Technology Research Explained....

Requies

Prince
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

Requies

Prince
Repercussions

1) It can be VERY important to establish contact with all the other civilizations in order to speed your beakers applied count. You could potentially be making 28% (17 known civs w/ tech/ 18 civs total) more beakers than you normally could on a tech. This is especially true on harder difficulties. If you just meet half of the other civs, your research on techs known by the others would improve by 14%. This is probably the biggest repercussion of the calculation.

2) If you're going to research several technologies and one is an optional requirement of another, research the optional one first as that will boost your research toward the other one unless you have a specific reason for researching the other one.

3) If you're researching the starting techs (no prerequisites modifier), try to reduce the amount of overflow you have, as you're multiplying it by the lowest amount possible. It would be better spent earning some gold which may be necessary to run a deficit research job.

4) If you're researching a tech which is known by a lot of people and which has many optional prerequisites which you already have, try to time it so that you end a turn with 1 beaker left to research that tech. The next turn INCREASE the amount of commerce you generate in order to increase the research overflow on the next turn to the max amount possible. You could potentially generate 104.8% ((1 + 17 known civs w/ tech/18 civs) * 1.6 [tech w/ 3 optional prerequisites]) more beakers of overflow than you normally would for that tech (assuming it's from Writing to a Starting Tech which no one knows. I know, it's unlikely. ). However, for a realistic overflow difference getting almost 46% (1.25 * 1.4 / 1.2) more beakers in overflow is very feasible.

[First tech = 6 known civs w/ tech out of 7 civs and 1 additional optional prerequisite obtained]
[Second tech = no known civs with tech and no additional optional prerequisites obtained]

like Paper w/ Civil Service and Theology to Education.

5) Pre-Alphabet (and possibly in non-tech trading games), you will be able to determine the number of known players with a certain tech but not who has this specific tech unless all known or no known civs have it. (thx to DaviddesJ for pointing this out).

6) Similar to repercussion #5, if the AI is ahead of you in tech, you will be able to determine the number of known players with a technology which is BEYOND your research ability (i.e., those you do not have the prerequisite technologies for) but not who has this specific tech unless all known or no known civs have it. NOTE: there would also be times where you would NOT know whether another known civ has the tech as the civ modifier would be small enough that no difference could be detected. (thx to Roland Johanson for pointing this out.)

7) If you don't choose a tech as soon as you found your first city, you are probably losing a bonus (if you don't choose a starting tech). This might not be that significant, but when every beaker counts, losing two beakers in the beginning might mean the difference between getting that iron rush 1 turn faster.

8) If you have a neighbor who you're thinking of killing off who has techs which you have not researched yet, it might not be worth it to kill them off UNTIL you've researched the tech (1 neighbor who knows the tech in a 7 player game will provide a 1.04 boost).

Difficulty, Map Size, and Speed Modifiers

Difficulty Modifiers
Will wait until the patches are done before posting a full list

Map Size Modifiers
Will wait until the patches are done before posting a full list

Game Speed Modifiers
Will wait until the patches are done before posting a full list

Additional Modifier for knowing 1 more civilization who has the tech out of....
2 Starting Civilizations = 0.15
3 Starting Civilizations = 0.10
4 Starting Civilizations = 0.075
5 Starting Civilizations = 0.06
6 Starting Civilizations = 0.05
7 Starting Civilizations = 0.0428...
8 Starting Civilizations = 0.0375
9 Starting Civilizations = 0.0333...
10 Starting Civilizations = 0.03
11 Starting Civilizations = 0.02727...
12 Starting Civilizations = 0.025
13 Starting Civilizations = 0.0230769...
14 Starting Civilizations = 0.0214...
15 Starting Civilizations = 0.02
16 Starting Civilizations = 0.01875
17 Starting Civilizations = 0.017647...
18 Starting Civilizations = 0.01666....

Thanks to
-LordTerror for his work dealing with the teammate modifier
-Zombie69, Roland Johanson, kryszcztov, jesusin, and LordTerror for suggesting ways to improve and/or clarify the article
-DaviddesJ for suggesting repercussion #5.
-Roland Johanson for suggesting repercussion #6.
-Arthog for his idea about dead civilizations possibly contributing to the modifier which led to repercussion #8 and for providing a save file to test the idea on.

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Zombie69

Emperor
I see a glaring mistake in your post :

"4) Multiply 3) by (1.2 * the number of requirements you have fulfilled - the minimum requirements count as ONE requirement) and take the FLOOR of the product."

You either mean "1.2 ^ nbr req fulfilled" or "1 + 0.2 * nbr req fulfilled".

As it stands, according to your formula, having just one more requirement than needed DOUBLES your research speed, and having 2 more than needed TRIPLES it. I highly doubt that's the case.

Regardless, i didn't know there was such a factor involved at all. This makes horizontal research, rather than vertical research, more appealing, especially if for whatever reason, you can't trade higher techs for lots of lower techs to compensate for slower research.

Requies

Prince
Zombie69 said:
I see a glaring mistake in your post :

"4) Multiply 3) by (1.2 * the number of requirements you have fulfilled - the minimum requirements count as ONE requirement) and take the FLOOR of the product."

You either mean "1.2 ^ nbr req fulfilled" or "1 + 0.2 * nbr req fulfilled".

As it stands, according to your formula, having just one more requirement than needed DOUBLES your research speed, and having 2 more than needed TRIPLES it. I highly doubt that's the case.

Regardless, i didn't know there was such a factor involved at all. This makes horizontal research, rather than vertical research, more appealing, especially if for whatever reason, you can't trade higher techs for lots of lower techs to compensate for slower research.

It's a typo. Trying to get too much data in on one line. I will break it apart.

Thanks,
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DaviddesJ

Deity
Requies said:
1) It can be VERY important to establish contact with all the other civilizations in order to speed your beakers applied count. If you don't, you're potentially making 21.8% (1/1.28) less beakers than you could on a tech. This is especially true on harder difficulties. This is probably the biggest repercussion of the calculation.

The first posting just says the number of civilizations with the technology; it doesn't say that it matters whether you have contact with them.

Roland Johansen

Deity
Thank you for this very well written and informative article. The modifier for number of prerequisites of a technology known is especially new to me. Also, I would have thought that the modifier for the number of opponents who know the technology would be bigger (it was bigger in civ3).

I really hate the repercussions 3 and 4, but that is not your fault. That is just lazy programming from Firaxis (the modifiers for the new technology should be applied to the overflow, not the modifiers for the previous technology). This will again mean that micromanaging the technological research is beneficial.

Still, I want to make a few critical remarks to try and make the article completely error free.

1) Zombie69's remark.
2) the 1.28 factor in repercussion 1 should be explained because otherwise people will ask why 1.28? It is probably the largest modifier you can get for other civilizations knowing the technology which is 1+ 17/18 * 0.3.
3) The modifier for 1 more civilization knowing the tech seems to depend on the number of starting opponents as seen in the formula that you posted:

1 + RDDW (0.30 * # Civs who know the tech / # of Civs who started the game)

If one civilization knows a technology in a 2 player game, then this results in a modifier of 1.15. If one civilization knows a technology in a 5 player game, then this results in a modifier of 1 + 0.3 * 1/5 = 1.06.
So the table in the repercussions section is wrong or the formula is wrong or I'm not reading your article the way I was meant to read it.

Thank you for a great article.

kryszcztov

Deity
A few questions, not sure if I understand it well :
- For each city, how are partial results and final results for gold, beakers and culture handled ? Rounded down, up, to the closest integer (what happens to 0.5 then ?), or nada ?
- I still don't understand if you have to make contact with the civs which already know the tech you're researching in order to have a discount or not. In Civ3 you had to, what is it in Civ4 ?
- I don't understand the prerequisite part of your theory very well. There are some techs which only have one or more mandatory prerequisite(s), some other techs which only have optional prerequisites (not 1, since it would be mandatory then ), some other techs which have both, and the starting techs. Care to explain for each case please ?
- I didn't catch your 3rd repercussion ; if you let science at max on the last turn, you'll get more overflow for the next tech, what's wrong with it ?

But all in all, I'm impressed to see such a complex theory already ! Thanks so much for the work done in so little time. Of course it needs to stand our own experimentation now, but in any case, you're surely very close to the truth (and probably ON the truth). I'll come back here if I find contradicting results.

What we'd need is a science calculator now !

Also, though I like some features that are driven from your theory (discount for optional prerequisites is one of those), I dislike some other features (the +1 beaker that you get in any case, totally NOT needed and wrong IMHO).

kryszcztov

Deity
Roland Johansen said:
Also, I would have thought that the modifier for the number of opponents who know the technology would be bigger (it was bigger in civ3).
I think it's fine that you don't get a fair discount, otherwise it leads you to wait for other civs to get it first, which shouldn't be the usual way to play a game and run a civ in RL. Also it is another counter-effect to Civ3's heavy tech trading (any AI would be pleased to sell you whatever techs they had).

I really hate the repercussions 3 and 4, but that is not your fault. That is just lazy programming from Firaxis (the modifiers for the new technology should be applied to the overflow, not the modifiers for the previous technology). This will again mean that micromanaging the technological research is beneficial.
Didn't understand #3. As for #4, I disagree with you for the moment. For once, it SHOULD be the same as for hammers in a city (and here it is the same, the overflow of hammers that you get on the next turn are kept with the former modifiers). I will be totally against a difference between hammers and beakers. Now, I also think this is better, since the hammers/beakers were produced on a turn when you were building/researching something with some modifiers. The overflow is just stored, you know it beforehand, and so, no surprise next turn. As for more MM, it depends on what you want : if you want to get more hammers/beakers, then you'll have to delay the thing by 1 turn, which often means 1 turn of not-profitting from the building/unit/tech. On hard levels I'm sure it can sometimes be critical. It's a trade-off, you choose. And when you can run science at 100%, there's a cost for delaying the discovery, since you won't be able to run science higher on the next turn to catch back the delay.

3) The modifier for 1 more civilization knowing the tech seems to depend on the number of starting opponents as seen in the formula that you posted:

1 + RDDW (0.30 * # Civs who know the tech / # of Civs who started the game)

If one civilization knows a technology in a 2 player game, then this results in a modifier of 1.15. If one civilization knows a technology in a 5 player game, then this results in a modifier of 1 + 0.3 * 1/5 = 1.06.
So the table in the repercussions section is wrong or the formula is wrong or I'm not reading your article the way I was meant to read it.
Yes, another thing I didn't understand very well. Also, your table goes from 2 civs to 18 civs. Shouldn't it be from 1 other civ knowing the tech to 17 civs ?
And regarding the number of civs which started the game, does it include our own civ as well ?

Requies

Prince
kryszcztov said:
A few questions, not sure if I understand it well :
- For each city, how are partial results and final results for gold, beakers and culture handled ? Rounded down, up, to the closest integer (what happens to 0.5 then ?), or nada ?

Darn you, I was hoping someone wouldn't notice this . I just thought up that part when I was posting the article, but since I was more than halfway through it, I just decided to finish posting it. OTOH, I just checked, and actually, it's very simple. So, I'll just add it now.

kryszcztov said:
- I still don't understand if you have to make contact with the civs which already know the tech you're researching in order to have a discount or not. In Civ3 you had to, what is it in Civ4 ?

The updated article clarifies this.

kryszcztov said:
- I don't understand the prerequisite part of your theory very well. There are some techs which only have one or more mandatory prerequisite(s), some other techs which only have optional prerequisites (not 1, since it would be mandatory then ), some other techs which have both, and the starting techs. Care to explain for each case please ?

Hmmm, perhaps I should have better examples.... The techs with one or more mandatory prerequisites and NO optional prerequisites = 1.2. Techs with only optional prerequisites = 1.2 * # of optional prereqs you have. Techs with one or more mandatory prerequisites and optional prerequisites = 1.2 * OPTIONAL prereqs you have.

It really is more a question of what is the MINIMUM requirements to research a technology. Whatever that is gives you a 1.2 modifier. Each additional optional requirement gives you another 0.2 added on to that modifier.... Hmmm, perhaps, I should explain it that way.

kryszcztov said:
- I didn't catch your 3rd repercussion ; if you let science at max on the last turn, you'll get more overflow for the next tech, what's wrong with it ?

The problem is that you're likely getting NO or very little bonus with the starting techs (Mining, Hunting, Fishing, etc.) since they have NO MINIMUM requirements.

kryszcztov said:
But all in all, I'm impressed to see such a complex theory already ! Thanks so much for the work done in so little time. Of course it needs to stand our own experimentation now, but in any case, you're surely very close to the truth (and probably ON the truth). I'll come back here if I find contradicting results.

You're very welcome. And don't worry about posting contradicting results. I'm pretty sure I got everything nailed (that's what took me the better part of half a month ), but peer review is always helpful.

kryszcztov said:
What we'd need is a science calculator now !

Errrm, hmmm, that doesn't sound like something someone would mod, perhaps? Maybe, in an advisor or something?

kryszcztov said:
Also, though I like some features that are driven from your theory (discount for optional prerequisites is one of those), I dislike some other features (the +1 beaker that you get in any case, totally NOT needed and wrong IMHO).

Yeah, I like the optional prerequisites, but I DON'T like the way overflow is calculated for the reason Roland points out. And I really don't understand why they put in the +1 beaker when THEY DON'T USE IT IF YOU HAVEN'T FOUNDED A CITY.

Req

DaviddesJ

Deity
Another repercussion is that you can try to figure out whether the players you've met have a particular technology by looking at the turns to research it on the Science Advisor screen. This would be a lot of effort for not much benefit, but it could be useful once in a while. Of course, it doesn't work for techs that you already have.

Requies

Prince
Roland Johansen said:
Thank you for this very well written and informative article. The modifier for number of prerequisites of a technology known is especially new to me. Also, I would have thought that the modifier for the number of opponents who know the technology would be bigger (it was bigger in civ3).

I really hate the repercussions 3 and 4, but that is not your fault. That is just lazy programming from Firaxis (the modifiers for the new technology should be applied to the overflow, not the modifiers for the previous technology). This will again mean that micromanaging the technological research is beneficial.

I concur. It just sucks that micromanaging becomes somewhat important again.

Roland Johansen said:
Still, I want to make a few critical remarks to try and make the article completely error free.

1) Zombie69's remark.

Fixed.

Roland Johansen said:
2) the 1.28 factor in repercussion 1 should be explained because otherwise people will ask why 1.28? It is probably the largest modifier you can get for other civilizations knowing the technology which is 1+ 17/18 * 0.3.

Good point. Fixed.

Roland Johansen said:
3) The modifier for 1 more civilization knowing the tech seems to depend on the number of starting opponents as seen in the formula that you posted:

1 + RDDW (0.30 * # Civs who know the tech / # of Civs who started the game)

If one civilization knows a technology in a 2 player game, then this results in a modifier of 1.15. If one civilization knows a technology in a 5 player game, then this results in a modifier of 1 + 0.3 * 1/5 = 1.06.
So the table in the repercussions section is wrong or the formula is wrong or I'm not reading your article the way I was meant to read it.

Clarified hopefully. Please let me know if this makes it clearer.

Roland Johansen said:
Thank you for a great article.

You're welcome and thank you for the great feedback.

Req

Requies

Prince
DaviddesJ said:
Another repercussion is that you can try to figure out whether the players you've met have a particular technology by looking at the turns to research it on the Science Advisor screen. This would be a lot of effort for not much benefit, but it could be useful once in a while. Of course, it doesn't work for techs that you already have.

Isn't this already done in the Foreign Advisor? Or is that different somehow?

Req

DaviddesJ

Deity
Requies said:
Isn't this already done in the Foreign Advisor? Or is that different somehow?

I don't think the Foreign Advisor gives you any information about the techs of opposing civilizations until tech trading is enabled via Alphabet.

(Also, it may not give you any information in games with tech trading turned off---but I haven't played that variant, so I don't know.)

Requies

Prince
DaviddesJ said:
I don't think the Foreign Advisor gives you any information about the techs of opposing civilizations until tech trading is enabled via Alphabet.

(Also, it may not give you any information in games with tech trading turned off---but I haven't played that variant, so I don't know.)

Ah, I see. So, you mean pre-Alphabet tech info or non-tech trading tech info.

Ok, I'll add in that to the Repercussions section.

Req

Shillen

Deity
Calculating the Known Civilizations w/ Tech modifier

1) Multiply 0.30 by the number of KNOWN 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

Are you sure this applies to all difficulty levels? In the xml for the difficulty levels there is a field with "TechKnownModifier" or something like that in it. This value is 0 for all difficulties above Warlord.

Requies

Prince
Shillen said:
Are you sure this applies to all difficulty levels? In the xml for the difficulty levels there is a field with "TechKnownModifier" or something like that in it. This value is 0 for all difficulties above Warlord.

I'm not completely positive about this, but the actual field is called "iTechTradeKnownModifier" which I believe is related to tech trading. I could be wrong about this, but someone else can test it out and let me know .

Req

Shillen

Deity
Well that's kind of what I'm interested in most is the value of the tech when trading. I'd like to know if the techs devalue as I trade them around to other AI's. But I guess someone else will have to figure that one out. I'm not tech savvy enough myself.

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