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    Your Elvenar Team

Manufactory Math With a Surprising Conclusion

MaidenFair

Well-Known Member
Okay, @Darielle, you asked for it! ;) I didn't want to take over @JerseyMeeko76 's post, so I'm starting a new thread. There are a couple of caveats: 1) it took me longer than expected, so I've only done the Human Marble Manufactory so far in the spreadsheet. Eventually I'd like to do all the race/good combos (probably each in their own spreadsheet) but that will take a lot longer. 2) I did not run the calculations beyond Woodelves, since the next upgrades for Marble are in Elementals which adds Sentient Goods, and I don't know what that might do to the supply/demand levels for T1 goods. Plus I got tired of copying numbers. :D 3) This uses calculations based on only regular (non-magic) residences and building tab culture buildings, with no allowance for culture/pop buildings or other event/magic/one-time-only type buildings. This of course means that the Per Square values of many calculations will be different in actual cities but since the numbers would change in an even proportion to each manufactory level, I think the ratios represented here are still accurate, and therefore the basic math is still pertinent.

https://docs.google.com/spreadsheet...-lFrM-Cz8Kpu1fwN-VsKGiGNew2wddhkF3WkO/pubhtml

In case my spreadsheet organisation is unclear, here's the long-winded explanation section: it's well-known that to calculate the true space cost of a manufactory, you have to take into account not only the manufactory space but also the people and culture required by the manufactory itself, and then again the culture required by the residences that you needed for the manufactories. This makes for a complicated formula of the *actual* footprint of a manufactory. As you can see, I put tabs in the spreadsheet; the ones at the end are mainly information to provide the formulas on the other tabs something to draw from but I thought it would be good to make those visible too, in case it isn't clear what base numbers I was using. Most info is pulled from the official Wiki and ElvenArchitect, with a few culture-related numbers coming from inspecting my research tree and building menu.

The first tab, labelled 'Chapter Specific Footprint' is all the math showing each manufactory level's efficiency, based on using the residence and culture numbers that become available at roughly the same time as the building itself, i.e., a level 15 manufactory which becomes available in Chapter III used Chapter III residential/cultural numbers, while a Level 16 manufactory which becomes available in Dwarves used Dwarves residential/cultural numbers. Based on these numbers, with the upgrades of manufactories and residences/culture buildings proceeding at the same pace, it looks like the manufactories get more productive per square with every upgrade (until there's a dip in Woodelves, which oddly has its most efficient manufactory as the first upgrade, with each successive level losing efficiency). This is probably the math most players look at when they are thinking about the efficiency of upgrading.

However, if we switch over to the 'Orcs Footprint' tab, it becomes a different story! On this tab, I ran all the same calculations, except that I only used the residence and culture building numbers from the Orcs chapter, regardless of manufactory level. This is useful for the concept of upgrading residences and culture buildings as those become available, while not upgrading the manufactories at the same pace. On this chart we can see that the Level 14 manufactory (available already by Chapter 3) is the most efficient, outperforming the Level 19, for example, (the last available upgrade before Woodelves) by more than an extra 8.5%! It's the same on the 'Woodelves Footprint' tab, which runs the same calculations again with only the residence and culture numbers from Woodelves. Here the comparison doesn't initially look quite as stark, with the first Woodelves upgrade being *almost* as efficient as the Level 14 but since the Woodelves numbers then drop off a cliff, the final upgrade available in Woodelves is significantly worse than the Level 14 manufactory which continues to be the best, on a square-for-square basis, of all the levels available.

While I don't have the spreadsheets ready for anything else at the moment, this has been the trend through all the buildings I have checked so far, both Elf and Human, with the most efficient level ranging mostly between 13 and 15 for any given manufactory. Basically, as you continue to upgrade the residence and culture buildings so that they get more people and culture per square, the earlier manufactory levels become relatively more and more efficient, since they have a smaller ratio of people and/or culture to production to begin with than the later manufactories do. Even by Dwarves, the several-levels-back production is noticeably better per square than the available most-upgraded manufactory levels, and by Woodelves it's almost a 10% difference. Now I did spot-check one of the later chapters (17 or 18, I can't remember which) randomly a few weeks ago, and that was more productive again with chapter-upgraded manufactories and culture/pop, with better numbers than anything Woodelves or below had shown, so at soooome point they do get more efficient again, but it seems to be quite a ways in. At the very least, there are 5 chapters (from IV to Woodelves) where it creates a loss in production to keep upgrading the manufactories.

The only downside I can see to starting out with this production method is that MM spells aren't as useful, since you are using them on lower production buildings. To partially offset that however, I think the Mountain Halls is actually slightly more useful on many small buildings than on 1 or 2 larger ones (possibly due to rounding; I don't have the data on hand to prove this one at the moment but when I ran the numbers for myself earlier, it came out to my satisfaction, so I think I'm right in saying that). Of course, as was very logically pointed out to me by @Iyapo1 when I showed her the first inklings of this data several months ago, applying this in an already established higher-level city might unbalance coin production (not as many residences needed), or affect certain wonder's effects or uses (fewer coins for using in the wholesaler with a high-level BTG, for example, or reducing the effect of the Thermal Spring of Youth by having fewer residences, less population return from a Golden Abyss because of having a lower working population, etc.). However, I think if a player starts out building a city with this method in mind, all of those can be accounted for ahead of time and still create a more efficient city (more space to play with!!).

I didn't seem able to leave visible comments on the document for sharing, so here are a couple of edited notes that were originally comments: Levels 16 through 19 on the 'Chapter Specific Footprint' tab are using Dwarves numbers because that is when those upgrades become available but since they don't actually get upgraded again until Woodelves, there are also Fairy and Orc culture/pop numbers which would make these more efficient than is currently shown.
The colored horizontal lines indicate the last in a series of upgrades which become available at the same time (in essence, Chapter breaks). For each new set in the 'Chapter Specific Footprint' tab, I calculated based on the best residence and culture numbers available at the same time the manufactories became available. On the other tabs, they are still inserted at the chapter break, but are mainly useful for easy tracking across all the data.
 

Darielle

Well-Known Member
Mama mia... looking over your spreadsheet makes everything so clear. And yes, the per square value is the main thing ... not only of the building itself but because of all the "support space". ... ie culture, etc it takes.

You're right, it is counterintuitive but true. These few "windows" where you are better off not upgrading are a good thing for players, especially players in affected chapters, to know.

The idea with the Mountain Halls is also fascinating. I'll have to check that out myself sometime, but you're right, that's a lot of work! I'm so sorry! :)
 

Linnea Shadowwalker

Active Member
This is fascinating. I had to run the numbers for myself, using my city (elf, steel, just started woodelves, so everything fully upgraded to orc level).

And you're right. I used elvenarchitect to see the space needed. I couldn't use fractions of buildings, so I got as close to even as I could. I compared my current 9 level-19 steel to 21 level-14 steel. The level 14's produced slightly more in total, but took up less space, once residences and culture were added (almost 16 expansions vs almost 18).

But then I placed a level 20 golden abyss, to see how that affected it. And the golden abyss erased the difference. Which kind of makes sense. Because the abyss replaces a percentage of working population. And the level 19's take up less space for the factories, but need more residences to support them. And the level 14's take up more actual space for the factories, but less overall space because the number of residences needed is fewer. But then when the golden abyss removes a certain percentage of residences, it will remove more from the situation that has more residences, giving the higher level factories the advantage.

Thank you for all the work you put into this, MaidenFair!
 

MaidenFair

Well-Known Member
@Darielle , aw, thanks!! <3 I've been meaning to post something about this for quite a while, just didn't have the drive to actually collect all my scattered notes and data. I'm glad to hear the spreadsheet was understandable! After I finish my taxes in the next day or two, I'll have more mental bandwidth to start expanding on this. I'm really curious to see where the cutoff actually is, when the manufactory upgrades start being more efficient again. Is it just beyond where I stopped calculating or is it in much later chapters? I'm excited to find out. :D

@Linnea Shadowwalker You're welcome! It is absolutely fascinating. (My mom, who also plays, laughs at me all the time because math is soooo not my thing, and yet for some reason, I spend most of my time in Elvenar doing math. Lol!)

Thanks for sharing your experiment! Isn't that amazing? I love seeing how it could affect an actual city, where you can't deal in fractions of squares (or buildings!). Even though I've seen the numbers over and over, it still sounds ridiculous to me to think that having double the number of buildings could actually be more efficient, yet somehow it is. XD I'm curious, do you think the Golden Abyss actually made the higher-level factories the better choice for overall space, or is it just that there were more available people? Because if the lower-level factories saved almost two expansions, that area could be used for event buildings which often have population as well as production or culture. There's also the Moutain Halls which could be used in place of the Abyss, since I think it has the same population percentage boost but adds to production as well.

Of course, there are so many variables; you can balance things in almost any number of ways, which is half the fun! Everyone's cities look so different, because there's no one right way to build.
 

Heymrdiedier

Active Member
Im sorry theres too much text to read, so ive skimmed most of it. But i have 1 question, is the "lvl 15/16 factories are the most effecient" the one still true, or did you end up with a different suprising conclusion? (the max level before the size changes in dwarf chapter)
 

ajqtrz

Well-Known Member
Wow, the work done here is a LOT. And I appreciate it a lot. It's good to see how even just calculating the value of a good based upon its production cost (as you do here) is so complex. And you don't, as you say, account for even more variables but only restrict yourself to four basic (space, goods produced, cost in coins, cost in supplies) and the Mountain Hall. All of which is why most players probably don't even try to determine the actual production cost of their current set of mfrs.

In addition, like all the formulas, though much more sophisticated than some, this measures the cost of production per square only. In other words, it tells you what the cost of production is, but not the value of the goods produced. As I've noted before, there are a whole lot of other considerations when you ask the question "is my production sufficient for my needs" since you usually need to trade for some of those needs. And trading is both production cost (the basis of supply) and demand based.

Great job on the supply side.

AJ
 

MaidenFair

Well-Known Member
@Heymrdiedier, sorry about that! Did you try looking at the spreadsheet? The data is much more succinct there. Yes, that was the surpising conclusion: for the Human Marble Manufactory, the most efficient level is 14, and it will continue to become increasingly more efficient than the higher-level manufactories as you upgrade residences and culture buildings in further chapters.

Thanks, @ajqtrz! I've been working on this on and off since late December, so I'm glad to hear that other people are as interested as I was. You're right, there are so many other variables that can play into not only the cost/production value of the goods themselves but also the player's desire on how to use the space. I was looking for the most efficient way to make a catering city, so I started with the question: "how can I cram the most production possible into the least amount of space?" Funnily enough, that pursuit of efficiency also freed up enough space that I've been able to put in some less efficient but more aesthetically-pleasing buildings, which also made me very happy. ;)
 

Darielle

Well-Known Member
It's funny ... once you know this can happen you start to look at other things, too. I just checked my Gentle Sorina airship in Traders of Unur. The most efficient collection is the shortest one, but it isn't a straightforward progression from the shortest collection to the longest. In other words, you get the most delicacies per Elvarian Zero from the shortest one, but you don't get the next highest number of delicacies per zero from the next shortest one.

I know I'm not saying it right, but check out how much Elvarian Zero it takes per Delicate Delicacy, and you'll see that there's some wonky math going on in selecting one of the four time periods to make delicacies.
 

Linnea Shadowwalker

Active Member
I'm curious, do you think the Golden Abyss actually made the higher-level factories the better choice for overall space, or is it just that there were more available people? Because if the lower-level factories saved almost two expansions, that area could be used for event buildings which often have population as well as production or culture. There's also the Moutain Halls which could be used in place of the Abyss, since I think it has the same population percentage boost but adds to production as well.

When I added the level 20 golden abyss, the two scenarios became equal in space requirements. I was able to decrease the level 14 factories from 16 expansions down to 15. And the level 19 factories went from 18 expansions down to the same 15. If your Abyss (or Mountain Halls, the effect on population is the same) is not up to level 20, I think the lower-level factories would still win. But as your levels go higher, the higher-lever factories would win.
 

MaidenFair

Well-Known Member
@Linnea Shadowwalker, oh, I see!! That's very interesting. I'll have to play around with that some more. As a caterer, I wonder if, all other things being equal, that might swing the difficulty formula against me since 20 wonder levels increase costs by roughly the same amount as an additional 4-5 expansions, so unless it's saving me that much in space, which it sounds like it only saves 3 in your scenario...hmm, definitely food for thought. Thanks for explaining!
 

MaidenFair

Well-Known Member
I find myself doing the math on all sorts of random things now too, @Darielle, just in case, haha! I see what you mean about the Gentle Sorena; that's interesting. A 15- and a 9-hour production make the same amount of shrimp in the same amount of time as two 12-hour productions but requires 200 fewer Elvenarin Zero. Weird.
 

Nerwa

Active Member
What an EXCELLENT analysis, @MaidenFair ! More charts like this, for the other goods & for both Human & Elves, would be very cool for obsessive-minded players. :cool:

I can see where some motivated (or bored) person could refine this & take into account things like roads (as @SoggyShorts mentioned) and/or workshops for supply needs. But that's a whole 'nother can of worms, and I suspect it'd be a case of diminished returns. After a point, the number of variables (type of roads, frequency of pick-ups for both supplies and goods; all the ones @MaidenFair already mentioned) creates so many fractals that you may as try to measure the coastline of Britain*.

Thank you so much for putting in the time!

footnotes

*"Coastline paradox": https://en.wikipedia.org/wiki/How_L...ical_Self-Similarity_and_Fractional_Dimension
 

SoggyShorts

Well-Known Member
On a relatedd note:
I just spun down on today's event daily, and here's why:
I usually log in once per day, twice tops.
My factories make 10940 per 9h
Call it 11,000
That's exactly what 2 shamanistic healing grounds make in a day.

(9 squares plus 1.5 roads)x2 = 21 squares of footprint
All of my pop comes from Goblin shops so I value that at 688 per square.
(1440x2=2880)/688 = 4.18
I value culture at 0 which gives a final footprint of 17 for the two SHG

My factory takes up about 51 squares all in

Convenient math:
6 SHG make 33,000 per day in 51 squares
1 factory makes 11,000 per 9h in 51 squares
 

MaidenFair

Well-Known Member
@SoggyShorts (random aside: I initially typed your name as SorryShorts, which made me laugh. I would probably be sorry if my shorts were soggy!) I did not account for roads here, since I couldn't immediately think of an easy equation to allow for the fact that, in an ideal placement, there would be buildings on both sides of a road, which means they can share road square usage, but if there is an uneven number of buildings then one of them has to count road squares all on its own. (ETA: Upon rereading your message, I think your calculation might work here...I'll have to try it in the spreadsheet later and see.)

When I've done the math by hand several times, there were still more road squares required for the larger manufactories as a whole because they require so many more residences, which also need roads. I'm not sure my brain is up for the challenge of trying to figure out the formula to go into a spreadsheet right now but if you're interested to see the types of numbers I was getting, I can run a few scenarios manually and share them after supper.

@Nerwa, thank you!! :D I've been working on it again today (Elven Marble and Human Silk) but those spreadsheets still need a double-check to make sure I adapted all the formulas correctly before they're ready to share. Thankfully, it's definitely faster with new buildings now that I have the template established, since part of the info (residence and culture numbers) and some of the formulas don't need to be redone each time.

Your link is fascinating. I never thought of measurement like that before but it makes perfect sense, and yes, I was trying to avoid that dangerous spiral, haha!
 

MaidenFair

Well-Known Member
@SoggyShorts Congrats on your prize haul! I love being able to use event buildings like that.

Okay, here are two road scenarios with different outcomes. Make of that what you will. ;)

In the random case of a Woodelves player with 5 fully upgraded manufactories (Level 23), we would need 14 Level 14 manufactories to match the marble production. These manufactories are 6x3 and 4x3 respectively, and Woodelves residences are 4x3. So the math comes out as:

Level 23 manufactories - 7 roads((5manufactories/2)x3shortside-2roads)
5x33.17 residence squares = 165.85/12 squares in a residence = 13.83 residences = 19 residential roads((14/2)x3-2)
for a total of 7+19=26 roads

Level 14 manufactories - 19 roads((14/2)x3-2)
14x6.69 = 96.66/12 = 8.08 = 13 roads((9/2)x3-2)
for a total of 19+13=32 roads

So this scenario has 6 more roads for the lower manufactories but this isn't enough to eliminate the overall space savings that would be obtained, with 5 manufactories x 61.85 squares each making a pre-road total of 309.25 squares for the higher manufactories and 14 manufactories at 20.58 squares making a pre-road total of 288.12 squares for the lower manufactories. Even adding the 6-road difference in, the lower level manufactories still save 15 squares in this scenario. Not a ton, I'll grant you, but it is almost 2/3rds of an expansion.

For another scenario, I looked at my own city in Orcs, where I have 12 marble manufactories (I'm still in the process of upgrading these all to level 14 but for the sake of easy math, I'm going to pretend they're already there). To produce the same amount of marble, I would need 7 manufactories as fully upgraded as they can get in Orcs, which is level 19. Orc residences are also 4x3.
Level 14 manufactories - 16 road squares ((12/2)x3-2)
12x8.92 = 107.4/12 = 8.92 = 13 roads ((9/2)x3-2)
for a total of 13+16=29 road squares

Level 19 manufactories - 10 ((7/2)x3-2)
7x22.88 = 160.16/12 = 13.34 = 21((14/2)x3)
for a total of 10+21=31 road squares

In this scenario, the roads are almost the same, with a very small advantage to the smaller manufactories. The total pre-road squares needed is 12x23.84=286.08 vs 7x45.50=318.5, giving a savings of 32 squares, which becomes 34.42 when the roads are factored in.

Clearly, since two similar scenarios ended up with an 8-square swing in advantage, the road situation must depend largely on the amount of production desired as well as potentially the residential efficiency/chapter number. In neither case is there such a large number that it negates the basic premise of smaller manufactories taking less space for the same production amount (although based on these numbers, I can imagine the roads potentially making a difference to that in a further chapter, depending on how much production a player needs to run).
I won't be offended if you want to check my math. I seem to have a fuzzy brain today and had to do several calculations twice. :p
 

ajqtrz

Well-Known Member
In examining the basic formula to compute the production value of a building in comparison to a second building I begin with the following variables used in a simple formula.

S=short length of first building type
L= long side length of the building
D = daily production of the building

To compare types of buildings when you know the size and daily production of each building and want to figure out if the space is better is pretty easy. Daily production (D) divided by S*L (the area of the building).

To add the number of road squares needed would just add the short side to the area and recompute with that in mind. So it's D/S1*S2+S1. This assumes the short side is where the road is.

And to compare two types you use the same formula for each and subtract one from another.

The formula for each building, including their road needs, is: D1/(S1*L1+S1) and D2/(S2*L2_S2). Compare the two by combining them in the negative: D1/(S1*L1+S1) - D2/(S2*L2+S2) and you get either a positive or negative number. Negative says the second type is better, positive, the first. If the end up at 0, they are even.

Now lets consider something else, besides roads. Perhaps you wonder if two buildings, producing different goods are equal. Say a T2 boosted and and a T1 boosted of a higher level. Maximizing your production means, in this case, using a ratio between the goods. The standard cost ratio between T1 and T2 is 1:1.5. While this is not the value of the goods, we are considering production and thus it is about the best we can do.

Since, we will assume, D1 is that T1 Boosted, and D2 is the T2 boosted, we need only multiply D2 by 1.5

So now the formula, which includes roads and now cross tier production is D1/(S1*L1+S1) - 1.5(D1/(S1*L1+S1)) -
The same interpretation applies. Negative = second building is more productive, Positive, the first.

This formula can be generalized if we replace the 1.5 with R. R being any ratio between any two goods. One can even make up their own ratios. You can, for instance, say that supplies are worth 2 times gems. R=2, in that case, and the first building produces gems and the second supplies -- the higher good (the one to which the first is being compared -- should always be second. However, if you Took R1 and R2 with the ration expressed as R1:R2 you could a more reliable formula of R1*(D1/S1*L1+S1) - R2*(D2/(S2*L2+S2)) I would be interesting to come up with a chart of ratios, wouldn't it?

And this brings me to another thought. If you have several types you could take this formula and find, in a group, which building is best, second, third and so on. You would have to have a "base good" that would always be 1, but then you would just use MAX(R1*(D1/S1*L1+S1), R2*(D2/(S2*L2+S2)), R3....) and so on.

If you put this in a spreadsheet you could find the best building for your space...provided you did all the data entry and ratios between all the things that can be produced.

And finally, just for the fun of it, you can use the same formula to compare buildings producing multiple types of items. Here's what it looks like. Each subsequent type of production gets the next D and R number.

Building 1: (D1*R1+D2*R2+D3*R3,....)- [Building 2: (D4*R4+D5*R5...). The ratio evens out the production values and puts them on an even scale. This allows comparison. Of course, the ratio is now the variable that is most personalized. If one is producing a lot of supplies, a supplies, gems and crystal building may mean that building is not as good in your situation as some other building. But then, that just means you will need to adjust the ratios to reflect your needs. If you have supplies at 2, and are overproducing, you can drop it to 1.5. Keep changing it and eventually you'll find out what it's worth in your city, compared to other goods.

Wow, once you start thinking of all this, you can really get carried away!

AJ
 

Vigali

Active Member
@MaidenFair This is terrific -- I hadn't really ever thought to look at how manufactory efficiency changes as the "input" efficiency grows, without actually upgrading the manufactories themselves. Very, very cool, I love having new stuff to think about!

I had 2 thoughts for you that may be helpful as you move forward for this. Soggy already mentioned road square costs (which can pretty easily be thought of as 0.5*Shortest side) -- but one thing I didn't see on your spreadsheet was the cost in squares of the supplies production required to run your manufactories. I may have missed it (sorry if I did!) but just wanted to mention it either way. The second thing (and you touched on it already) was that these numbers will actually change quite a bit with a higher percentage of magic residences. Definitely something to account for.

If this helps, I have a building cost calculator spreadsheet here (just click the "Building Cost Calculator" tab): https://docs.google.com/spreadsheets/d/1Oz2L54hADyK447-RMRcPp0tMx4M_MSXl3PQJ_ASiS-0/edit?usp=sharing

My spreadsheet was not intended to tackle the question you're tackling -- it assumes that you're always fully leveled in your buildings for each chapter (which is obviously the opposite of what you're trying to look at). However, I think it could be pretty easily expanded and adapted to include the per-level data. If so, some of the stuff in there may be helpful to you -- it does a couple things in particular that may help:

1) It includes roads/workshop square costs.
2) It allows you to specify your manufactory Boost percentage so you can see your "actual" manufactory production numbers instead of just base production numbers.
3) It makes a base culture assumption that culture costs are born by Lava Codex's, which are easily craftable and will save you from having to find different culture buildings for each chapter.
4) It allows you to specify your 'magic/standard' makeup. You can enter in your # of standard residence/workshops, and # of magic residence/workshops, and it will properly calculate square costs based on your specific makeup (instead of just assuming all standard, or all magic).

Hopefully there's something in there that you can use as you continue on with this -- very very cool, interesting stuff!
 

SoggyShorts

Well-Known Member
I won't be offended if you want to check my math.
At a glance, It all looks good, although I wouldn't "-2" for the roads. Realistically the roads continue in both directions so just "0.5*" is enough imo.

One thing that's changed since the last time I had this discussion is the "set all" feature implementation. The idea of setting 14 buildings individually instead of 5 was very unappealing (to me) but now? Not really an issue :)
 
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