Tax Income

[therother]

I've learned my lesson: investigating RTW takes time, and will probably not be short. Anyway, to war:

Edit:There are 4 tax rates. Normal tax bestows no growth rate benefit/penalty and has the values plotted below. Low gives a 0.5% in population for a 20% drop in tax. The corresponding figure for high and very high, are -0.5%/+20% & -1%/+50%.

The primary determinant of the level of taxation appears to be population.


http://www.totalwar.org/patrons/lm/research/therother/tax.gif

The image hereinbefore (wonderful word that) is a study of the relationship between taxes and population in a settlement with neither Governor nor buildings (including Governor's House). For the moment I'm just throwing this out there for the moment as a FYI with a few general comments.

Note the non-linearity of the relationship between 400 - 2000, then the linearity until 7905, whence it takes an unexpected jump from 1000 to 875, then continues linearly, but at a less steep gradient, i.e. you are getting less money per man. In fact you get more per money at the lower population levels, which I have to say was not unexpected.

At this level, no difference was noted in tax income for different %PO, which was one of the main things I'll be investigating, based on the reports of a number of players.

Health warnings:

I was pushing it a bit, as it's highly unlikely that CA expected anyone to have a settlement without a Governor's House for more than a turn or two, and certainly not up to 30,000.
A very odd thing happened at between 3200 and 3600 - the public order froze at 51%. Which is odd for two reasons. I've never anything other than an integer multiple of 5 for PO. I've never had PO freeze before, and remain completely unaffected by increases in squalor, tax rate, removal of garrison, etc...

Oh and perhaps I should mention - as there are a lot more buildings that affect tax than squalor, as well as a separate tax level - that this thread could be significantly longer that the squalor (https://forums.totalwar.org/vb/showthread.php?t=37586) one, unless the effects of these functions are elucidated in short order. Which should put the fear of death into the site admin!

Anyway, to bed, the new Iain M. Banks book is calling!

[therother]

Well, it seems like the graph for the Governor's House exactly matches the one above. Which is curious, and may mean that I can eliminate his residence as a factor. I'll try the Imperial Palace next to be sure.

Edit: Well, it seems like there is an additional tier at ~36,000 men, after which the rate of increase is approximately halved.

Quick rules:

1st tier (

[therother]

Edit of post above, wouldn't let me post it for some reason ~:confused: :

Well, it seems like there is an additional tier at ~36,000 men, after which the rate of increase is approximately halved.

Quick rules:

1st tier (below 7905): Tax = 500+ 0.064Ps - 31922091/Ps^2. Which is really not that helpful, but thankfully things become a little more linear at 2000.

2nd Tier (2000-7905): Tax: y= 0.0625Ps + 505.40904, or 500 + 62.5 per 1000 men

3rd Tier (7906-~34000): Tax= 0.0154Ps + 756.32, or roughly 750 + 15 per 1000 men.

Last tier: (35000+): Tax = 0.0079Ps + 1007.5, or roughly 1000 + 8 per 1000 men.

Ps is Population Size in men.

It would seem that these are the basic tax levels, and that various buildings and other effects act upon them.

[Soulflame]

A quick noteworthy thing:
There is a HUGE gap between the first and second tier in terms of income.
Once you get past 7905 population, you will not get that high income until you reach a population of about 15800 (used the non-rounded numbers to come to this, then rounded it to hundreds).
Whereas the gap between second and third tier is considerably smaller; to get the same income as you had when you had 35000 people, you only need 36400 people (again using non-rounded numbers, then rounded on hundreds)

[therother]

A quick noteworthy thing:
There is a HUGE gap between the first and second tier in terms of income.
Once you get past 7905 population, you will not get that high income until you reach a population of about 15800 (used the non-rounded numbers to come to this, then rounded it to hundreds).
Whereas the gap between second and third tier is considerably smaller; to get the same income as you had when you had 35000 people, you only need 36400 people (again using non-rounded numbers, then rounded on hundreds)Remember, this is just the basic rate. There are not even roads in this settlement. The game could factor in that by 2,000, you really should have started building these. But we'll see when the time comes. I'm going to be pretty busy with work for the next day, so it might take a while. Assuming no one decides to take up the baton!

Edit: It's actually the 2nd and 3rd tiers that the gap appears. I know it's a little confusing as the 4th tier is not yet plotted. I'll get round to it eventually. [Graph Done]

Additional edit: Just changed the boundary slightly for the 3rd to 4th tier. Makes little difference, although I believe it's now more accurate.

[RedKnight]

Very cool stuff, Therother. Wow - you must've had to hit the Turn button hundreds of time!

[Soulflame]

Remember, this is just the basic rate. There are not even roads in this settlement. The game could factor in that by 2,000, you really should have started building these. But we'll see when the time comes. I'm going to be pretty busy with work for the next day, so it might take a while. Assuming no one decides to take up the baton!

Edit: It's actually the 2nd and 3rd tiers that the gap appears. I know it's a little confusing as the 4th tier is not yet plotted. I'll get round to it eventually. [Graph Done]

Additional edit: Just changed the boundary slightly for the 3rd to 4th tier. Makes little difference, although I believe it's now more accurate.

Right well I was dismissing the first part of the graph ~;).
Even if roads or other buildings have influence, it's abit weird that there is such a huge gap from 2 to 3, while the gap from 3 to 4 is not so much.

I just heard I have a new family member, so I'll be with my brother and his wife tonight, so no experimenting for me tonight. ~;)

[RedKnight]

I just heard I have a new family member, so I'll be with my brother and his wife tonight, so no experimenting for me tonight.
Did you get the little faction announcement with the baby crying, and such?

[Dorkus]

This is just really great stuff, as always therother.

wish i could help out, but i have a paper 2 weeks overdue. ;o

[Tamur]

Wow, nice work. This all gives me a great deal of respect for those one- or two-line descriptions of economic formulae!

[therother]

Hmm, looking over my rather sparse (*) tax data leads me to believe that it's possible that I may have been wrong about the length of investigation yet again. Barring the addition of the effects of various traits/retinue characters (**), I believe that this may indeed be all there is to say about tax income. Surprisingly enough, buildings seem to do nothing to change these values, only the Governor's traits and the tax rate of course. (I'll try to confirm this to the best of my ability later, when I get back to my home desktop, on which RTW is installed.)

Which, if true, I have to say, is a little disappointing, as it very much plays into the hands of the mass murderers who butcher their cities in the revolt/extermination tactic. But then there is always trade, which is the biggest earner in the game, and one that is very definitely affected by population sizes. That'll be my next target, and I'm sure that'll be more complex!

Honest.

PS Thanks guys.

PPS As always, if anyone finds a mistake/exception, post it here. I'll be more than happy to reopen the investigation: "No one who cannot rejoice in the discovery of his own mistakes deserves to be called a scholar." Donald Foster

(*) For the 2nd time in a row, I seem to have lost my data in an Excel spreadsheet. ~:pissed: Serves me right for not using a proper program!

(**) Will post them later on today, when I get back to my home desktop, assuming no one beats me to it.

[therother]

One thing I should mention is that tax income is affected by the difficulty level of the campaign map, but no the battles. The data above was generated using Medium.

From my current data, it would appear that easy adds 20%, whilst hard and very hary subtract 5.5% and 11% respectively (preliminary numbers).

So multiply the overall result of the above equations by:

1.2 for Easy
0.945 for Hard
0.89 for Very Hard


For the moment, just as a FYI, mining and trade income don't seem to change between difficulty levels, although testing for the latter is still ongoing as it’s much harder to pin down.

Farming, though, is definitely affected though. In fact, even more so than taxes:


Up 12.5% for Easy
Down 8% for Hard
Down 15% for Very Hard

[Soulflame]

Did you get the little faction announcement with the baby crying, and such?

Didn't get a card/electronic message yet... she's only a day old... and ony today officially registered at the town hall.
I did already hear her cry... and she got some lungs ~:eek: ~;). She's cute and they called her Camille Rosemarijn.

Anyway... on topic:
Nice progress therother. One question: how do you increase the population (or any other variable for that matter), without altering the rest?
Do you mod the variable using the console/texts? or are you breaking down stuff afterwards?

[therother]

Didn't get a card/electronic message yet... she's only a day old... and ony today officially registered at the town hall.
I did already hear her cry... and she got some lungs ~:eek: ~;). She's cute and they called her Camille Rosemarijn.Congrats, Soulflame.


Nice progress therother. One question: how do you increase the population (or any other variable for that matter), without altering the rest? Do you mod the variable using the console/texts? or are you breaking down stuff afterwards? Occasionally I mod, but I usually use a memory address editor to change the population of the city directly, without altering anything else. I then check the levels in a normal game to see if they are correct.

Recently, though, I've been using RomeSAGE to alter the difficulty of a saved game. A big thank you to ShellShock for it. You can download it: here (http://www.twcenter.net/forums/index.php?showtopic=11393)

[therother]

All right, here are the tax affecting Character Traits:


Line: Good Taxman
Triggers: Random birth, Government building complete in a disillusioned city with > high tax (75%) +1 to the trait (-1 to anti-trait).
Faction info: Not barbarians
Anti-Traits: Bad Taxman


Tax Assessor, TaxCollection +10%, Threshold 1
Efficient Taxman, TaxCollection +20%, Unrest +5%, Threshold 2
Cruelly Efficient Taxman, Tax Collection +30%, Unrest +10%, Threshold 3


Line: Bad Taxman
Triggers: Random birth, Government building complete in a city with loyalty > disillusioned city and with > high tax (15%) +1 to the trait (-1 to anti-trait).
Faction info: Not barbarians
Anti-Traits: Good Taxman


Useless Assessor, Tax Collection -10%, Threshold 1
Inefficient Taxman, Tax Collection -20%, Threshold 2
Cruelly Efficient Taxman, Tax Collection -30%, Threshold 3


Line: Cheapskate
Triggers: Random birth, Government building complete in a city with loyalty > disillusioned city and with > high tax (15%) +1 to trait. Self perpetuating, 4% chance per turn of +1 to trait. If father has Expensive Tastes, 10% chance at birth of +1 to trait. Didn't move from settlement that has at least a Temple of Trade for a turn 8% chance of +1 to trait .
Faction info: None
Anti-Traits: Expensive Tastes, Aesthetic
No Going Back Level: 2


Frugal, Tax Collection +5%, Construction costs -5%, squalor +5%, Threshold 1
Downright Miserly, Tax Collection +10%, Construction costs -10%, squalor +10%, Threshold 2
Cheapskate, Tax Collection +15%, Construction costs -15%, squalor +15%, Threshold 3

[therother]

Ancillaries:

Freeman Clerk: Tax Collection +10%, Management -1. Trigger 15% when general stayed, without moving for the turn, in a settlement with a Temple of Governors (Zeus, Macedon & Pontus only) and at least an Academy.

(NB There are two Freeman Clerks, only one affects Tax though. The other has an effect on trading instead of tax.)

Geographer: Tax Collection +10%, Movement Points 3. Not barbarians. Trigger 15%, when general stayed, without moving for the turn, in a settlement with at least a Scriptorium.

Idiot Savant: Tax Collection +10%, Management 1. Not barbarians. Triggers: 5% when general stayed, without moving for the turn, in a settlement with a Governor's Palace and a Temple of Trade or greater. (Mercury/Brutii, Milqart/ Numdians, Hermes/Greeks, Britannia/Britons)

Procurator: Tax Collection +10%. Not barbarian, eastern, Egyptian, Greek. Trigger 20%, when general stayed, without moving for the turn, in a settlement and at least a Temple of Trade Awesome temple. (Mercury/Brutii, Milqart/ Numdians, Hermes/Greeks, Britannia/Britons) (*)

Tax Farmer: Effect Tax Collection 5%, Influence –1. Excludes Treasurer, not barbarian, eastern, Egyptian, Greek. Trigger 8% when Governor build completed, and the General has at least the first Bad Taxman trait.

(*) This would appear to be an impossible combination for the Greeks, and indeed it is. But if you are not barbarian, eastern, or Egyptian faction, and you conquer the settlement, your General could pick up the trait if you leave the temple in situ.

[Tamur]

It's very cool to see the triggers here -- they even make sense! ~:) I had wondered where the Tax Farmer came from, have had a couple of those. I'm still unsure from the description how the tax-affecting traits are given. Is it random per-turn?

[therother]

It's very cool to see the triggers here -- they even make sense! ~:) I had wondered where the Tax Farmer came from, have had a couple of those. I'm still unsure from the description how the tax-affecting traits are given. Is it random per-turn?Sorry, forgot to put in what each percentage means. Thanks for spotting that! Will get to it ASAP.

[RedKnight]

Great work, therother.

For folks that don't know about it, there's a listing of all V&Vs here (http://www.twcenter.net/downloads/db/?mod=44) ~:cheers:

[zhuge]

Nice work. Checked through a few formulas and they seem to work well.
The formula for the 1st tier appears a bit messy though. Thought I'd add some extra data points here (the data for the 1st tier is a bit sparse for a non linear relation) and pool them with yours for better accuracy.

d32 Population Tax
Vicus Venedae 447 298
Domus Dulcis D 480 312
Aquincum 524 328
Salona 530 330
Segestica 640 353
Iuvavum 730 372
Lovosice 780 383
Trier 823 392
Caralis 860 400
Narbo Martius 922 413
Vicus Gothi 933 416
Segesta 980 426
Cyrene 980 426
Lugdunum 1015 433
Lepcis Magna 1024 435
Lemonum 1368 504
Massilia 1370 504
Condate Redonum 1473 515
Campus Iazyges 1540 522
Batavodurum 1635 532
Chersonesos 1773 547
Osca 1854 555

Sorry if the table doesn't turn out right. Forum posts may alter the 'formatting' a little.
Also all data above was taken from a game played on VH settings on turn 32(all taxes are set to normal though) so you should note that a 0.90 or 0.89 modifier as already been applied to them before comparing with your own data set. Factors like town size, roads, traders, governor's management don't seem to affect taxes so I've not mentioned them.

Looking at the Excel graph based on the above data points (which I can't post) it appears to me that the 1st tier might be further broken down into 3 tiers based on population: 1300 (which again appear to be linear).
Would be nice to have more data for confirmation.

[zhuge]

Seem to have problems posting certain bits. ~:confused:
Those last sentences should read:
Looking at the Excel graph based on the above data points (which I can't post) it appears to me that the 1st tier might be further broken down into 3 tiers based on population: less than 600, 600 to 1300, 1300 (which again appear to be linear).
Would be nice to have more data for confirmation.

[therother]

Many thanks for your work, zhuge. I'll generate some data in the ranges you suggest, probably sometime later on today.

PS I find it best to place tables within the code markups.

e.g.

Domus Dulcis D 480 312
Aquincum 524 328
Salona 530 330

[zhuge]

A few quick notes here on farming which is pretty straightforward, summarizing findings by therother and andrewt.

Factors involved for Farming Income (F):
1)Base farming (B) - ie 2.5% for Arretium (unique for each region)
2)Farming upgrade (U) - each upgrade confers a 0.5 benefit
3)Harvest (H) - poor = 0.95, ave = 1.00, good = 1.04, excellent = 1.08
4)Campaign difficulty (D) - easy = 1.125, medium = 1.000, hard = 0.920, very hard = 0.850

F = (160)(B+U)(H)(D)

For example, Arretium which starts with Land Clearance with a poor harvest on Very Hard settings will receive:
F = (160)(2.5 + 0.5)(0.95)(0.85) = 387.6 (in actual play rounded up to 388)

[RedKnight]

Very cool, zhuge! Thanks for that.

Has somebody posted the base farming levels for each region? I could swear I've seen it somewhere. Or maybe even pulled it out myself. :dizzy2:

[zhuge]

As mentioned previously I felt the 1st non-linear tier actually comprises of 3 linear tiers joined at the ends with each other as to give the impression of a curve. Collected more data recently using queueing up multiple units to give fine control over all values and below are the summarized results.

Since you cannot decrease population below 400, that starts as the base.
The formulas with (Tax income = T, Population = P) for

Tier 1a (For population size 400 - 510):
T = 0.475(P) + 120

Tier 1b (For population size 511 - 1327):
T = 0.2375(P) + 240

Tier 1c (For population size 1328 - 2050):
T = 0.11875(P) + 400

Note that the gradient is cut by half each time we go up a tier.

The difference between tier 2 and tier 3 (illustrated by therother) is most probably a bug, since their ends do not meet and are in fact very far apart. It should be noted to CA for correction.

EDIT: All formulas have been converted to Normal campaign difficulty with a Normal tax rate, although my data is in Very Hard campaign difficulty with a Normal tax rate (by applying the 0.895 modifier in reverse to all variables).

EDIT2: I think that wraps up tax rates nicely with the general formula being
T = (D)(R)(mP+c) where D is campaign difficulty, R is tax rate as described previously and m and c depend on which of the 6 linear tiers is being used (1a, 1b, 1c, 2, 3 or 4).
This forum's rather quiet... would be nice to see a little more activity.

[RedKnight]

great stuff, zhuge! thanks!

As for it being quiet, I'm playing HL2 atm but will be back on RTW as soon as I'm done the solo campaign.