New City Growth Formula

Sullla

Sullla

Patrician Roman Dictator
Joined
Feb 9, 2002
Messages
2,835
Location
Baltimore MD
Hey folks. One of the most important aspects of the newest Civ5 patch was somewhat buried in the notes:

Reduced amount of food needed for cities to grow at larger sizes.
Click to expand...

Has anyone managed to test this in practice yet, and see what exactly has changed? I don't suppose anyone has the numbers on hand to compare the old city growth formula to the new one...? For me, this is one of the key subjects that needs to be improved for Civ5 to become a viable game longterm. I think most people would agree that cities need to grow faster - MUCH faster - at larger sizes compared to the pre-patch version.

Thanks for any help. :)
 
A quick test revealed the sequence:

15, 24, 33, 44, 55, 66, 77

So it looks like the food box is 11N after the first three stages. A linear progression like that, coupled with Maritimes, is going to lead to some large cities.

At first glance, the implication would appear to be that you want to go up, then out, in order to maximize early Science. You can grow a food-rich capital rapidly under Tradition with Maritimes, and that makes a Library worthwhile. However, further testing is needed before I'm willing to draw that conclusion.
 
I haven't downloaded the patch yet.

However, someone wanting to be helpful could point out:

Whether anything has changed in steamapps\common\sid meier's civilization v\Assets\Gameplay\XML\GlobalDefines.xml

... the following values are pre patch ...

Code: 
		<Row Name="BASE_CITY_GROWTH_THRESHOLD">
			<Value>15</Value>
		</Row>
		<Row Name="CITY_GROWTH_MULTIPLIER">
			<Value>6</Value>
		</Row>
		<Row Name="CITY_GROWTH_EXPONENT">
			<Value>1.8</Value>
		</Row>
 
EDIT: Fixed values using below function:

8: 89
9: 101
10: 114
11: 126
12: 139
13: 152
14: 165
15: 179
16: 193
17: 207
18: 221
19: 235
20: 249
21: 264
 
PieceOfMind said:
I haven't downloaded the patch yet.

However, someone wanting to be helpful could point out:

Whether anything has changed in steamapps\common\sid meier's civilization v\Assets\Gameplay\XML\GlobalDefines.xml

... the following values are pre patch ...

Code: 
		<Row Name="BASE_CITY_GROWTH_THRESHOLD">
			<Value>15</Value>
		</Row>
		<Row Name="CITY_GROWTH_MULTIPLIER">
			<Value>6</Value>
		</Row>
		<Row Name="CITY_GROWTH_EXPONENT">
			<Value>1.8</Value>
		</Row>
Click to expand...

Post Patch values:
Code: 
                <Row Name="BASE_CITY_GROWTH_THRESHOLD">
			<Value>15</Value>
		</Row>
		<Row Name="CITY_GROWTH_MULTIPLIER">
			<Value>8</Value>
		</Row>
		<Row Name="CITY_GROWTH_EXPONENT">
			<Value>1.5</Value>
 
Martin Alvito said:
Then it's a step function where the additive term is increasing in N. If I had to guess (imputed values in italics):

8: 88
9: 100
10: 113
11: 126
12: 139
13: 152
14: 165
15: 179
16: 192
17: 205
18: 219
19: 234
20: 249
21: 264

Best guess is that there's an underlying function that's being rounded, but I'm not seeing the function.
Click to expand...

Based on the other posts I think this is it:

n=target pop-1

food needed = floor(15+(8*n)+n^1.5)

Code: 
TargetPop NewFoodNeeded OldFoodNeeded
--------- ------------- -------------
        2            24            22
        3            33            30
        4            44            40
        5            55            51
        6            66            63
        7            77            76
        8            89            90
        9           101           105
       10           114           121
       11           126           138
       12           139           155
       13           152           174
       14           165           194
       15           179           214
       16           193           235
       17           207           258
       18           221           280
       19           235           304
       20           249           329
       21           264           354
 
Cut-and-paste from alpaca's number crunching thread:

f(n) = 15 + 8 (n - 1) + (n - 1)^1.5 rounded down to the next integer. (n=# of cities)

EDIT: Same thing as Scarpa, use whichever seems more intuitive to you.
 
On a cumulative basis, this will mean slower growth up to size 10, and faster growth thereafter.

To grow a city to size 5, will take about 8% more cumulative excess food.
To grow a city to size 10, will take about 1% more cumulative excess food.
To grow a city to size 11, will take about 1% less cumulative excess food.
To grow a city to size 20, will take about 14% less cumulative excess food.
To grow a city to size 25, will take about 20% less cumulative excess food.

Not a huge difference, but it's something. A bit slower for ICS growth up to size 5. A bit faster for those growing bigger cities.
 
This is good to see. This is what I tried to do in Icey No mod - decrease the exponent while increasing slightly the linear term. As wurstburst has pointed out, this makes growth a tiny bit more expensive at the smaller city sizes, and becomes less and less expensive at higher city sizes (relative to pre patch).


EDIT: This table has the old and new values, and the difference between them.
Essentially the same data as scarpa posted.
Code: 
size	Pre	Post	Delta
2	15	15	0
3	22	24	2
4	30	33	3
5	40	44	4
6	51	55	4
7	63	66	3
8	76	77	1
9	90	89	-1
10	105	101	-4
11	121	114	-7
12	138	126	-12
13	155	139	-16
14	174	152	-22
15	194	165	-29
16	214	179	-35
17	235	193	-42
18	258	207	-51
19	280	221	-59
20	304	235	-69
21	329	249	-80
22	354	264	-90
23	380	279	-101
24	407	294	-113
25	435	309	-126
26	464	324	-140
27	493	340	-153
28	523	355	-168
29	554	371	-183
30	585	387	-198
31	617	403	-214
32	650	419	-231
33	684	435	-249
34	719	452	-267
35	754	468	-286
36	790	485	-305
 
A few interesting bits:

- Below size-10, there is almost no change to the food requirements
- Previously, the exponential term surpassed the linear term at size-11
- Now, the linear term is not surpassed until size-66!

My biggest city before was size-90. Now I can get to size-120 with the same amount of food.
 
I would have done different changes (increase base but decrease the linear part and slightly decrease the exponent) but ok. You can still get a city up to size 4 in no time for ICS.
 
Thanks for the update guys.
Based on PoM's numbers, even more interesting can be to look at the cumulative food requirements:
Code: 
size	Pre	Post	Delta	%Pre
2	15	15	0	0.00%
3	37	39	2	5.41%
4	67	72	5	7.46%
5	107	116	9	8.41%
6	158	171	13	8.23%
7	221	237	16	7.24%
8	297	314	17	5.72%
9	387	403	16	4.13%
10	492	504	12	2.44%
11	613	618	5	0.82%
12	751	744	-7	-0.93%
13	906	883	-23	-2.54%
14	1080	1035	-45	-4.17%
15	1274	1200	-74	-5.81%
16	1488	1379	-109	-7.33%
17	1723	1572	-151	-8.76%
18	1981	1779	-202	-10.20%
19	2261	2000	-261	-11.54%
20	2565	2235	-330	-12.87%
21	2894	2484	-410	-14.17%
22	3248	2748	-500	-15.39%
23	3628	3027	-601	-16.57%
24	4035	3321	-714	-17.70%
25	4470	3630	-840	-18.79%
26	4934	3954	-980	-19.86%
27	5427	4294	-1133	-20.88%
28	5950	4649	-1301	-21.87%
29	6504	5020	-1484	-22.82%
30	7089	5407	-1682	-23.73%
31	7706	5810	-1896	-24.60%
32	8356	6229	-2127	-25.45%
33	9040	6664	-2376	-26.28%
34	9759	7116	-2643	-27.08%
35	10513	7584	-2929	-27.86%
36	11303	8069	-3234	-28.61%

So, growing a size to size 20 costs nearly 13% less total food than it did before.
 
Don't forget that growing cities to large sizes isn't just about how much food it takes to go from size 20 to size 21. It also has a lot to do with how much food it takes to grow a large city compared to a smaller city, this has been evened out significantly. Another reason it was so hard to get large cities pre patch was that if you had say 4 surplus happiness, even if it would only take 10 or so turns to grow from size 12-13, all your smaller cities would grow first plunging you back into unhappiness and halt the growth of you large city. Since the exponent value has been lowered now, this shouldn't happen as drastically although it still seems pretty hard to reach very big sizes.

Also not that all these numbers don't factor in hospitals or med labs which significantly speed up growth late game.
 
Sullla said:
Thanks for the numbers! :goodjob: Personally I still think these food requirements are much too high (you still need 2500 food to reach size 20), but at least it's a step in the right direction.
Click to expand...

Still light years away from good old 20+n*2 or whatever it was in CIV 4 - which also had the ancient age granary to speed things along!

I can't see the reason why population is so much more expensive in this version. Is it to balance out the maritimes? the granary and waterwheel? the earlier higher yield farms? the fact that citizens = science? (even more so with this patch)
 
EscapedGoat said:
Still light years away from good old 20+n*2 or whatever it was in CIV 4 - which also had the ancient age granary to speed things along!

I can't see the reason why population is so much more expensive in this version. Is it to balance out the maritimes? the granary and waterwheel? the earlier higher yield farms? the fact that citizens = science? (even more so with this patch)
Click to expand...

That's because CIV4 had fewer passive bonuses. For example, having Merchant Navy policy equals a citizen in every city in terms of :c5production: effect. When you see a pop 10 city in CIV5 its effects are usually more in line of a pop 13-15 city in CIV4.
 
Bibor said:
That's because CIV4 had fewer passive bonuses. For example, having Merchant Navy policy equals a citizen in every city in terms of :c5production: effect. When you see a pop 10 city in CIV5 its effects are usually more in line of a pop 13-15 city in CIV4.
Click to expand...

I'd say it's just the opposite. The the tile yields in civ 4 were much higher, and had a lot more ways to boost them. The most you can get in civ5 is a riverside lumbermill with 1 food, 3 hammers, 1 gold. Compare that to a riverside iron mine in civ 4 with 6 hammers! (plus 1 food and 1 gold). And then the percent multipliers are higher there too... not to mention the granary and slavery...
 
EscapedGoat said:
Still light years away from good old 20+n*2 or whatever it was in CIV 4 - which also had the ancient age granary to speed things along!

I can't see the reason why population is so much more expensive in this version. Is it to balance out the maritimes? the granary and waterwheel? the earlier higher yield farms? the fact that citizens = science? (even more so with this patch)
Click to expand...

Happiness, mostly. If you had city growth at Civ4 levels happiness would always be the limiting factor, not only for large empires.
 
pi-r8 said:
I'd say it's just the opposite. The the tile yields in civ 4 were much higher, and had a lot more ways to boost them. The most you can get in civ5 is a riverside lumbermill with 1 food, 3 hammers, 1 gold. Compare that to a riverside iron mine in civ 4 with 6 hammers! (plus 1 food and 1 gold). And then the percent multipliers are higher there too... not to mention the granary and slavery...
Click to expand...

Actual yields are irrelevant; I discuss active vs. passive yields.

CIV4: Citizen makes 20 science, it gets multiplied by 100%, you get 40 science.
CIV5: Citizen makes 5 science, buildings make 5 science, it gets multiplied by 100%, you get 20 science.
 
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