civilizations w/ Tech modifier
1) Multiply 0.30 by the number of KNOWN, LIVING civilizations, who have the tech.
2) Divide by the number of civilizations which STARTED on the map and ROUND DOWN to the hundredth place (0.01) of the quotient.
3) Add 2) to 1
Tech Known by Civilizations modifier = 1 + RDDW (0.30 * # known Civs who have the tech / # of Civs who started the game
Calculating the Prerequisites modifier
1) Start with 1. If the technology does NOT have a minimum requirement (i.e., the starting techs = Fishing, The Wheel, Agriculture, Hunting, Mysticism, Mining), then use 1 AS the modifier.
2) Add 0.2 to 1) if a Technology has a MINIMUM Requirement that the player has met. Note: Even if a tech has MANY MANDATORY PREREQUISITES, it will still only give you a boost of 1.2 because you MUST have all those prerequisites to research the tech. (IOW, the minimum requirement IS all of those prerequisites.)
3) Add 0.2 to 2) for EACH ADDITIONAL OPTIONAL Prerequisite that the player has met.
Requirements modifier = 1 + (0.2 * MINIMUM Req. met) + (0.2 * # of Optional Prereq. met)
Calculating the Actual Amount of Beakers Generated Toward a Tech
To calculate the amount of beakers which you generate toward the technology:
1) Take the total sum of beakers generated by all your cities (the result from the basics part).
2) Add 1 to it if you have a city.
3) Multiply 2) by the Known Civilizations w/ Tech modifier and take the FLOOR of the product.
4) Multiply 3) by Prerequisites modifier and take the FLOOR of the product.
The formula to calculate the amount of beakers applied to your technology is:
Beakers applied to Technology = FLOOR (FLOOR ((Total Base Beakers + 1) * KCwT modifer) * Prerequisites modifier)
An example
I always seem to understand better with an example, so here's a basic one.
Say you want to research Code of Laws which has a base cost of 350 beakers, the mandatory requirement of Writing and the optional (meaning you must research one of them) requirements of (Priesthood or Currency).
You know Writing and Priesthood
You produce 37 net beakers per turn and you have met 3 other civilizations who know it out of 7 who started the map.
You started on a standard map (1.4 modifier) at the monarch difficulty level (1.15 modifier) at epic game speed (1.5 modifier) and have 1 teammate.
Your cost would be:
FLOOR (FLOOR (FLOOR (350 * (1.15 + 0.5 * 1)) * 1.4) * 1.5)
FLOOR (350 * 1.65) = 577
FLOOR (577 * 1.4) = 807
FLOOR (807 * 1.5) = 1210
Total cost = 1210
The amount of beakers applied to code of laws would be:
FLOOR (FLOOR ((37 + 1) * (1 + RDDW (0.30 * 3 / 7))) * (1 + 0.2 + (0.2 * 0))
1 + RDDW (0.30 * 3 / 7) = 1.12
FLOOR (38 * 1.12) = 42
FLOOR (42 * 1.2) = 50
Beakers applied to Code of Laws/turn = 50
Note that having Writing AND Priesthood only gives you a bonus modifier of 1.2 because you must have at LEAST Writing PLUS one of the optional prerequisites to be able to research Code of Laws. If you also had Currency, then the modifier would be 1.4.
Overflow
The overflow is calculated by the modifiers from the PREVIOUS Technology. Therefore, if you finished researching Writing this turn, and you had all THREE optional requirements, the overflow beakers which applied to your next technology would be equal to however many you had left USING THE MODIFIERS FOR Writing after finishing Writing. So, your Requirements modifier would be 1.6 (1.2 * 3). So, you could conceivable get a significant boost toward your next tech OVER WHAT YOU SHOULD HAVE GOTTEN if you have a lot of overflow.
Req
Fortunately for you all, I've done all that. This article came about because I was interested in what the optimal start to the game was. However, upon working out that information, I was startled to discover that the amount of research differed from what my lone city was producing. I dug further in depth into the mechanisms of the game and figured out how research is priced, accumulated, and applied in the game.
This article will explain the ins and outs of how your beakers get put to work to research the technologies that make or break your game of Civ. To learn more, read on....
One important note.
FLOOR means rounding DOWN to the nearest integer AND it has higher precedence than all other operators EXCEPT FOR parentheses. You will see it used a lot in the article.
The basics (of generating beakers)
1) Each city generates a raw amount of commerce via the squares that are being worked and the trade routes in the cities.
2) This commerce is in turn translated into beakers (research), coins (gold), or notes (culture) via the technology and culture sliders. The actual amount of beakers and notes are gained by using the specified slider rate in the following equation:
FLOOR (total commerce * the specified slider rate).
The remainder is then given in gold.
So, yes, you WILL get AT LEAST one gold from each city that has a commerce that is not a multiple of 10, if your science or culture is not 100%.
3) Each city then takes each amount and adds in any additional sources of research, gold, or culture (via shrines, production processes, and specialists, mainly).
4) Each city then multiplies it by whatever modifiers it has depending on what buildings it has built (e.g., beakers are multiplied by 1.25 if it has a library, gold is multiplied by 1.5 if it has a bank, etc.). NOTE: multipliers are ADDITIVE (i.e., if you have a library and university, your beakers will be multiplied by 1.5 (1 + 0.25 + 0.25) NOT 1.5625 (1 * 1.25 * 1.25)).
5) The beaker totals are then added up across the cities and the sum is your base beaker total.
Technology Costs
To calculate the technology cost of a technology:
1) Take the base cost of the technology. (This can be found for each technology in Assets\XML\Technologies\CIV4TechInfo.xml).
2) Take the Difficulty Modifier and add 0.5 * the Number of teammates you have to it. (The difficulty modifier can be found in Assets\XML\GameInfo\CIV4HandicapInfo.xml.)
3) Multiply 1) by 2) and take the FLOOR of the product.
4) Multiply 3) by the Map Modifier and take the FLOOR of the product. (The map modifier can be found in Assets\XML\GameInfo\CIV4WorldInfo.xml.)
5) Multiply 4) by the Speed Modifier and take the FLOOR of the product. This generates the actual cost of the technology. (The speed modifier can be found in Assets\XML\GameInfo\CIV4GameSpeedInfo.xml.)
Thus the formula to calculate a Technology's cost is:
Technology Cost = FLOOR (FLOOR (FLOOR (Base Cost * (Difficulty Modifier + 0.5 * # of teammates)) * Map Modifier) * Speed Modifier)
Applying the Research to the Technology
The amount of beakers applied to the technology cost is dependant upon the number of civilizations which know the tech and the number of requirements you have fulfilled for the technology.
Calculating the Known Civilizations w/ Tech modifier
1) Multiply 0.30 by the number of KNOWN, LIVING civilizations, who have the tech.
2) Divide by the number of civilizations which STARTED on the map and ROUND DOWN to the hundredth place (0.01) of the quotient.
3) Add 2) to 1
Tech Known by Civilizations modifier = 1 + RDDW (0.30 * # known Civs who have the tech / # of Civs who started the game
Calculating the Prerequisites modifier
1) Start with 1. If the technology does NOT have a minimum requirement (i.e., the starting techs = Fishing, The Wheel, Agriculture, Hunting, Mysticism, Mining), then use 1 AS the modifier.
2) Add 0.2 to 1) if a Technology has a MINIMUM Requirement that the player has met. Note: Even if a tech has MANY MANDATORY PREREQUISITES, it will still only give you a boost of 1.2 because you MUST have all those prerequisites to research the tech. (IOW, the minimum requirement IS all of those prerequisites.)
3) Add 0.2 to 2) for EACH ADDITIONAL OPTIONAL Prerequisite that the player has met.
Requirements modifier = 1 + (0.2 * MINIMUM Req. met) + (0.2 * # of Optional Prereq. met)
Calculating the Actual Amount of Beakers Generated Toward a Tech
To calculate the amount of beakers which you generate toward the technology:
1) Take the total sum of beakers generated by all your cities (the result from the basics part).
2) Add 1 to it if you have a city.
3) Multiply 2) by the Known Civilizations w/ Tech modifier and take the FLOOR of the product.
4) Multiply 3) by Prerequisites modifier and take the FLOOR of the product.
The formula to calculate the amount of beakers applied to your technology is:
Beakers applied to Technology = FLOOR (FLOOR ((Total Base Beakers + 1) * KCwT modifer) * Prerequisites modifier)
An example
I always seem to understand better with an example, so here's a basic one.
Say you want to research Code of Laws which has a base cost of 350 beakers, the mandatory requirement of Writing and the optional (meaning you must research one of them) requirements of (Priesthood or Currency).
You know Writing and Priesthood
You produce 37 net beakers per turn and you have met 3 other civilizations who know it out of 7 who started the map.
You started on a standard map (1.4 modifier) at the monarch difficulty level (1.15 modifier) at epic game speed (1.5 modifier) and have 1 teammate.
Your cost would be:
FLOOR (FLOOR (FLOOR (350 * (1.15 + 0.5 * 1)) * 1.4) * 1.5)
FLOOR (350 * 1.65) = 577
FLOOR (577 * 1.4) = 807
FLOOR (807 * 1.5) = 1210
Total cost = 1210
The amount of beakers applied to code of laws would be:
FLOOR (FLOOR ((37 + 1) * (1 + RDDW (0.30 * 3 / 7))) * (1 + 0.2 + (0.2 * 0))
1 + RDDW (0.30 * 3 / 7) = 1.12
FLOOR (38 * 1.12) = 42
FLOOR (42 * 1.2) = 50
Beakers applied to Code of Laws/turn = 50
Note that having Writing AND Priesthood only gives you a bonus modifier of 1.2 because you must have at LEAST Writing PLUS one of the optional prerequisites to be able to research Code of Laws. If you also had Currency, then the modifier would be 1.4.
Overflow
The overflow is calculated by the modifiers from the PREVIOUS Technology. Therefore, if you finished researching Writing this turn, and you had all THREE optional requirements, the overflow beakers which applied to your next technology would be equal to however many you had left USING THE MODIFIERS FOR Writing after finishing Writing. So, your Requirements modifier would be 1.6 (1.2 * 3). So, you could conceivable get a significant boost toward your next tech OVER WHAT YOU SHOULD HAVE GOTTEN if you have a lot of overflow.
Req