[R&F] Mathematical Model Comparison

[Boyan_Sun]

Why do many Civ4/Civ5 players hate Civ6 (This is very common in our community, many people considered R&F a failure )? I made 2 comparisons, just several simple diagrams.

Production vs Prices, with the progress of the tech tree.

1. In Civ4/Civ5, many buildings can provide percentage bonus, which make the city production growth exponentially. But in Civ6 there are no such buildings.
2. In Civ4/Civ5, chop value are constant, but in Civ6 it scales by science/culture progress.
3. Overflow exploit finally makes the chop value explode.
   
4. In Civ4/Civ5, unit/building cost are increasing nearly linear, but in Civ6 it is exponential.

Cost vs Yield(science, culture, production, gold) of a single city, with population growth.

1. Specialists in Civ4/Civ5 provide big yield, and GPP. But in Civ6 they don't.
2. Citizen yield in Civ4/Civ5 can be scaled by many buildings, but in Civ6 there are no such building scalars.
3. So there are only a few good jobs left, which makes the marginal effect on population very severe, but the needs grow exponentially.
4. Districts(and buildings in it) yield a lot, and first 2~3 districts are what player really wants, so they provide the most.

So what do you think? Very appreciate for your thoughts.

 

[Forster]

It would appear that 4/5 preference is for exponential city yield and stable/lower unit/building cost while 6 players prefer the opposite, or at least don't consider the difference to spoil their play. I liked 4, did not really like 5, and really enjoy 6.

 

[Xunin]

I guess this puts the finger on why I consider the core mechanics of the older games more solid compared to 6.

Seems to me like Firaxis instead of realigning the wheel tried to reinvent it and came out with a square. I think Civ4 had a much more elegant economic system to prevent city sprawling by inducing city maintenance as a function of number of cities and their proximity to the capital. City maintenance, In addition to being mechanically transparent also makes sense conceptually (because you know, larger empires are more costly to maintain because of corruption and inefficiency and other things) but there were still player options to mitigate its effects. Ironically, Civ6 pigeonholes players into going as wide as possible and keeping the population low to the point that other strategies become suboptimal if not unviable. In addition to reducing strategic depth and variety (rather than increase it), it adds several artifacts on a conceptual level.

For instance, I don't think inflating settler/builder costs make a lot of sense, other than as a means to keep city sprawling in check. If that's the case the cost increase should apply not as a function of how many civilians have been built but how many cities are in possession. The way it currently is implemented means it's always going to be more beneficial to conquer cities than developing your own. And the same is true for districts. It makes no sense why a campus is easier to construct in the ancient era compared to the classic era. And the solution to circumvent said inflation? "Locking in" districts as soon as they are available... Just seems like broken game design to me.

In closing: brilliant ideas, lackluster execution.

 

[Boyan_Sun]

For single city's food cost, I came up with a model that was more accurate. This suits both Civ5 and Civ6.

Blue - Growth food needed for a new citizen follows this formula: 15+8*(N-1)+(N-1)^1.5, so that's easy to accumulate the growth food you need.
Green - Consumption accumulation is a little difficult, for it was related to growth rate. I simply assume this city always has +15 growth food (each citizen consumes 2 food, so 1 citizen = 17 food yield, 2 citizen = 19 food yield, etc). In fact, I think +15 is quite fast a growth rate. So turn number to growth will be T = GrowNeeded/15, and consumption will be T * pop * 2.
Yellow - Then add these 2 above, we get the real food need for a city with certain citizen number, if no harvest involved. Of course, this is still an ideal situation, ignoring the effects of housing and so on.

So I got this result:

That shows high-population cities are completely unimaginably inefficient and expensive. And the benefits of harvesting food are far greater than they appear, for example, harvesting from pop 8 to 10 appears earn 89+101 = 190, but actually earn
926-520=406.

In Civ5 it is the same curve, but there are aqueducts which can +40% growth food after growth (and medical laboratories in late game), and more +N% to growth like “love king day”, actually reduce the entire curve by almost half. At the same time, the citizens of Civ5 yields much more than Civ6, and that yield will be improved by many techs, even scaled by many buildings, or become specialists to gain GPP.

 

[acluewithout]

This thread should be in the general discussion forum and have a catchier title - it deserves way more attention.

@Boyan_Sun I think you’ve really nailed this issue. And with maths!

Mid and late game cities don’t produce enough production or other yields, and units etc are too expensive, so your mid and late game cities don’t feel like they can “do” anything. It doesn’t help that those same mid and late game units and buildings don’t feel very impactful either, so why bother.

And then chopping gets thrown into the mix. In a sense, chopping provides a partial
solution, letting you get around weak city production. But it does it so effectively there’s actually almost no point using cities to build anything.

There are multiple things that need to be tweaked to fix this in a satisfactory way. It’s not as simple as nerf chopping (cities still can’t produce units etc) or boost production (now every city is productive, so you just get ICS).

I think the solution is something like:

- chopping needs to get capped around the industrial era;

- cities don’t all need production boosts, instead there needs to be a way that newer / smaller cities can boost a small number of core power cities (ie concentrating productive capacity in a few cities);

- campuses and science buildings need a soft or hard cap so you can’t keep spamming them;

- late game units and buildings need to have more impact;

- generally the late game needs to matter more - not just have more things to do (busy work) but actual impact.

 

[Boyan_Sun]

This thread should be in the general discussion forum and have a catchier title - it deserves way more attention.

Really, should I put it there? I'm not sure, because many people don't care about efficiency and don't like to play utilitarian games. Maths of Civ6 leads to the most effective play method particularly counter-intuitive, I am afraid it will be... not only possible, it will be inevitable to arouse the antipathy and discomfort of most people, even this was a cliche in this Strategy and Tips forum for a long time. After all, Civ6 isn't just a math game, it's also a history simulation game, at least need a better immersion, isn't it?

• Step-by-step development will ruin your country, chop should be the main source of production. (Corollary - IZ is useless)
• Culture is the top priority. Much easier to get and much less needed than science to push the progress, and the progress will significantly increase chop value.
• High population means nothing but only waste. Food resources are more suitable to be harvested than improved.
• AI did not know above principles at all, so its production was very insufficient, resulting in the failure of the arms/tech race. (what's more, high-difficulty AI is simply get bonus to city yield only, chop value is equal to the players)

Besides, I don't know how to move the thread. Feel free to re-post or link~ and thank you for reading.

Moderator Action: This is a quintessential S&T thread. It does not need to be moved. -- Browd

 

[acluewithout]

Well, I’m happy for the thread to stay put. Just hope people see it.

My point is that, although there are strategic implications to what you’re saying, I think the maths actually explains what people are complaining about when they say “the mid / end game is boring” or “chopping is too powerful”. It’s not just perception - there’s a real reason the game feels that way.

 

[Boyan_Sun]

My point is that, although there are strategic implications to what you’re saying, I think the maths actually explains what people are complaining about when they say “the mid / end game is boring” or “chopping is too powerful”. It’s not just perception - there’s a real reason the game feels that way.

Yes, that's what I want to show too. But I don't know what kind of experience Firaxis officially want to bring to our players. Just because the "strange" math model then accuse official not to be professional, I felt that it may be inappropriate, perhaps Firaxis does have some other thoughts? For example, make each generation different, so as to attract players of different interests, prevent products from homogenization, and so on.

As far as I am concerned, I do hope the game can be changed in the direction to more of common sense, similar to your previous advice. I would be happy if the Firaxis designer could see my analysis.

 

[Eliminator_Sr]

Interesting, but I have some questions. Why do the gaps in overflow chop and Magnus chop get wider over time? I thought those were fixed multipliers. I'm probably missing something simple here. Also, Is there any reason why there are no numbers on the graphs? Shouldn't the plots be stepwise by era in civ6 or do those yields actually increase with each tech/civic researched and is that solely due to district scaling? I'm having trouble following this without more detail.

 

[Boyan_Sun]

Why do the gaps in overflow chop and Magnus chop get wider over time? I thought those were fixed multipliers.

Because the multipliers represents the slopes. The higher the slope, the greater the multiplier. And overflow chop in that graph is already counted Magnus, just to show how amazing the output is.

1. chop: y1 = ax + b (accurate formula is 20*(1+9 * progress%), see formula thread)
2. chop with Magnus: y2 = 1.5(ax + b)
3. and with overflow: y3 = (1.5~2) * 1.5(ax+b) - c, c is a small cost from previous build

And you see, "In Civ4/Civ5, many buildings can provide percentage bonus, which make the city production growth exponentially", that means every time you build such a building, you increase the slope. Of course, in addition to the slope, it also includes the increase of tile output and pop growth. Taken them together, they will be that exponential trends. But in Civ6 there are no slope buildings, only 2 mine improve techs (apprenticeship, industrialization), after industrialization the production growth will nearly stagnant. So that trend is nearly logarithm.

why there are no numbers on the graphs?

Because this is just a few simple trends from my own (and some players in our community) game experience, and there must be some deviation from the actual situation. My purpose is to discuss with everyone. I hope someone can correct the mistake. But these experiences of Civ6 do seem to us to be working well, like science victory in BC or so on.

If in doubt, I can provide some more accurate statistics. For example, price - this graph is an accurate statistics of the cost of the melee units (warrior - swordsman - ... - mechanized infantry).

You can see Civ6 is just a bit of an exponential trend, and my simplified diagrams are slightly exaggerated. Forgive me, I just wanted to make simple things more intuitive.

 

[Eliminator_Sr]

Ok thanks for the response. I think I need to go visit the formulas page because I'm still not getting it, but looks like there's enough detail here to point me in the right direction.

 

[acluewithout]

@Boyan_Sun

I don’t want to create work, but do you have any ideas on how the production graph might have differed had FXS kept factory / powerplants overlapping bonuses?

There’s a theory a few of us have that production costs were originally balanced around overlapping bonuses, but that when FXS nerfed that it through out the costs for the late game. The fact FXS have now years later sort of reintroduced overlapping via Magnus’ last promotion suggests this might be right.

Anyway, I’d be interested to hear your thoughts on how overlapping might impact these numbers.

 

[Boyan_Sun]

I’d be interested to hear your thoughts on how overlapping might impact these numbers.

I did this analyze in 2016, before the overlapping was nerfed. I said this was probably the only thing that could keep production in the old tradition of post-industrial explosive growth, in other words, exponential. But it may be not true now. As long as chopping is not nerfed, overlapping will still not make too much sense if recovered. Workshops and factories are too expensive, IZ too, and even a district place. Of course I'm not so sure, the only thing I'm sure is that high population was still useless.

 

[acluewithout]

That’s pretty grim. FXS nerfed their only counter to rising costs, and the counter they nerfed didn’t make much difference anyway...