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Detailed analysis: # of specialist cities needed per era

Discussion in 'Civ4 - Strategy & Tips' started by futurehermit, Jul 13, 2006.

  1. futurehermit

    futurehermit Deity

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    As you know from my other two threads, I'm currently working on combining a specialist econ with being quite aggressive on emperor level.

    I've been struggling getting my econ right. Either I go too strong on econ and fall behind on military or vice versa. So I crunched some numbers, and here is what I came up with. I'll break it down by classical era and medieval era and compare running representation and not running it.

    Please, if anyone notices errors in my math or logic, let me know. I don't claim this is perfect, I'm putting it out there for discussion. I hope it is accurate, but I'm of course subject to human error.

    Classical Era with Representation

    Average tech cost (in beakers): 315 (rounded to nearest beaker; includes hbriding)

    # of specialists required to maintain a rate of 1 tech/10 turns: 5(rounded to nearest specialist) (math: [315/6]/10)

    Great library provides 2 free specialists.

    # of specialists required to maintain tech rate in addition to those provided by great library: 3 (math: 5-2)

    From the pyramids, you will receive a great engineer, who provides 6 beakers when settled (3 base + 3 from representation). This works out to 1 specialist since a regular scientist with representation amounts to 6 beakers.

    # of specialists required to maintain tech rate in addition to those provided by GL and GE: 2 (math: 5-2-1)

    Conclusion: With Great Library and a settled great engineer you can achieve a classical tech rate of 1 tech per 10 turns running only one city with two specialists! Obviously, the rate is much faster if you run additional cities.

    Classical Era Without Representation

    I'll spare you the rhetoric and just give you the numbers.

    # specialists for tech rate (base): 10.5
    # specialists less great library: 8.5

    The great engineer provides 3 beakers which is comparable to 1 scientist without representation.

    # specialists less great library and GE: 7.5

    Conclusion: To achieve a comparable tech rate, you need to run approximately 4 cities or four times the amount! Thus, although representation doubles the beakers produced, the cummulative impact is in fact 4x at this point.

    Medieval Era with Representation

    Average medieval age tech cost: 733 beakers

    # specialists for 1 tech/10 turn rate: 12 (rounded to nearest specialist) (math: (733/6)/10)

    # specialists less GL: 10 (math: 12-2)

    # specialists less GL and GE: 9 (math: 12-2-1 [note: remember that when running representation the GE is worth one specialist because a regular specialist is worth 6 and the GE also 6])


    By medieval age, you'll likely have received a Great Scientist, which provides 9 beakers/turn with representation (6 base +3) when settled. This is equivalent to 1.5 scientists.

    # specialists less GL, GE, and GS: 7.5 (math: 12-2-1-1.5)

    Conclusion: To run a 1 tech/10 turns econ during the medieval age you'll need 4 cities running 2 specialists per city. Therefore, you will want to have conquered 2-3 additional commerce cities during the classical age. For the peaceful player, if there is sufficient and good quality land around you could even build these cities yourself!

    Medieval Era without Representation

    Again, sparing the rhetoric, giving the numbers.

    Number of specialists for tech rate: 24! (math: (733/3)/10)

    Number less GL: 22 (math: 24-2)

    Number less GL and GE: 21 (math: 24-2-1 [note: remember that without representation the 3 beakers from the GE is equivalent to one specialist])

    Number less GL, GE, and GS: 19 (math: 24-2-1-2 [note: the 6 beakers from the GS is equivalent to 2 specialists])

    Conclusion: Without representation, you would need to either run 10 cities with 2 scientists/city, adopt caste system and then running say 4 scientists per city you could trim this down to around 5 cities, or use great merchants from markets and the science slider a bit to also come closer to 5 cities. Notice that this is 2.5x more than the 4 cities with 2 specialists per city required when running representation. It's interesting to note that the effect has decreased from 4x to 2.5x. If this rate continues to go down (I will consider adding the next era soon) then it demonstrates that the benefit of running representation is strongest early on and that would indeed strongly endorse the benefits of getting the pyramids early on.


    Final Thoughts: Running a specialist econ with representation gives you twice the beakers, but it gives you four times the economic impact early on! Clearly when running a specialist econ, representation is a huge asset as it substantially limits the number of commerce cities required to maintain a respectable economy. Thus, you can either keep your empire smaller [conquest] or else have more production centers [domination]. Not to mention that if you need to 1] reduce war weariness or 2] pump out some units fast, OR if you already have the tech lead and want to put a hurting on a rival civ, you can switch over to police state!!

    I look forward to your thoughts and some discussion.


    EDIT: Thanks to Nares for pointing out the correct numbers on the GE. After going back to my spreadsheet, I saw that for running rep vs. not running rep the GE was worthwhile to settle during the classical era (i.e., it made a small impact on the number of specialists required for the tech rate). *However*, once I moved on to the Medeival era, I noted that it made negligible impact (i.e., it made no noticeable impact on the number of specialists required for the tech rate). Therefore, I would argue that the best use of the GE is to unlock metal casting early. It's an expensive tech. The AI rarely goes for it early, so it's great trade-bait. Plus, it gives you forges, cheap ones if you're industrial (good idea since you need the pricy pyramids to get the GE). You can use the forges in your production centers to support your war effort.

    EDIT2: Thanks to DarkFyre99 for pointing out the correct numbers on the GP. He's not worth settling either, so please disregard the GE lines of the analysis. DarkFyre99 also suggested building an academy instead of settling the GS, so feel free to focus solely on the lines discussing the numbers of the GL.
     
  2. Nares

    Nares Emperor

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    My initial reaction is that you miscalculate the Great Engineer. It provides only 3:science:, or 6:science: under Representation. You also fail to calculate the effect of the Library.

    The Great Scientist provides 6:science:, or 9:science: under Representation.

    The conjunction of running two specialists and the Great Library in the same city provides :science: as follows:

    3 X 4 = 12 X 1.25 = 15:science:, without Representation
    6 X 4 = 24 X 1.25 = 30:science:, with Representation

    To incorporate a Great Scientist without Representation, I would incorporate it into a city without the Great Library, but with a Library, and run it with two Scientist specialists.

    To incorporate a Great Scientist with Representation, I would incorporate it into a city with a Library and a Monastery.
     
  3. futurehermit

    futurehermit Deity

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    Hmm...I must've looked at the gs and ge #s when running representation. does the display of how many beakers it provides change when you turn on and off the civic? I thought the display just stayed the same. That's good to know, thanks!

    As for the great library, why does it get the x1.25?
     
  4. Nares

    Nares Emperor

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    No, it changes. You must have checked while running Representation, and made the mistake of thinking it does not change. Great Engineers provide 3:hammers: and 3:science:, Great Scientists provide 1:hammers: and 6:science:.

    Because you need a Library in place in order to build the Great Library in that city.
     
  5. futurehermit

    futurehermit Deity

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    Ok, thanks. The library thing makes sense. Good point. I haven't included libraries in the analysis because I just want to keep it a bit simple at this point. Do you think it would make a significant enough difference between running rep and not to include libraries in the analysis?

    Also, could someone please let me know the beakers (if any) provided by a settled great prophet. I don't think a GE is accurate for the non-rep condition since you won't get one if you don't build the pyramids.

    EDIT: I fixed the numbers for the great engineer. Thanks for picking out that mistake! I haven't changed it for the impact of libraries. I'll leave buildings out of it for now unless someone makes a strong case for adding them in. I will change it again when I get the numbers on the great prophet.
     
  6. DarkFyre99

    DarkFyre99 Prince

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    My initial reactions are:

    1) The Great Engineer is wasted if you settle it. This Great Person is so rare, you truly are better off using it to rush a Wonder than as a free scientist.

    2) The Great Scientist is being wasted if you settle it. You want to use that GS to build an Acadamy in your Great Library city. That provides you with the equivelant of an additional free scientist from the Great Library, plus an additional 50% more free scientists for every scientist supported by that city.

    3) You are far more likely to get a Great Scientist before you get a Great Engineer.

    4) The beakers produced by settled Great Scientists and Great Engineers are off. The base rate is 6 beakers for a GS, and 3 beakers for a GE.

    5) What? No Libraries? No monestaries?

    6) A tech every ten turns seems rather slow, IMO.

    If you're going for a rate of 1 tech every 10 turns, by building an Acadamy as soon as you get a Great Scientist, you need:

    You need to support just one specialist in your science (aka Great Library) city under Representation and an Acadamy during the classical era. That's a total of three scientists (1 supported + 2 free from Great Library) for a total of 31 beakers per turn (rounded down). Throw in a monestary in the mix (a must for early science cities) and you've got a total of 33 beakers per turn.

    During the medieval era, under Representation, your science city needs to support just five scientists to maintain your target tech rate... not an unreasonable population for a single city in that era.

    *heads off to look at your other two threads*
     
  7. DarkFyre99

    DarkFyre99 Prince

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    A settled Great Prophet produces +2 hammers and +1 gold to his city. Under representation, he'd also produce +3 beakers.
     
  8. futurehermit

    futurehermit Deity

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    Yeah, I editted this. I made the case for unlocking metal casting, but rushing the great library is also a great idea (or another wonder).

    I'd like to hear discussion on this. In my other threads, people argued for settling the great scientists. I'm definitely open to building an academy. What are peoples' thoughts?

    Whenever I build the pyramids, I always get a great engineer first.

    Fixed this thanks to Nares.

    Hey, I'm not a math whiz, gimme a bit of time :) The main thing I'm interested in is comparing rep and no rep. Imo buildings don't make a huge difference in this regard (I'm open to being proven wrong). Give me some time and I will get libraries especially factored in. Monasteries are a bit tricky because it requires you to first of all get a religion and secondly to spread it to your cities. I don't often have this successfully done by medieval due to my focus on warmongering. I will try and get the #s though for the sake of completeness (this takes time to do, so if anyone wants to help out, please feel free!).

    It's just an arbitrary # to give a sense of comparison. Feel free to use whatever # you would like.

    Great, thanks, so definitely you wouldn't want to settle him then! Much better to unlock CoL or CS (since you won't be getting masonry for pyramids) or you could consider theology for theocracy.

    Thanks everyone for your help, much appreciated :)
     
  9. DarkFyre99

    DarkFyre99 Prince

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    futurehermit, regarding Acadamies

    Acadamies give +50% beakers in the city where they are built. A settled Great Scientist gives a base of +6 beakers per turn.

    Without Representation, the "break even" point is five scientists. If you can't support five scientists (three with Great Library), then you're better off Settling that GS.

    four scientists + an acadamy + a library = 21 beakers
    four scientists + a Super Scientist + a library = 22 beakers

    five scientists + an acadamy + a library = 26 beakers
    five scientists + a Super Scientist + a library = 26 beakers

    six scientists + an acadamy + a library = 31 beakers
    six scientists + a Super Scientist + a library = 30 beakers

    Given your parameters: Emperor + Great Library + no Caste System (based on your other threads), you won't have more than four scientists for quite a while, so you're better off Settling that first GS. The second one should definitely build an acadamy, however.

    However, with Representation, the break even point is lower:

    three scientists + an acadamy + a library = 31 beakers
    three scientists + a Super Scientist + a library = 33 beakers

    four scientists + an acadamy + a library = 42 beakers
    four scientists + a Super Scientist + a library = 41 beakers

    Again, given your parameters, you can probably support four scientists with the Great Library, so building an acadamy first is a better option. Later ones can be safely settled.
     
  10. futurehermit

    futurehermit Deity

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    ^^excellent analysis, I'm 100% sold. With representation, build an academy in GL city. Without, settle the GS and consider academies later. Thanks!

    One thing: Since you need a library to run a scientist (w/out caste system), do scientists essentially put out 7.5 beakers/turn (6 base + 1.5 from 25% library bonus)?

    EDIT: One other thing: If the above is true (6 + 1.5 = 7.5), does the additional 10% from a monastery come from the base (6 + 1.5 + .6 = 8.1) or does it come from the total (6 + 1.5 + .75 = 8.25)? Thanks!

    Thanks again!
     
  11. DarkFyre99

    DarkFyre99 Prince

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    You're welcome. I've been experimenting with the Specialist Strategy too, but at a lower level (prince) so I don't hit the happiness cap as quickly. I think I'll try it with Slavery instead of Caste System, to see how that works. When I need a building built, I've been shifting my specialists from their usual jobs to the mines.

    That's correct. All research buildings boost base beakers, so scientists essentially get a +25% bonus when produced by libraries.

    Edit:

    Yes, monasteries apply to the base too. That would be +10%, for a total of +35% with a library... a single scientist (under Representation) produces 8.1 beakers (6*1.35 = 8.1 beakers).
     
  12. futurehermit

    futurehermit Deity

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    Thanks, much appreciated! About to post a large update based on the feedback so far...Thanks everyone :)
     
  13. futurehermit

    futurehermit Deity

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    UPDATE!

    Ok, thanks to the great feedback I've received so far, I've crunched some more numbers. I'm basing it now on 1 tech per 5 turns and also have taken out the settled specialists since settled priests kinda suck, the GE is better used elsewhere (e.g., unlocking metcast or hurrying great lib), and the first GS should build an acad in the GL city. the exception, as has been mentioned is the case with no representation. without representation, it is better to settle the specialist instead of building the acad. I will leave that to everyone to figure out themselves, as I am focusing on the main issues at hand.

    I have included libraries in the analysis and will provide separate numbers for a single monastery (if you are building 2+ monasteries, you can do your own number crunching :) ). I will mention the academy, but can't handle the math tonight.

    All calculations assume libraries, thus giving scientists a rate of 7.5 w/representation and 3.75 w/out it.

    I will spare the rhetoric and just post the numbers.


    Classical Era with Representation


    Number of specialists for 1 tech/5 turns rate: 8

    Number of specialists for same rate but w/GL: 6

    Number of specialists for same rate but w/GL and single monastery: 6

    Conclusion: With great library and representation you need 3 cities running two specialists in each to maintain a 1 tech/5 turns tech rate in classical. A monastery fails to make an impact at this point, so don't waste your precious early hammers on them.

    Classical Era no Representation

    Number of specialists for 1 tech/5 turns rate: 17

    Number of specialists for same rate but w/GL: 15

    Number of specialists for same rate but w/GL and single monastery: 14

    Conclusion: Without representation you need 7.5 cities w/out monasteries and 7 w/monasteries. In classical??? Seems a bit far-fetched to me, especially on emperor. I think w/out representation you're better off going cottages. But that's a whole different analysis...

    Medieval Era with Representation

    Number of specialists for 1 tech/5 turns rate: 20

    Number of specialists for same rate but w/GL: 18

    Number of specialists for same rate but w/GL and single monastery: 16

    Conclusion: At least one monastery will save you a city come medieval, so that's something to keep in mind. I didn't mention it, but you also will likely have an academy in your GL city, which will make the GL line numbers slightly lower. W/out monasteries, you'll need 9 cities to support the tech rate and with the monasteries, only 8 cities. Keep in mind, if you want to, or have to, keep your empire smaller, but can keep your pop up, you can run caste system to run more scientists per city

    Medieval Era without Representation

    Number of specialists for 1 tech/5 turns rate: 39

    Number of specialists for same rate but w/GL: 37

    Number of specialists for same rate but w/GL and single monastery: 34

    Conclusion: Same thing applies about monasteries and academies. They'll make a slight impact. To support the tech rate you'll need 18.5 cities w/out monasteries and 17 w/monasteries. That's a helluva lotta cities folks. You pretty much have to run caste system here and even then, I dunno if it's worth it...
     
  14. Dr Elmer Jiggle

    Dr Elmer Jiggle King

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    They probably don't make much of a difference in terms of how much better is Representation vs. no Representation, but one of the conclusions I reach based on your numbers is that a specialist economy without Representation isn't always possible or practical. Ten cities with +6 food (assuming 2 specialists and another 2 food so you can keep growing) aren't always available. I suspect that if you work libraries, an academy, and/or some monasteries into the equations it might start looking more reasonable.

    Just as a first order approximation, I would assume that if you had a library in every commerce city, you would need 25% fewer cities or 7 to 8 instead of 10. With an academy or some monasteries you could probably get that down to 6 without too much difficulty.
     
  15. futurehermit

    futurehermit Deity

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    ^^heh, i was posting the update when you wrote this :) thks!
     
  16. Nares

    Nares Emperor

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    I feel as though a tech per five turns is an extreme rate. The cheapest techs may fall into this category when researched at the appropriate time. However, I think the majority of techs take far longer to research. I also do not think a Cottage based economy could research at so significant a clip, whether it utilized binary research or a mixed slider.

    One tech per ten turns seemed much more realistic than one tech per five turns, though perhaps a rate closer to one tech per 7.5 turns would be more appropriate.

    With regards to the GS, I always felt the assumption was to build an Academy first, though I am surprised to discover that without Representation, incorporating it as a Super Scientist first and building an Academy with the second GS pop is a more efficient course of action.
     
  17. UncleJJ

    UncleJJ Deity

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    Sorry but I am dismayed by this analysis :sad: . It seems to me that the wrong question is being asked and that is why you are not getting answers that make much sense in a real game. An analysis of science output per turn cannot ignore commerce :eek: Even if you don't quantify it exactly you need to consider it.

    The general equation for the science output of each city can be expressed as follows:

    Science = (C * R + S) * B

    Where,
    C = Commerce in that city (in capital with bureaucracy *1.5)
    R = The global science rate
    S = Specialist base beakers from food specialists, settled specialists, free specialists as modified by representation.
    B = The science multiplier in that city (library, monastries and academy)

    The science output for your empire is simply the summation of that equation over all your cities from the largest and most powerful and longest established to the smallest and newly created.

    In my current game I find that although I am concentrating on studying the effects of specialists in fact the bulk of my global science still comes from commerce, although specialists now contribute a larger proportion than in any of my previous games.

    Consider 2 cities, the largest and most powerful and a newly created one to illustrate my point. First my capital which is special, as it has the highest value for B with library, a monastry and an academy. That gives it a +85% science boost. Also it runs bureaucracy so all the commerce C (including the 8 from the palace) are multiplied by 150% before the 185% bonus from B. Obviously building some cottages here is a good idea ! Also since B is high it makes sense to settle any GS here particularly considering that this where Oxford will be built.

    At 200 AD my capital has 24 base commerce giving 36 after Bureaucracy (so C = 36) and has 1 settled GS and is running 2 Scientists to limit further growth (S = 12). It has an academy, library and one monastry for B = 85%. The science at R = 100% is then 88 beakers per turn and note only 22 come from specialists hence the value of commerce.

    Now consider the other end of the spectrum, a newly settled (or conquered) city with no buildings and 4 commerce. Build a library here and the 4 commerce becomes 5 and you can run 2 specialists. This city is not impressive and will never contribute as much as the capital from commerce or specialists (with or without Representation) but it can help a lot by making another GS for the empire. That GS will be moved to the capital and gain the benefit of the currently higher value of B and knowing that B there will eventualy reach 225% :king: In some senses in the analysis this new city can claimn that its "science output" includes the GS which was parked in the capital getting the large value of B there and producing science for the rest of the game. That improves its contribution to total science ouput for your empire over time a lot more than a consideration of whether you are currently running representation or not.

    I'll end here but wish to return to this situation later.
     
  18. UncleJJ

    UncleJJ Deity

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    Sorry this analysis is flawed :(

    Considering reasonable amounts of commerce it will nearly always be better to build an academy in your capital rather than settle the first GS. Also it will probably be better to build an academy in the city with the Great Library (if different from capital).

    Conclusion, you need to consider commerce and great scientists when deciding whether to build an academy in a city. And you should anticipate future increases in commerce and possible settling other great specialists.
     
  19. Killroyan

    Killroyan Deity

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    Nope the analysis is not flawed because it revolves around running a 0% science rate if I am not mistaken. If commerce is pulled into this analysis then indeed it has to be changed. But it is very interesting stuff I have to say.
     
  20. malekithe

    malekithe King

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    That's pretty much the conclusion I've always come to.
     

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