Everything you wanted to know about corruption

[Spaced Cowboy]

Alexman,

Dude, you rock.

RPM

[alexman]

Thanks to everyone for all the support to your local Apolyton Nerd...

By the way, I'm attaching the corruption calculator that I used to check my formula for anyone that is interested. If you get the zip file corrupted (no pun intended!) blame Apolyton, not me!

[Edit: calculator moved to FAQ thread]

[Franses]

Alexman,

Great work. I love this kind of investigations. Planned to do it myself one day but did not think of the nice and relatively easy way you did it. However....

Tried to verify your formula on the tiny map I am playing at the moment, but did not succeed. It looks like the distance factor on a tiny map does not comply to the formula.

Do you know whether water has a special effect? I have this city on position (5,41) with the palace on position (16,46) but the city is on a different continent. The continents are separated by two tiles of water.

I am in republic on a tiny map and the city has a harbor. The geometrical distance is 12 (if I understood you correctly) meaning that the distance corruption according to your formula is expected to be 3.4*12=40.8%. The city has one or two (dependant on how you calculate the number of cities between it and the palace) cities between it and the palace. Being on emperor level the optimal number of cities is 12 * 0.8 = 10. This adds another 8.5% or 17% for a total of 49.3 or 57.8% maximum.

The city has a commerce of 11 (no marketplace etc.) so I would expect a corruption of about 5, maximum 6. In reality it is 8. Did I make a mistake here or have the water tiles a negative influence?

Also the cities on the "palace continent" seem to have a higher corruption as indicated by your fornula but it is a tiny continent so rounding factors may play a significant role here and I do not dear to draw final conclusions from it.

[Aeson]

Good work on the formula Alexman. I had to go back and do some more testing to see the difference that Commercial makes. I think perhaps working with a small optimum number of cities is why you didn't see any difference. I definitely see a ~5% difference between Commercial and Non-Commercial corruption.

The tests I ran matched up well with my previous results. The main difference is a made sure to have 100 commerce in all the tests. I have a table of results for my tests on Distance and Number of Cities.

[Aeson]

Corruption by Distance



Distance
Despotism
Monarchy
Republic
Democracy



2
14
11
11
11



3
21
14
14
11



4
28
21
21
14



5
31
24
24
14



6
41
28
27
21



7
44
31
31
24



8
54
38
37
27



9
58
41
41
27



10
64
44
44
31



11
71
48
47
37



12
78
54
54
41



13
81
58
57
41



14
91
61
61
44



15
94
64
64
47



16
95
71
71
54



17
"
74
74
54



18
"
78
77
57



19
"
81
81
61



20
"
88
87
64



21
"
91
91
64



22
"
94
94
71



23
"
95
95
74



24
"
"
"
77



25
"
"
"
77



26
"
"
"
81



27
"
"
"
87



28
"
"
"
91



29
"
"
"
91



30
"
"
"
94



31
"
"
"
95

[Aeson]

Test Settings

Optimal Number of Cities: 12

Difficulty: Chieftain (100%)

Corruption was measured in a city 10 spaces from the capitol, all other cities were inside that distance. I would have subtracted out the Corruption by Distance for 10 spaces, but I'm too lazy. You can check the table above for those numbers.

All numbers are out of 100 commerce.

Corruption by Number of Cities



Commercial Non-Commercial 



Cities
Despotism
Monarchy
Republic
Democracy



1
64
68
44
48
44
48
31
34



2
68
73
48
53
47
52
34
38



3
72
77
52
57
51
55
37
42



4
75
81
55
61
54
59
41
46



5
79
85
59
65
58
63
45
50



6
83
89
63
69
61
67
48
54



7
87
93
67
73
65
71
52
57



8
91
95
71
78
69
75
55
61



9
95
"
75
82
72
78
59
65



10
"
"
78
86
76
82
62
69



11
"
"
82
90
79
86
66
73



12
"
"
86
95
83
90
70
77



13
"
"
90
"
86
95
73
84



14
"
"
95
"
90
"
77
92



15
"
"
"
"
95
"
84
95



16
"
"
"
"
"
"
91
"



17
"
"
"
"
"
"
95
"

[alexman]

Frances: From your example it does look like cities on another continent have an additional penalty. I'll look into it tonight.

Aeson: Our results aren't that far apart. Rounding (probably at some intermediate step in the Civ3 engine) is definitely an issue. Look at your results by distance for Democracy. They go in steps! I'm still confused about what's going on with commercial civs... I will do a couple more tests tonight.

Like I said, the formula is not 100% accurate. But it gives a very good idea on how the various parameters (except commercial trait!!!) affect corruption.

Anyway, here are the values that my formula gives for your test conditions:

[B]Corruption by Distance[/B]
Distance Despotism    Monarchy       Republic       Democracy
2          17             13            13          10 
3          23             17            17          13 
4          29             21            21          15 
5          35             25            25          18 
6          41             29            29          21 
7          47             33            33          23 
8          53             37            37          26 
9          59             41            41          29 
10         65             45            45          31 
11         71             49            49          34 
12         77             53            53          37 
13         83             57            57          39 
14         89             61            61          42 
15         95             65            65          45 
16         95             69            69          47 

[B]Corruption by Number of Cities[/B]
(excluding capital)
Cities     Despotism    Monarchy       Republic     Democracy
1          65             45            45          31 
2          69             49            49          35 
3          73             53            53          40 
4          77             57            57          44 
5          81             61            61          48 
6          85             65            65          52 
7          90             70            70          56 
8          94             74            74          60 
9          95             78            78          65

[Franses]

I think I made a mistake. I thought that Fc was:
0.5 x nrofcitiesbetweenthisoneandthecapital/optimalnumber

I reread your first post (perhaps you edited it??) and now understand that it should be:
0.5 x cityrank (in closeness to the capital)/optimalnumber

This does explain the difference I measured since there were 5 cities on the small continent that of course were all closer to the capital than the one I calculated the corruption for.

[PerpetualNewbie]

Aeson, would you mind checking just one or two data points at Monarch or higher? Or if you would rather post the test map you are using, I would try it. Back in the dim recesses of my memory, it seems I once read that the corruption model changes slightly between Regent and Monarch, I think.

[Aeson]

Yes, your formula is quite close with all the numbers. There is a difference for the Commercial trait that at least shows up with the Optimum Number of cities at 12. It isn't a great deal of difference in any case though.

1) Number of cities factor, Fc
Obviously. The value of this factor is 0.5 times the rank of the city (in closeness to the capital) to the "optimal" number of cities for the current map size. For example, the 10th city on a standard map has this factor equal to 0.5*9/16 = 0.28. Again, this is different for Communism than it is for the rest of the governments. For communism it is 0.1 times the ratio of ALL cities to the "optimal" cities.

The Commercial trait could be accounted for by a small addition here. Not sure if adding to the optimum number of cities or subtracting from the rank of the city would be more accurate. This wouldn't account for the scaling of the difference as the number of cities reaches it's limit though.

Perhaps the 0.5 modified to a 0.4 for Commercial civs comes closer to the mark. With the general formula still somewhat inaccurate it's hard to tell.

[Aeson]

would you mind checking just one or two data points at Monarch or higher? Or if you would rather post the test map you are using, I would try it. Back in the dim recesses of my memory, it seems I once read that the corruption model changes slightly between Regent and Monarch, I think.

One (or a combination) of the changes I made in the .bic was causing it to crash quite a bit. Not exactly sure what. It seems to have stopped loading for me at all. I would have done more testing last night otherwise. The changes I made in the .bic were just in areas to speed up testing, and shouldn't have affected the corruption numbers.

- Warriors, Spearmen, Archers not available to build. Speeds things up by not having to set new cities to wealth, or deal with units being completed.

- Courthouses, Police Stations, Airports, Aqueducts, and Hospitals with no tech requirements and cost 1 to build. Wasn't able to get to the tests I had planned for these.

- Settlers take no population to build, cost 1, added offense, defense, and movement rates.

- Desert (terrain that filled the map) with 25 commerce, food, and production.

I think that was it, not sure what caused the crashes.

The only difference between corruption by difficulty level seems to be in the Number of Optimum cities. These values can be found in the editor, and Alexman included them in his formula.

2) Difficulty level, Fv
This is a percentage that multiplies the number of cities factor. 1.0 for chieftain to 0.7 for deity.

The steps are by .05 per difficulty level, with the exeption being Emperor to Deity, which takes two steps. I was just using Chieftain because a modifier of 1 gives the cleanest numbers. I'll do some other difficulty testing once I get a stable .bic

Chieftain: 1.00
Warlord: 0.95
Regent: 0.90
Monarch: 0.85
Emperor: 0.80
Deity: 0.70

[chiefpaco]

I just did a minitest and found pretty much no difference between commercial & non-comercial civs for the corruption by distance. Same test as CivFanatics' Bamspeedy did.

I'll post it up here. I haven't gone through your calculations for it yet, I wish to try it soon as I get a chance. Also, I have to find out why my non-commercial numbers don't match Bamspeedy's.

Edit: Test done on Chieftan level.

[alexman]

Two quick notes:

1) Cities being on different continents does not affect corruption. If you can have a trade route connecting them, they count as connected and get the 15% bonus.

2) Difficulty level has a strange effect. On Chieftain I get Aeson's results exactly. On Regent and Deity, but with percent of optimal cities set to 100 (like chieftain) I get Aeson's results for commercial civs, no matter if the civ is commercial or not! (chiefpaco, perhaps this is why you are also seeing dircepancies for non-commercial civs. Are you testing on a higher level?)

[Zachriel]

Aha!

Originally posted by alexman
Corruption gets calculated as a percentage of the base commerce of the city. This means that marketplaces, banks, factories, libraries, et cetera, effectively reduce corruption percentage, because the extra gold, science, and shields that they generate is corruption-free. Think of the income from city improvements as corruption-tax-sheltered!

Aha! Thanks alexman. That explains why I've rarely have a problem with corruption. I always improve my cities with cash. Such as this rush job on a recently captured city on the frontier:

http://www.crowncity.net/civ3/ForbiddenPalace.htm

[chiefpaco]

Originally posted by alexman
Two quick notes:

2) Difficulty level has a strange effect. On Chieftain I get Aeson's results exactly. On Regent and Deity, but with percent of optimal cities set to 100 (like chieftain) I get Aeson's results for commercial civs, no matter if the civ is commercial or not! (chiefpaco, perhaps this is why you are also seeing dircepancies for non-commercial civs. Are you testing on a higher level?)

I was testing on Chieftan, same as Bamspeedy. I was trying to isolate corruption by distance, but have since realized it impossible because the # cities always factors. He had 12 cities on a tiny & I had 7 and there came the discrepancy. I took his game & abandoned a few cities & his #s started looking like mine.

BTW, after all this I discovered the ability in Gramphos' C3MT to alter the game rules. I re-ran the tests toggling off "allow civ-specific abilities" for a commercial civ & got the same results. I also tried changing the difficulty level. However, I didn't see much effect in the testing so far. One note, you have to let 1 turn pass for the numbers to re-calculate.