Corruption

Before starting, like a good scientist, I tried to predict the outcome of the experiment. I suspected that corruption would increase the further from the capital the settlement was, and that corruption would be a fraction of the settlement income (so that you can’t have 3000 Denarii corruption from a settlement only making 2000 gross). Taking a wild guess, I suspected the two would be related, i.e. that the distance from the capital would determine the fraction of income taken. I wasn't sure if it would be total income, or net, or any part thereof (e.g. only trade income).

All that being said, here's the basic graph:

http://www.totalwar.org/patrons/lm/r...r/Corrupt2.gif

Now, I may post the full dataset to help others understand what this is all about.

For a start, the linear fit currently put through the data is nonsense. As I say above, I don’t believe there is a direct correspondence between distance and corruption. I think that income plays a part.

For instance:

Aquicium and Iuvavum (below 5000 pop), which have total incomes of 859 and 749 Denarii respectively. They are 39 and 45 squares away from my capital. They have corruption rates of 154, 172. But the one in the middle, Kydonia, has a more normal income of 5244, and corruption of 1048 Denarii. Now, if you are still paying attention, and took in what I said at the beginning of this post, you should notice that 154/859, 172/749, and 1048/5244 have similar values, in fact ranked, strangely, by their distance to the capital! I think some of you will see where I'm going with this...

Anyway, to cut the chase, here's the graph.

http://www.totalwar.org/patrons/lm/r...alCorrupt3.gif

Now maybe it's the not inconsiderable amount of alcohol I've consumed this evening, but that looks strangely like a correlation!

So here's what I'm suggesting: the fraction of income pinched by corruption rises linearly with the distance from capital. You have a grace distance of around 16 squares.

Code:

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Dist        Fraction
15        0
20        0.0333958
25        0.0739447
30        0.114494
35        0.155043
40        0.195592
45        0.236141
50        0.27669
55        0.317239
60        0.357788
65        0.398337
70        0.438885
75        0.479434
80        0.519983
85        0.560532
90        0.601081
95        0.64163
100        0.682179

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So at 80 squares away, corruption will take 50% of your gross income (this doesn't take into account upkeep, wages, etc.) This tells you why the decision to move your capital is not just a public order decision, but a financial one as well.

Edits:

Thanks to zhurge for this equation:

Corruption is based on distance to capital (DTC) and gross income (GI) which is a total of farming (Fa), trade (Tr), taxes (Tx), mines (Mi).

Law temples (ie Athena) reduce corruption by (0.03)(GI) for each level. So level two reduces corruption by 6% of GI, and so on.



Alphabetical list of the coordinates of all settlements:


As always, comments, suggestions, clarifications, errors, etc. gratefully received.

Wow that was a lot of research.. thanks for the info man. With so much of this game a mystery, like corruption for example, we need to figure it all out ourselves.

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Originally Posted by element

Wow that was a lot of research.. thanks for the info man. With so much of this game a mystery, like corruption for example, we need to figure it all out ourselves.

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And I think we're doing a fine job of it too. A number of us have unwrapped quite a few of the mysteries of the game, from squalor to the diplomacy system. I think it's a testament to the resourcefulness of the patrons of The Org. Plus we've had some help from a Dev or two.

Speaking for myself, my next goal is to understand the trading system. That's the last thing I feel needs investigating before a comprehensive picture of the economic and city management systems can be constructed. Hopefully I'll have time over the weekend.

@therother,
brilliant work! I wish my real life research data looked so neat. You set out the hypothesis before testing, which is always a nice touch in science.


I suspected before that distance was measured as travel time, but now you have proven it is fixed as a square distance.

THe only other parameter I suspected was time. I thought corruption may rise over time for a particular city. I guess that was a wrong assumption as well.


thanks for the work

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Originally Posted by afrit

@therother,
brilliant work! I wish my real life research data looked so neat.

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As do I!

Anyway, a few notes. The above data is for the Medium campaign difficulty. It appears that corruption is one of those things that varies with difficulty level. I will endeavour to find a conversion factor for the above data so we don't need 4 separate equations.

Also, corruption is also affected by buildings and Governor's traits/characters that deal with the Law. Improvements to Law decrease corruption.

Anyone know of anything else?

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Originally Posted by therother

The above data is for the Medium campaign difficulty. It appears that corruption is one of those things that varies with difficulty level. I will endeavour to find a conversion factor for the above data so we don't 4 separate equations.

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Good news, the corruption is only affected by the other income effects of changing the difficulty level, i.e. farming and taxes. The formula for calculating corruption remains unaffected.

Very pretty work, as always, therother!! There's so much info in this game, waiting for someone like you, with the skills - and gracious enough to donate the time - to make it clear. This game takes the basic Civilization concept and throws in a bunch more variables. That concept being, have a few simple things that interact in logical ways - which wind up needing quite a few decisions as one goes along.

Cool observation, afrit! The digital world, especially games, are so much more precise than messy organic things. ~:cheers: Woe be unto us the day that game programming gets so sophisticated that coders just drop in "fractal noise and occasional great irregularity generators" to spice up each parameter. It's coming, but I think us datamongers still have a couple decades before it gets really bad. Then again, we'll have even better tools then.

Therother, I wouldn't be surprised if some of the (very slight) variation you see at your lower end (small distances) are due to rounding in RTW's distance calculations. (Who knows whether they round up or down or off or something more complex due to several internal roundings?) Past that though, the points in the upper right show some clear variance. I wonder what that could be due to? Little rounding errors should've become relatively smaller at that point, when both values are larger. I have no clue.

thanks again m8! have one on us! ~:cheers:

Great info!

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Originally Posted by RedKnight

Past that though, the points in the upper right show some clear variance. I wonder what that could be due to? Little rounding errors should've become relatively smaller at that point, when both values are larger. I have no clue.

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The relationship could very well be non-linear. Quite a few of them are away from "normal" ranges (e.g. they have caps, or after a certain limit the equation changes). Problem is that I don't have a large number of cities far enough away from my capital to be sure, and I can't (easily) create cities to test!

Nice work. This makes all those provinces in the middle of nowhere much less valuable, especially the big ones where the city is in the corner e.g. Tribus Sakae.

That's a good point about the cut-offs, TR. They certainly happen in this game. And understandably so. If anyone has a savegame with almost all cities conquered, perhaps they could send it to TR? (The capitol can easily be changed - and I wonder what it would look like if your capitol was way off in a corner?)

Right, AT... I just occurred to me, "do I really wanted to tie one of my major stacks up in Dimmudi (SW Sahara) for tons of turns when it's got a 70% distance hit to Arretium?" :dizzy2:

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Originally Posted by RedKnight

That's a good point about the cut-offs, TR.

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Something does seem to be happening at distances of 80+. But I'm a little too tired to continue on at it for now. Perhaps a 2nd tier, but still far too few points to be sure. Will get back to it later on today.

You've done enough work for 10 men for a day. So relax and play if you like, the brew's on us ~:cheers:

Oh sorry - I meant to say, "The omens are good, and the portents speak well." ~:cheers:

There is actually an error in top point (forgot to remove the Governor). Will correct it in a moment.

Edit: Graph corrected. Despite the fact that the data know looks very good, I've been fiddling with a data point all the way up at 118, and that seem to be lower (very possibly significantly) than it should be.

But I have a few tricks left up my sleeve. In the meantime, if anyone wants to generate data, you will need top remove all the buildings/Governor's that affect Law before doing the calculations.

Quote:

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Originally Posted by therother

There is actually an error in top point (forgot to remove the Governor). Will correct it in a moment.

Edit: Graph corrected. Despite the fact that the data know looks very good, I've been fiddling with a data point all the way up at 118, and that seem to be lower (very possibly significantly) than it should be.

But I have a few tricks left up my sleeve. In the meantime, if anyone wants to generate data, you will need top remove all the buildings/Governor's that affect Law before doing the calculations.

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Uh... Can anyone make a map centered on, say, Rome, and have "corruption radius" labeled every 10 percent or so? I have no idea how long a "square" is.

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Originally Posted by vodkafire

Uh... Can anyone make a map centered on, say, Rome, and have "corruption radius" labeled every 10 percent or so? I have no idea how long a "square" is.

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The map is 254 by 155 squares. The distance between Rome & Tarentum in the South of Italy is 21 squares. The distance to the Patavium at the top is 34.4 squares. A square is each individual piece of the campaign map. Probably the best way to get a handle on the size is to right-click on an empty square. A little box will appear to tell you some info about that particular tile, e.g. high fertility or hills. It will also tell you what province the tile is in, and which faction owns as the colour of the box and the icon on the lower right will be that of the owner.

To see the different tiles, keep the RMB down, and move the mouse. Within the same tile, the box will stay at the same location. It will move when your cursor is outwith the first tile to a position it will maintain until you move out of the boundaries of that one. And so on.

Here's an image to give you a better handle on the distances:

http://www.totalwar.org/patrons/lm/r...r/TarDist2.jpg

Well, it seems that there may well be a hard limit to the proportion of your gross income that can go as corruption. As the new graph shows, it would seem to be 0.65 or 65% of your income. It reaches that point around 100 squares (tiles) away from your capital. This is roughly where the line on the graph above stops.

I still need more data points -- especially with cities ~100 squares apart -- so if anyone has a widespread empire, I'd appreciate it if you could either confirm this is the limit, or email the game to me.

Very good work and some surprising results. I would not have, personally, expected linear correlation and two independent variables (distance and income). In my game play, I routinely look at the Financial parchment for my faction to see what income I will earn next turn. Then I move the capital and go back to the parchment to see if income increased (as a result of decreased corruption). In some cases, I have seen that the 'absolute middle' is NOT the base place for the best capital -- namely, if you have a number of wealthy cities skewed to one side of your empire.

Can't wait for your further work. Maybe you can send it to the moderator to turn it into a sticky.

My first campaign with Julii had an empire stretching from Londinium to Halicarnassus. Would that be useful for you?

You can view the minimap at:
http://home.earthlink.net/~tonymakhl...julii_mini.jpg (48KB)

http://home.earthlink.net/~tonymakhl...julii_mini.jpg

and download the file at:
home.earthlink.net/~tonymakhlouf/rtw/julii_spreadout.sav (1.9 MB)

Afrit

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Originally Posted by afrit

My first campaign with Julii had an empire stretching from Londinium to Halicarnassus. Would that be useful for you?

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Looks great, thanks. Just downloading it now.

PS I messed up the graphs there for a second. Should be fixed now though.

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Originally Posted by Tzar Kaloyan

In some cases, I have seen that the 'absolute middle' is NOT the base place for the best capital -- namely, if you have a number of wealthy cities skewed to one side of your empire.

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Well, yes, it's a trade off between a number of factors. The main two are, of course, corruption and public order. The "Distance to Capital effect" is purely to do with the straight-line distance from your settlements to the capital, whereas -- as you rightly point out -- there is a 2nd variable at work with corruption. It makes no sense in minimising corruption in your poorer cities at the expense of increasing it proportionally in your richer ones. In other words, saving 10% of 1000 Denarii at the expanse of 10% of 5000 Denarii makes little sense, all other things being equal.

There is also the fact that family members and Senate rewards appear in the capital, but I suppose that’s minor.

Quote:

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Originally Posted by Tzar Kaloyan

Can't wait for your further work. Maybe you can send it to the moderator to turn it into a sticky.

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In terms of research, I think I'm almost there, with just the hardest bit to do - trade. I suspect this is going to be a bit of a nightmare, but it might surprise me. In terms of collating all the data into a guide of some sort, I'm working on it slowly. If I get swamped with work I may just post an annotated index of relevant threads in the hope of someone else collating it into a comprehensive guide to economics and city management in RTW.

In fact, I might as well post the links of my various threads:

Squalor
Distance to Capital PO penalties
Tax Income
Slaves Resource (not enslaving)
Culture and Unrest Public Order penalties - the only one of these I can't take any credit for.

And one on devastation:

Quietus's devastation breakthrough

Couple those with Sinner's Temple Guide

and

Tamur's Diplomacy Guide

Edit Also useful is Spartan's Trait guide: here


And I'm sure there's a kernel of a great guide.

I'm also sure there are other good threads hiding away in the forums. If anyone could point me to them, I'd be grateful.

Just updated the 2nd graph again, probably the final update. Thanks to afrit I'm now pretty sure that corruption is capped at 65% of total income, and that this cap is applied at around 100 squares away from your capital.

All that remains is to discover the effects of Law buildings and traits on corruption. I expect this will be pretty straightforward. Just need to find a Governor with the appropriate traits/retinue.

afrit, if you move your capitol, is corruption immediately reflected on the financial parchment, or do you have to end a turn? If it's immediate then it makes it that much easier.

Therother, I am not seeing your second graph. Did you post it correctly?

Does anyone know whether the capitol has any other effects at all, besides Distance Disorder and appearance of new generals & gifts?

For the longest time I've been keeping my faction leader at my capitol (Arretium) since it was also close to Rome. Just in case my leader's Influence was distance related or something. But I have no idea if it is.

Edit: Ok, I see your second graph now, TR

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Originally Posted by therother

Me again, I'm afraid.

http://www.arar86.dsl.pipex.com/TW/Corrupt2.gif

For a start, the linear fit currently put through the data is nonsense.

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Unfortunately, you'll find figures just like this in every medical journal but they dont make the connection that the correlation is bogus and unduely influenced by the two outliers.

Nice work BTW

hey Therother (or anyone else), does anyone know just how much governor management points influence income? I can't seem to find hard numbers in the manual or online help. Tamur did an analysis here but didn't find anything conclusive - I'm asking him if he can be any more specific. Also, which of the various income sources are affected? Tamur thinks it's all of them.

Thanks if you can help! ~:cheers:

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Originally Posted by RedKnight

afrit, if you move your capitol, is corruption immediately reflected on the financial parchment, or do you have to end a turn? If it's immediate then it makes it that much easier.

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It changes immediately.

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Originally Posted by RedKnight

Does anyone know whether the capitol has any other effects at all, besides Distance Disorder and appearance of new generals & gifts?

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I have suspected that the capital may get more trade income than other settlements. But this is based on entirely circumstantial evidence, which I wouldn’t put much faith in.

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Originally Posted by RedKnight

For the longest time I've been keeping my faction leader at my capitol (Arretium) since it was also close to Rome. Just in case my leader's Influence was distance related or something. But I have no idea if it is.

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I don't think it is, but as with the above, I've no evidence to prove it decisively.

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Originally Posted by RedKnight

hey Therother (or anyone else), does anyone know just how much governor management points influence income? I can't seem to find hard numbers in the manual or online help.

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The manual isn't good with hard numbers! Last time I looked at this, it seemed to me that admin amounts to 5% per scroll of your total mining income. I think the % varies for other incomes. I seem to remember tax having no impact though, which surprised me a little.

Quote:

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Originally Posted by RedKnight

Tamur did an analysis here but didn't find anything conclusive - I'm asking him if he can be any more specific. Also, which of the various income sources are affected? Tamur thinks it's all of them.

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Yes, but Tamur, bless him, has now decided to drop it all on me! Talk about pressure! ~;)

Thanks for pointing me to the thread, BTW. I'd forgotten that Admin was still unsolved, and don't know how I missed it first time around.

ha, whoops. Yes, I'm unfortunately rather tied up at home for a while here, my research will have to wait a week for some broken bones to heal up (my wife's, which is actually MUCH worse than mine being broken ~:) ) Sorry therother!

Corruption as elucidated by therother, is based on distance to capital (DTC) and gross income (GI) which is a total of farming (Fa), trade (Tr), taxes (Tx), mines (Mi) and admin (Ad).

Law temples (ie Athena) reduce corruption by (0.03)(GI).

By comparison, Trade temples (ie Hermes) improve trade income by (0.1)(TrL+TrSE) for each level. Trade income (Tr) is a total of land trade (TrL), sea imports (TrSI) and sea exports (TrSE).
Note that sea imports are not affected (which may explain the disparity in earlier reports). Building Traders has the same effect on trade as Trade temples.

There is therefore a good possibility that having a Law temple is not only better for public order but also better for finances.

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Originally Posted by zhuge

Note that sea imports are not affected (which may explain the disparity in earlier reports).

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A quick note: sea import values are defined by the exporter, and are always 20% of that income. So if city A is making 1000 Denarii by exporting to City B, City B will get 200 Denarii import income irrespective of other factors.