The math behind the science penalty?

[Outlandish]

So in my last game I'm winning in a fairly standard 4 city tall tradition science method. There are sites for 2 more cities available nearby, one good along a river, one excellent once I expand to all the seafood, and I had plenty of money to just buy the tiles. I decided not to expand due to the science penalty. But just how bad is it, should I have expanded?

Just how much science does a city need to produce to be worth expanding, is it 5% of your total science per turn(spt)? So if I'm producing 100 spt out of 4 cities (just for easy math, I know that number is low), do I just need 5 spt to be worth expanding? Or is it 5% for each city you already have, so I'd need 20? Or something else entirely?

Obviously there are other considerations that make it a more complicated decision, claiming resources, denying the spot to the AI, happiness, but from a purely science perspective how much do I need to be able to get out of a 5th city before expanding?

 

[kaltorak]

It's not so bad, it's summative not multiplicative, so you need 5% of what you produce to compensate, not 5% per city

 

[The QC]

What the penalty does is to increase the cost of a tech with 5% multiplied with the number of cities.

How I calculate, in order to do it very fast:
- I look at a tech that I can research right now, but haven't started. I check in the Civilopedia how much it should cost (let's cal this X) and I check in the game how much it really costs (a higher number, let's call it Y).
- I calculate (Y-X), then divide by the number of cities I have and then divide it further by the number of turns it would take to research that technology (as shown in the tech tree). The resulting number is the number of beakers a city needs to produce per turn in order to break even at the current stage of the game.

The result is usually an easily achievable number, which is why I've pretty much stopped doing it and I've started assuming it's always worth making another city.

I hope that was understandable.

 

[Outlandish]

Perfectly understandable, thanks. I figured that would be the case, but just wanted some verification. More cities next time around then!

 

[I_pity_the_fool]

What the penalty does is to increase the cost of a tech with 5% multiplied with the number of cities.

How I calculate, in order to do it very fast:
- I look at a tech that I can research right now, but haven't started. I check in the Civilopedia how much it should cost (let's cal this X) and I check in the game how much it really costs (a higher number, let's call it Y).
- I calculate (Y-X), then divide by the number of cities I have and then divide it further by the number of turns it would take to research that technology (as shown in the tech tree). The resulting number is the number of beakers a city needs to produce per turn in order to break even at the current stage of the game.

The result is usually an easily achievable number, which is why I've pretty much stopped doing it and I've started assuming it's always worth making another city.

I hope that was understandable.

eta: I'm not sure I understand this. Hold on.

 

[I_pity_the_fool]

Oh I've got it. The QC is doing the same thing I would do beakers per turn/1+(0.05 * number of cities) and taking 5% of this figure.

All that needs to happen OP for you to break even is for a newly founded city to produce 5% of the average beakers of your other cities.

 

[Soronery]

Take your current science divide by 20.
Here are some numbers:
Current science/science needed for that city to earn to not be hindering research:
1000=50 science
500=25 science
200=10 science
100=5 science

 

[Browd]

I look at a tech that I can research right now, but haven't started. I check in the Civilopedia how much it should cost (let's cal this X) and I check in the game how much it really costs (a higher number, let's call it Y).

Unless you are playing on a map smaller than Standard, using Civilopedia tech costs will lead to inaccurate results. On Standard maps, tech costs are 110% of base tech costs, while Large are 120% and Huge are 130%. Also tech costs are reduced slightly by the number of AI civs that you have met that have already researched a tech.

The point is that this is at best an indirect way of determining whether a new city is worth building.

Also, using current beaker rate is just as poor a method, in my view, as some methods advocated when deciding whether culture cost increases were worth an additional city. If your culture rate is low enough, any city with a monument is worth building, but that is obviously not the right long term answer in game. Similarly, if you constrain your cities' growth and neglect science buildings long enough, you can justify founding 20+ cities.

 

[AlazkanAssassin]

Over in another thread i posted this:

To determine the needed population of a new city to break even:
[number of cities] is the number of cities you have BEFORE building a new one, including your capitol.
[tech cost]=[base]*(1+.05*[number of cities])
[base tech cost]*0.05=[increased cost]
[tech cost] / [current total beaker rate] = [turns to research]
[turns to research] * [new city beakers] = [contribution of new city]
The break even point is when [contribution of new city]=[increased cost]

This set of equations can be manipulated into [new city beakers]=[current total beaker rate]*0.05/(0.05*[number of cities]+1)
So the population required of a new city is:
[current total beaker rate]*0.05/(0.05*[number of cities]+1)
or if you buy a library in the new city:
[current total beaker rate]*0.0333/(0.05*[number of cities]+1)

If you want to account for odd sources of science (e.g. mayan pyramid, Great Barrier Reef) in the new city, the amount of science you need your new city to produce to break even is:
[current total beaker rate]*0.05/(0.05*[number of cities]+1)

Or put another way, [current total beaker rate]/([number of cities]+20)

This is always LESS than 5% of your current beaker rate.

num cities % of current science %of average city
1 4.76 0.05
2 4.55 0.09
3 4.35 0.13
4 4.17 0.17
5 4 0.2
20 2.5 0.5
30 2 0.6
80 1 0.8

The percent of your current science keeps dropping as you add cities, but by less and less. The quality of the city relative to your existing cities, however, increases. Once you have twenty cities, the new city must be half as good as your average city, over its entire life, to justify it.
I find that as long as the new city has a good source of food or a food trade route it grows to productive levels of science very quickly.

 

[uncle bulgaria]

I generally think it's worth it but late game you have to boost the city so it's not a drain. By this I'd send it food via internal trade and buy the science buildings with gold.

You can get a new city up and running and pulling its weight pretty quickly.

 

[Jaybe]

On a Large Epic (+3% tech/city, not 5%) game, the cost of Future Tech goes up by a flat 513 beakers per city number increase.

Checked with number of cities 6, 7, 8 & 9.

 

[FrostK]

- I look at a tech that I can research right now, but haven't started. I check in the Civilopedia how much it should cost (let's cal this X) and I check in the game how much it really costs (a higher number, let's call it Y).

Its wrong. Tech cost less for each civilization which already knows it. U also should know this civilization.

I believe that if u have a lot of money new cities on nice spots will always boost your science.

 

[The QC]

Unless you are playing on a map smaller than Standard, using Civilopedia tech costs will lead to inaccurate results. On Standard maps, tech costs are 110% of base tech costs, while Large are 120% and Huge are 130%. Also tech costs are reduced slightly by the number of AI civs that you have met that have already researched a tech.

Damn, I didn't know any of that.

 

[Browd]

As an aside, that is one of many reasons why the Mayans on a Huge map can't get super-early (< turn 61) Theology -- ~20% (more precisely, 18.2%) longer tech times than Standard for each tech along the way.

 

[tomplum68]

Its sounds like the 5% "penalty" is more of a check than a penalty. Just a way to rein in REX empires a bit.

 

[ahawk]

5% is actually more noticeable to me in early-game rather than middle or late:

In the early game, if I jump out to 6 cities right away without libraries in the first two or three, I tend to notice that things bog down fairly significantly. This is a situation that I find happens more with early war than with REX, because with a REX strategy I already have some plan as to how to manage science, happiness, and population, while with an early war, if I find myself on the winning end, I may end up taking land I don't want to give up and having to puppet a city that doesn't have a library and that has enough high-gold low-production tiles that it won't get one for quite some time.

Quantitatively, there's formulas on what has to get done within such-and-such a time depending on how many cities you have in order to not be a drain. But qualitatively, the worst drain to science now seems to be early puppets, because IIRC it's 5% per city regardless of puppeting, and early puppets often both lack libraries as well as the correct worked-tiles to build them in a timely manner. At least as a Mayan REX you're going to have the UB to help out, and as Rome the UA should allow you to build libraries more quickly. But as an early war-monger, you're maybe best off not even building a 2nd city and instead just trying to capture two good cities to annex quickly and put libraries up in, or, alternatively, puppeting two decent cities and finishing NC in the capital before moving on.

 

[Cromagnus]

But as an early war-monger, you're maybe best off not even building a 2nd city and instead just trying to capture two good cities to annex quickly and put libraries up in, or, alternatively, puppeting two decent cities and finishing NC in the capital before moving on.

Change that to "capture two good capitals to annex quickly" and you have a decent strategy. ;-)

I just ran into this in a recent game. I capped Persepolis as Brazil, because he was building all the Wonders I wanted, but he had built Petra in Pasagardae, so I had to puppet both, increasing my research costs and taking me to negative happiness. (which hurt my Rationalism bonus as well)

For puppets though, the 5% is much less of an issue unless you're capping a small city. If it's size 14 before capture, it's size 7 afterwards, which is decent enough unless you have a large number of high beaker cities.

That being said, in my games it's usually a few cities generating 90% of the beakers, because I tend to specialize my cities... so puppets can hurt. But tactics determine which cities I puppet. Sometimes I can't afford the immediate unhappiness from razing. Sometimes I need to relocate bombers there. Or it has a key resource. Since you should only puppet cities you absolutely need, why worry about the penalty?

As far as libraries, I guess you could try to only puppet cities that have decent production. My biggest determining factor now with puppet vs raze (as I usually choose to annex really good cities) is whether I think that city is self-sufficient as-is, because you have to assume it'll be working useless tiles for eternity.

To mitigate that, I have a train of workers come through after my army to replace existing improvements.

Generally I favor gold over production for puppets, but if I want a puppeted city to have good production, I replace mines with TP, and if I haven't pillaged all plains and grassland, I spend one turn building a tower over their existing improvements. Minimal growth + maximum production/gold output that way. If you leave that farm as-is, or put a trading post on grassland, the AI will always choose that 2food 2gold tile over any production. So the city will grow (usually bad) and not produce.

Usually though, I want gold, so I place trading posts on the grassland too, since the AI will often be forced to work at least a few food tiles. And too much production just means he'll build that granary faster.

But I digress.