06-04-2002 15:56									#1
	Everything you ever wanted to know about corruption Put an end to popups!

This thread is somewhat difficult to follow if you are not already familiar with the concept of corruption. There is another, more user-friendly, FAQ in the general forum.

FIRST SOME GENERAL COMMENTS

1) Corruption can never exceed 95%, no matter what.

2) Corruption calculations do not use Euclidean geometry, nor unit movement points, to get distance. Instead, the distance is based on the shortest path, where each orthogonal move costs 1.0 and each diagonal move costs 1.5, and the total is rounded down to the nearest integer. Another way of writing the distance formula is Distance = floor(max(x,y) + 0.5*min(x,y)), where x and y are the distance in the NW/SE and NE/SW respectively. (Formula discovered by DaviddesJ, rounding discovered by Qitai)

3) Corruption is divided into corruption due to number of cities, and corruption due to distance. These two components are independent.

4) The following corruption calculations yield a percentage. To get the actual corruption/waste, multiply the percentage/100 by the total number of shields/commerce on tiles being worked, and round to the nearest integer (verified by DaviddesJ).

5) Factories, marketplaces, et cetera, multiply the city's shields/commerce after corruption. This means that the number of red (lost) shields/commerce remains unchanged in the city view after you add one of those buildings (but the uncorrupted shields/commerce increase). It does not mean, of course, that you actually reduce the corruption percentage when you build these improvements (but it seems like it does, just because the percentage of red shields/commerce out of the total is visually lower compared to before).

CORRUPTION DUE TO DISTANCE FROM CAPITAL

The corruption due to distance, depends on these parameters:

1) Distance factor, Fd
This is 3.6 times the distance, divided by the map size. The distance here is the minimum between the distance to the capital and the distance to the Forbidden Palace. So for a standard map size (100x100) this factor would be 0.36 for a city 10 tiles away from the capital (when the FP is more than 10 tiles away). For a tiny map (60x60), it would be 0.6. It looks like the capital is taken as a distance 1 tile (not zero) from itself, that's why there is some corruption there. Communism is a special case, because corruption does not depend on distance. For communism replace the distance factor by the value 1.0.

2) Government factor, Fg
The distance factor is multiplied by a factor that depends on government. Here are the values:
Despotism: 1.0
Monarchy: 2/3
Republic: 2/3
Democracy: 4/9
Communism: 0.3

3) Improvement factor, Fi
The above product is multiplied by 0.5 to the power of N, where N is the number of city improvements that reduce corruption (courthouse and police station). If there is a WLTK celebration, increase N by one for shield waste calculation (but not for commerce lost).

4) Connection factor, Ft
This is 0.85 if the city is connected to the capital through roads, harbors, or airports. It is equal to 1.0 if not connected.

CORRUPTION DUE TO NUMBER OF CITIES
(Seriously edited since first posted)

The corruption due to number of cities depends on these parameters:

1) Optimal number of cities, Nopt
This is an integer number that depends on map size, and is found in the editor.

2) OCN (Nopt) multiplier, Fn
This is a factor that multiplies Nopt, and depends on difficulty level, city improvements, government, WLTKD, FP, and the commercial trait.

Specifically:
Fn = d*(1 + g + fp + imp*N + c)/100
where
d : percentage of optimal cities for this difficulty level (found in editor)
fp: zero for no FP, otherwise 0.2 for Communism and 0.1 for other governments
g : 0.1 if Republic or Democracy, 0.2 if in Communism, 0.0 otherwise
N : the number of improvements (including WLTKD for waste) as for distance corruption
imp: 0.1 for Communism, 0.25 otherwise
c : 0.25 for Commercial civs, 0.0 otherwise

3) Rank of the city, Ncity
This is equal to the number of cities that are closer to the capital than this city (including the capital). So Ncity is equal to 0 at the capital, 1 at the closest city to the capital, et cetera.

The above parameters are combined to get corruption due to number of cities, Fc, in this way:

code:

          Ncity / (2*Fn*Nopt),         if Ncity <= Fn*Nopt,
Fc =     
          Ncity / (Fn*Nopt) - 0.5,     if Ncity > Fn*Nopt,

Last edited by alexman on 11-09-2003 at 03:29

	06-04-2002 19:50									#2
	Inflate your Upload Space

Great post!

It might not solve the problem, but at least it's defined.

I've always thought "waste" is a bigger problem then corruption, so I think it's funny no one ever complains about the "waste problem."

Yes, they're both covered under corruption here, I know.

A day without playing Civ3??? Was someone dying or something?

	06-04-2002 21:08									#3
	Support Apolyton, buy Call to Power 2

Agreed, great post alexman. I have some questions though. Are you sure there was no Corruption decrease for Commercial civs? You were able to discover all these factors, but none for Commercial civs? Where then does the purported Commercial bonus to Corruption apply?


Dominae

	06-04-2002 23:04									#4
	Increase Your PM Length

great post.

i often wondered if the FP had an effect on communism, now i know it doesnt.

will firaxis confirm there is no commercial civ bonus to corruption?

	07-04-2002 00:38									#5
	Re: Everything you ever wanted to know about corruption Browse Apolyton AD-FREE

quote: Originally posted by alexman 5) I could not find any effect whatsoever of the commercial civ trait on corruption!!!

Quite bad news . If Firaxis confirm it (I doubt they will) I think I will give up with India to come back to Babs.

However, it's a great work !

	07-04-2002 11:36									#6
	Remove this text

Interesting post. Nice work too. I've been wondering how it worked precisely & just starting to set up some tests too! Anyway, great stuff.

Aeson recently did a test showing that corruption by number of cities decreased for a commercial civ. The results were posted here:

http://apolyton.net/forums/showthre...30&pagenumber=2

Maybe take a look & see if you agree. I'm not sure what you've done exactly, nor am I sure what Aeson did exactly, so I can't speak for you guys, but anyway...

I'm also not sure I've seen conflicting reports on the effect of connecting your city to your empire or the corruption reducing buildings' effectiveness, I will double-check.

	08-04-2002 01:02									#7
	Got spare money?

Wow, this is great.

One point. The commercial bonus kicks in at higher city sizes; it's something like an extra 1 commerce (over non-commercial civs) at size 12. There are a couple of threads on this (Dan posted in one of them), one of which you'll probably find if you search for 'commercial' and 'bonus' etc.

	08-04-2002 08:19									#8
	Put an end to popups!

Excellent work at the CivLab, alexman! It harkens back to the CivII days and the Great Library in the CivII Strategy forum. It's good to see this sort of work done instead of more whining...

	08-04-2002 08:57									#9
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

I have to give a big

	08-04-2002 10:17									#10
	Full PM-box? Change here!

Wow. I'm sure impressed. Good post.

	08-04-2002 10:44									#11
	Commercial Civs Support Apolyton, buy Civilization 2

Yes, for commercial civs, I'm sure that there was no benefit in my tests, and I was not pleased by this at all. Already the fact that all civs get a bonus commerce in cities over size 6 reduces the value of commercial civs a lot. Maybe (even though I think it would be stupid to do it that way) their bonus comes into effect under conditions that I never tested. For example, I never tested commercial civs with a large number of cities. It was much easier to get the number-of-cities corruption results by setting the "optimal number of cities" value in the editor to something very low once I figured out the corruption model for non-commercial civs. I also never had a city population larger than 7. Who knows what Firaxis did, but I think it must be a bug.

I had seen Aeson's tests before doing this, and I really can't say why we don't get the same results for commercial civs. I tried to isolate the various causes of corruption as much as I could. For example, to test the effect of distance corruption, I did all my tests with optimal number of cities=1000. Then, once I figured out that aspect of it, I picked a city at a fixed distance from the capital and started adding cities (closer and farther from the capital) to see what number of cities did to their corruption. This part of my test was similar to Aeson's, so we should have gotten similar results. On the other hand, Aeson's tests for commercial and non-commercial civs show different amounts of base commerce (without corruption) for a size 2 city under the same government. Where is the extra commerce coming from?

Aeson, (or even Firaxis) what do you think of all this?

	09-04-2002 00:04									#12
	Support Apolyton buy from Amazon

okay, so corruption is maxed at 95%... BUT the amount of corruption calculated for the city can exceed 100% as evidenced by the fact that cities with a courthouse AND police station very far away from the center of the civ still have a corruption rate of 95%.

i generally don't mind an insane level of corruption. i have no problem with 95% at the extreme. but i maintain that the 95% should be adjusted by courthouses and police stations... ALWAYS. there should be a visible effect when building these structures. especially if you are going to rush build one. otherwise in the present model, they are completely worthless structures except for a VERY few cities a reasonable distance from the capital.

or maybe it's just me.

	09-04-2002 00:39									#13
	Lose 30 kilos (of popups)

I think math was a secondary concern for these guys. I would be willing bet money they never even knew that corruption got over 100%. How the hell can you have more than 100% of something like corruption???

	09-04-2002 01:50									#14
	Enter the AD-FREE zone

Thank you, alexman!
Interesting and useful work.
I have started a study of corruption and waste under communism (willing to publish some results when it will be a bit more complete). One good point: your results don't contradict mine .

	09-04-2002 02:03									#15
	Support Apolyton or Terrorists Win

quote: Originally posted by watorrey I think math was a secondary concern for these guys. I would be willing bet money they never even knew that corruption got over 100%. How the hell can you have more than 100% of something like corruption???

Oh, go keep your *****ing to threads I don't read! In case you guys don't remember, this is the same guy who complained that the hard difficulty levels are too hard.


Anyway, after that reprimand, to alexman. Excellent research. Of course, Firaxis could just tell us...

	09-04-2002 03:32									#16
	Enter the AD-FREE zone

Alexman,

Dude, you rock.

RPM

	09-04-2002 11:07									#17
	Support Apolyton, buy Civilization III: Complete

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]

Last edited by alexman on 01-02-2003 at 01:05

	09-04-2002 15:19									#18
	Get a bigger avatar today!

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.

Last edited by Franses on 09-04-2002 at 15:28

	09-04-2002 15:58									#19
	Avatar Enlargement: We've got the solution

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.

	09-04-2002 15:59									#20
	Support Apolyton, buy Call to Power 2

code:




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

Last edited by Aeson on 09-04-2002 at 16:33

	09-04-2002 16:28									#21
	Avatar Enlargement: We've got the solution

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.

code:





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
"

	09-04-2002 19:59									#22
	Remove this text

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:

code:


Corruption by Distance
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 

Corruption by Number of Cities
(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 

Last edited by alexman on 09-04-2002 at 20:08

	09-04-2002 21:16									#23
	Support Apolyton buy from Amazon

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.

	09-04-2002 22:38									#24
	Got spare money?

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.

	10-04-2002 00:50									#25
	Support Apolyton, buy GURPS/ Alpha Centauri

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.

quote: 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.

	10-04-2002 01:12									#26
	Inflate your Upload Space

quote: 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.

quote: 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

	10-04-2002 01:19									#27
	Support Apolyton or Terrorists Win

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.

Attachment: corruption study3.zip
This has been downloaded 13 time(s).

	10-04-2002 04:44									#28
	Remove this text

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?)

	10-04-2002 05:40									#29
	Aha! Support Apolyton

quote: 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

	10-04-2002 09:16									#30
	Help yourself to an AD-FREE life

quote: 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.