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 Post subject: Taxes, now with numbers!
PostPosted: Sun Feb 03, 2008 7:21 am 

Joined: Sat Jan 26, 2008 12:50 am
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One night on the radio we were trying to figure out the tax rates, after a lot of number crunching things just did not make sense. Then a dev got on and we were able to pick his brain for a couple key pieces of information that led us to the solution.

1) Each Commodity has it's own tax rate.
2) Tax rates are the same for purchasing and selling.
3) Tax rates are the same across all Skylands.

So we started buying and selling items to generate some numbers for us, and came up with some solutions that are too clean not to be correct. Here is the formula we used, broken into pieces for ease of understanding:

Code:
(buyPrice + sellPrice) / 2 = truePrice

buyPrice - truePrice = tax -or- truePrice - sellPrice = tax

tax / truePrice = taxRate



For example, I purchased Wood for 111.36 and then immediately sold it for 74.24.

Code:
(111.36 + 74.24) / 2 = 92.80

111.36 - 92.80 = 18.56 -or- 92.80 - 74.24 = 18.56

18.56 / 92.80 = 20.00%



Using that method I never calculated a tax rate that was not withing a few tenths of a percent of a nice, logical, number. And the variances I am sure were due to the normal fluctuation of the prices from buying/selling.

Here is the list I've been able to fill in so far:

Code:
Wood = 20%
Food = 20%

Fish = 18%
Paper = 18%

Ore = 15%
Tools = 15%

Oil = 20%
Iron = 20%

Grog = 25%



These numbers are not derived from a large data set (just one island, just one item each), but I feel confidant that they are correct. I would welcome some confirmation from other people running the numbers themselves.

As far as Tax skills and Traders go, the percentage bonus you get from them are all additive and (obviously) only discount the tax itself. For example when I buy Oil I get a 27% discount on the tax.

Code:
Tax Evasion 1 = 6%
Industry 1 = 6%
Two Level 4 Traders = 15%

Total = 27%



So if I was going to buy 50 Oil at for 15.00 each my bonuses would save me 39.00

Code:
{Tax on each item}
15.00 * 20% = 3.00

{Discount on Tax}
3.00 * 26% = 0.78

{Price After Discount}
(15.00 - 0.78) = 14.22

{Total Price}
14.22 * 50 = 711.00


{Total Discount}
(15 * 50) - 711.00 = 39.00



One last thing I would like to mention, the "Crew Logs" are displaying incorrect data, and this has been confirmed by the Devs as a bug. The amount displayed is the X% of the total price, where X equals the discount to taxes received from your crew in a %. For the previous example the log would say that my crew saved me 106.65. Where as their contribution is actually only 22.50.

Code:
{Tax on each item}
15.00 * 20% = 3.00

{Discount on Tax}
3.00 * 15% = 0.45

{Total Discount}
(0.45 * 50) = 22.50



I hope all of this is useful to you all. But more than that I hope to receive some confirmation on this from other members of the community through testing. Above all I would *LOVE* to be able to look at a Commodity and know that based on its rarity, and Skyland, that the price will fall between X and Y. I hope this helps us get closer.

-Zee

PS. m4ths r kewl


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 Post subject:
PostPosted: Sun Feb 03, 2008 5:48 pm 

Joined: Wed Oct 24, 2007 9:23 pm
Posts: 126
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Nicely done. Using the (buy + sell / 2) is such a simple and great idea.

Here's unobtanium:

buy: 8242.75 - 1582.61 = 6660.14 (6660 rounded)

sell: 4945.65 + 1582.61 = 6528.26 (6528 rounded)

real price: (8242.75 + 4945.65) / 2 = 6594.2
tax: 8242.75 - 6594.2 = 1648.55
tax %: 1648.55 / 6594.2 = 0.25

discount %: 1582.61 / 1648.55 = 0.960001213 (odd, should be 93%)

So unobtanium has a 25% tax.

The discount % doesn't seem to match though. I should only get 96% on paper and steel. So there's either a flaw in my calculations/logic or a bug in the game.
luxury schmuxury: 5 x 6% = 30%
cutthroat business/tax evasion: 5 x 6% = 30%
trader: 33%
total: 93%

Interesting in that it further reinforces that the navigator is the best possible crew member to get. Saving 33/66% on the 15-25% sell tax (5-16% overall savings) is much less compared to saving 30+% on your flight time. The buy tax can be disregarded unless you're buying at yellow/red.


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 Post subject:
PostPosted: Sun Feb 03, 2008 6:45 pm 

Joined: Wed Oct 24, 2007 9:23 pm
Posts: 126
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Some additional percentages:

diamond:
buy: 2612.56 - 501.61 = 2110
sell: 1567.54 + 501.61 = 2069
(2612.56 + 1567.54) / 2 = 2090.05
2612.56 - 2090.05 = 522.51
tax %: 522.51 / 2090.05 = 0.249998804
discount %: 501.61 / 522.51 = 0.960000766

catnip:
buy: 5247.71 - 1170.64 = 4077
sell: 2825.69 + 1170.64 = 3996
(5247.71 + 2825.69) / 2 = 4036.7
5247.71 - 4036.7 = 1211.01
tax %: 1211.01 / 4036.7 = 0.3
discount %: 1170.64 / 1211.01 = 0.966664189

grog:
buy: 126.65 - 24.32 = 102
sell: 75.99 - 24.32 = 100
(126.65 + 75.99) / 2 = 101.32
126.65 - 101.32 = 25.33
tax %: 25.33 / 101.32 = 0.25
discount %: 24.32 / 25.33 = 0.960126332

steel:
buy: 11.06 - 1.75 = 9
sell: 7.38 + 1.75 = 9
(11.06 + 7.38) / 2 = 9.22
11.06 - 9.22 = 1.84
tax %: 1.84 / 9.22 = 0.199566161
discount %: 1.75 / 1.84 = 0.951086957


Unobtanium: 25%
Diamonds: 25%
Catnip: 30%
Grog: 25% (matches yours)
Steel: 20% (matches yours)

I don't suppose we have anyone around who wants to do some calculus and find the price slope equation (it's not linear).


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 Post subject:
PostPosted: Sun Feb 03, 2008 7:01 pm 

Joined: Sat Jan 26, 2008 12:50 am
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Thanks for the follow up on this. The fact that you're getting a 96% discount instead of the expected 93% discount is odd. I would like to think that there is an error reporting the discount from the trader in the logs, because that would be the simple answer (for us). It's hard to say for sure, just need more data I guess.

The fact that our numbers are matching up gives me warm fuzzy feelings.

-Zee


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 Post subject:
PostPosted: Sun Feb 03, 2008 8:30 pm 

Joined: Wed Oct 24, 2007 9:23 pm
Posts: 126
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The rest of the data points:


oil:
buy: 4.21 - 0.67 = 3
sell: 2.81 - 0.67 = 3
(4.21 + 2.81) / 2 = 3.51
4.21 - 3.51 = 0.7
0.7 / 3.51 = 0.199430199

tools:
buy: 4521.29 - 550.42 = 3970
sell: 3341.83 - 550.42 = 3892
(4521.29 + 3341.83) / 2 = 3931.56
4521.29 - 3931.56 = 589.73
589.73 / 3931.56 = 0.149998983

ore:
buy: 210.79 - 25.66 = 185
sell: 155.80 - 25.66 = 181
(210.79 + 155.80) / 2 = 183.29500
210.79 - 183.29500 = 27.49500
27.49500 / 183.29500 = 0.150004092

paper:
buy: 1.51 - 0.22 = 1
sell: 1.05 + 0.22 = 1
(1.51 + 1.05) / 2 = 1.28
1.51 - 1.28 = 0.23
0.23 / 1.28 = 0.1796875

fish:
buy: 22.15 - 3.19 = 18
sell: 15.39 + 3.19 = 18
(22.15 + 15.39) / 2 = 18.77
22.15 - 18.77 = 3.38
3.38 / 18.77 = 0.180074587

food:
buy: 2301.37 - 364.38 = 1936
sell: 1534.25 + 364.38 = 1898
(2301.37 + 1534.25) / 2 = 1917.81
2301.37 - 1917.81 = 383.56
383.56 / 1917.81 = 0.199998957

wood:
buy: 0.85 - 0.14 = 1
sell: 0.57 + 0.14 = 1
(0.85 + 0.57) / 2 = 0.71
0.85 - 0.71 = 0.14
0.14 / 0.71 = 0.197183099

Wood: 20%
Food: 20%
Fish: 18%
Paper: 18%
Ore: 15%
Tools: 15%
Oil: 20%
Steel: 20%
Grog: 25%
Catnip: 30%
Diamonds: 25%
Unobtanium: 25%

All match your datapoints so I think this data is ready to be added to the skybrary.

Also, here's some points to plot out an equation using unobtanium based on qty available and true price (price excluding taxes). I know there's software (and calculators like the TI-89 which I don't have anymore) that might be able derive formulas based on them.

69, 6594.2
68, 6691.175
67, 6791.045
66, 6893.935
65, 7000


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 Post subject:
PostPosted: Sun Feb 03, 2008 8:35 pm 

Joined: Thu Dec 13, 2007 3:16 pm
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Faction: Flight School
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I'm not your man for the calculus, but to do it I think you're going to need to start recording at what color level some of these prices are found at. Obviously there'll be some fluctuation. But to get you started, these were from Tortuga earlier today:
Code:
Wood - Buy: 6.28  Sell: 4.19  True: 5.24  Color: Purple
Food - Buy: 233.72  Sell: 155.82  True: 194.77  Color: Red
Fish - Buy: 7.04  Sell: 4.89  True:  5.97  Color: Purple
Paper - Buy: 8.73  Sell: 6.07  True:  7.40  Color: Purple
Ore - Buy: 170.84  Sell: 126.27  True: 148.56  Color: Yellow
Tools - Buy: 301.11  Sell: 222.56  True: 261.84  Color: Yellow
Oil - Buy: 249.50  Sell: 166.34  True: 207.92  Color: Green
Steel - Buy: 229.22  Sell: 152.81  True: 191.02  Color: Green
Grog - Buy: 376.18  Sell: 225.71  True: 300.95  Color: Yellow


Sorry I don't have the others, I don't have the TL for them ^^;;


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 Post subject:
PostPosted: Sun Feb 03, 2008 10:33 pm 

Joined: Sat Jan 26, 2008 12:50 am
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Just for the sake of completness here are the original numbers I ran when calculating the tax rates, copied right out of my spreadsheet:

Code:
Commodity   Buy      Sell     Tax Rate
Wood      $111.36   $074.24   20.00%
Food      $015.53   $010.35   20.02%
Fish      $017.99   $012.50   18.01%
Paper     $111.30   $077.34   18.00%
Ore       $023.63   $017.47   14.99%
Tools     $600.86   $444.11   15.00%
Oil       $167.97   $124.12   15.01%
Iron      $278.27   $185.51   20.00%
Grog      $338.88   $203.33   25.00%



And here is another bunch of confirmations based on the prices Nighthawk was nice enough to post.

Code:
Commodity   Buy     Sell     Tax Rate
Wood      $006.28   $004.19   19.96%
Food      $233.72   $155.82   20.00%
Fish      $007.04   $004.89   18.02%
Paper     $008.73   $006.07   17.97%
Ore       $170.84   $126.27   15.00%
Tools     $301.11   $222.56   15.00%
Oil       $249.50   $166.34   20.00%
Iron      $229.22   $152.81   20.00%
Grog      $376.18   $225.71   25.00%



I feel really good about the tax rates we've calculated at this point.

If we want to track the range of prices at a given color we actually only need to post the buy price, sell price, OR true price. Given one we can figure out the others because we know the tax rates now. Nighthawk, I added your numbers to a spreadsheet I am working on trying to figure that exact thing out.

-Zee


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 Post subject:
PostPosted: Tue Feb 05, 2008 4:27 am 

Joined: Sat Jan 19, 2008 1:57 am
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Location: Playing with The Mechanic
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This is good stuff, someone should Skybrary it.


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 Post subject:
PostPosted: Thu Feb 07, 2008 8:24 am 
Developer

Joined: Tue Dec 12, 2006 7:05 am
Posts: 3631
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Agreed.
May I suggest http://skyrates.wikia.com/wiki/Trading or even, http://skyrates.wikia.com/wiki/Trading/ ... ng_Trading ?


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 Post subject:
PostPosted: Thu Feb 07, 2008 12:56 pm 
Helpful

Joined: Sun Jan 27, 2008 8:32 pm
Posts: 1767
Faction: Azure League

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Ooh, use the second one. Category:Deconstruction is lonely.


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 Post subject:
PostPosted: Thu Feb 07, 2008 1:29 pm 

Joined: Wed Oct 24, 2007 9:23 pm
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Alright, I added it to the Trading page. I really dislike it when confirmed evidence is put in deconstruction. Deconstruction should be reserved for unknown things.


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 Post subject: Skills question: Cutthroat Business and Tax Evasion
PostPosted: Fri Mar 07, 2008 12:45 pm 

Joined: Fri Jan 18, 2008 10:34 pm
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Location: Hockeytown, USA
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I started to compute it, but then my foxy brain went all to mush. :?

For the Cutthroat Business and Tax Evasion skills, does the "goods" in their description mean "any item you can buy and sell from the trader" or does it mean just some smaller listing, like "just steel and tools"?

I figured I would just ask all you trading wizards, since only took me until now to realize...
    Tax Evasion lowers the Buy Tax
    Cutthroat Business lowers the Sales Tax.

_________________
MrDolomite; see also Skybrarian


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 Post subject:
PostPosted: Fri Mar 07, 2008 2:39 pm 
RP Guide

Joined: Sat Mar 10, 2007 4:33 pm
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This is impressive work.

_________________
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 Post subject: Re: Skills question: Cutthroat Business and Tax Evasion
PostPosted: Fri Mar 07, 2008 5:50 pm 
Moostro

Joined: Sat Dec 08, 2007 10:56 am
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Location: Vancouver, WA
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MrDolomite wrote:
For the Cutthroat Business and Tax Evasion skills, does the "goods" in their description mean "any item you can buy and sell from the trader" or does it mean just some smaller listing, like "just steel and tools"?


Going to be getting the skills pages on the wiki fleshed out a bit better, but for quick response:
Both of these affect *all* goods, while each of the goods specific ones affect buy+sell for those specific goods. Paper and Steel have no skill, which is why the trader gets effectivel a double impact for those two goods.


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 Post subject:
PostPosted: Fri Mar 07, 2008 5:52 pm 
Moostro

Joined: Sat Dec 08, 2007 10:56 am
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Prince Harris wrote:
This is impressive work.


Thanks be to the dev that confirmed that taxes currently do not likely have any factor other than by-goods, otherwise we would've had a few more days of spewing our numbers in the radio. ;)


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