Question about ease of research

[Norselord]

I was reading through a very old guide recently and read the following claim in it:

"A tech is easier to research when more civilizations already know it"

Is this true? Or is this an illusion?

If it is true, what is the formula? It makes sense from a realistic perspective that the very last civ to research the wheel, for example, gets a little discount because he has seen all the other countries using those nifty round thingies.

I can see that it might be an illusion also, since the reason a tech that you have ignored while beelining something is only cheaper than it was initially because you have improved your rate of research.

If this is true, does it help to know the research paths of the other AIs/Players?

Thanks in advance for your feedback.

[wodan11]

It's true. I don't know the formula.

[rah]

Me either.
If you have already researched both prereqs, it's cheaper also.

[Norselord]

It's true. I don't know the formula.

Wow, learn something new every day.

So if in a random game I am surrounded by a bunch of hippy, pot-smoking, culture building civs, then I can beeline military techs, and backfill all the cultural techs easier?

Is there any way to take advantage of this? Are the primary tech paths for certain civs pretty well understood? If so, then there should be ideal times to backfill certain garbage techs.

Does this also mean that if you have disproportionately large number of religious civilizations, for example, that they are all boosting each others tech rate, since most of them would be going along the same paths? It would seem to me that this means that, in this example, the less tech-savvy religious civs get a boost from the other religious civs. Conversely, none of them would get much of a 'common knowledge' boost if the human is teching on a different branch of the tech-tree.

Would it be better for the human to allow himself to get pulled along by the ease of teching 'with the group' or is it better to forge his way down the path less travelled to increase the chance at getting the bonus of being the first to discover a tech or being able to get a critical wonder started first.

I am not sure this is making much sense, as i type it.

[Norselord]

Me either.
If you have already researched both prereqs, it's cheaper also.

huh?

Both prereqs for what?

Do you mean if more civs have the prereqs researched? or were you thinking of a specific tech?

[Dinner]

It's true. I don't know the formula.

It must be floating around this forum some where in an old thread. These sorts of formulas would be perfect for an Apolyton University article. Could someone find by looking at the code or is it all just a black box? I just don't know a damn thing about software but maybe Asher would know.

[wodan11]

Here's the formula. Be forewarned: I'm telling you there will be maths.

[Cort Haus]

Wow, learn something new every day.

So if in a random game I am surrounded by a bunch of hippy, pot-smoking, culture building civs, then I can beeline military techs, and backfill all the cultural techs easier?

In my experience the chances of being surrounded by pot-smoking, peaceful civs in a random game are approximately zero. The RNG Gods make sure that I am surrounded at all times by at least two, if not three, psychotic warmongers.

[Ming]

It does seem that way... on one side of the world, all the peace freaks... and around you, Monty, Shaka, and Toga.

[Blaupanzer]

It's just you, Cort Haus, the rest of get easy civs as neighbors.
Apparently the more civs that have a given tech, the cheaper it is for you to backfill. That can be checked in the diplomacy - Technology screen.

[Norselord]

Here's the formula. Be forewarned: I'm telling you there will be maths.

the link is blocked...can you copy and paste?

[Ming]

the link is blocked...can you copy and paste?

From our firends over at CFC

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.

[Norselord]

It's just you, Cort Haus, the rest of get easy civs as neighbors.
Apparently the more civs that have a given tech, the cheaper it is for you to backfill. That can be checked in the diplomacy - Technology screen.

That also means that if i gift a tech to anyone, essentially everyone that has not already researched that tech benefits slightly right away.

[Norselord]

Ming wow...that is VERY interesting.

Does this mean that gifting a tech, one that your enemy does not have yet, to a vassal, is a bad idea?

Oddly enough this also means that the more civs are eliminated the harder it is for backward nations to catch up in the tech race. If I understand it correctly the 'common knowledge' factor approaches 1.3 for the last civ to research a tech. For example the last out of ten is 1+0.3*(9/10)=1.27. However if instead three civs got eliminated early then the 'common knowledge' bonus drops to 1+0.3*(6/10)=1.18.

This would lead me to think that if I beeline towards steel to get cannons, then I reduce 3 civs to only one city each...until I have backfilled using the 'common knowledge' factor, after which I kill them off to prevent other (possibly distant) civs from catching up using the 'common knowledge' factor. I will have made good use of this idea...right?

Where is the tipping point? When do I know that I have enough of a tech lead that killing of other civs is going to preserve my lead? Rather then keeping them around?

How does this formula treat colonies? Does it count them as separate civilizations for the purpose of teching? Because if the map started with 10 civs and then you create two colonies, it would be possible for the 'slow' civs to get a bonus that exceeds 1.3.

Let me try to reorganize my thoughts here:
- with a tech lead kill off other civilizations
- with a tech lag (needing to backfill) keep civs vassalized

[Ming]

Here is the next post in the thread... again, thanks to the folks at CFC

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.