| Author | Thread: Progression of buildings |
StonestrikerPosts: 86 Location: Jaaron Magus Age: 109 years old Clan: OASIS | Message #14296 Posted: Oct 13, 2008, 3:11 pm |
| what is the progression of all the primary resources buildings in relation with how much they gain per level? is there a jump somewhere, a place that it increases more then normal? |
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| Yamikuronue Posts: 1288
Location: Mottonsborough
Magus Age: 116 years old
| Message #14298 Posted: Oct 13, 2008, 3:17 pm |
Our clan's records contain the following chart:
Level of Field...........Amount Produced
0...............................10
1...............................25
2...............................60
3...............................105
4...............................160
5...............................225
6...............................300
7...............................385
8...............................480
9...............................585
10..............................700
11..............................825
12..............................960
13..............................1105
14..............................1260
15..............................1425
16..............................1600
17..............................1785
18..............................1980
19..............................2185
20..............................2400
It was compiled by hand, there may be errors in it. |
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| Justyn Posts: 2
Location: Rildesjan
Magus Age: 112 years old
| Message #15662 Posted: Oct 25, 2008, 5:51 am |
I noticed a pattern there: the upgrade from each level to the next increases production by the previous increase plus ten (with the exception of the move from level one to level two, where the increase is twenty above the previous). Note that I am going with Yamikuronue's, rather than my own data here, so I cannot verify anything above level seven yet.
1 - 15 -- (10+15=25)
2 - 35 -- (25+35(15+20)=60)
3 - 45 -- (60+=45(35+10)105)
4 - 55 -- (105+55(45+10)=160)
5 - 65 -- (160+65(55+10)=225)
6 - 75 -- (225+75(65+10)=300)
7 - 85 -- (300+85(75+10)=385)
8 - 95 -- (385+95(85+10)=480)
9 - 105 -- (480+105(95+10)=585)
10 - 115 -- (585+115(105+10)=700)
11 - 125 -- (700+125(115+10)=825)
12 - 135 -- (825+135(125+10)=960)
13 - 145 -- (960+145(135+10)=1105)
14 - 155 -- (1105+155(145+10)=1260)
15 - 165 -- (1260+165(155+10)=1425)
16 - 175 -- (1425+175(165+10)=1600)
17 - 185 -- (1600+185(175+10)=1785)
18 - 195 -- (1785+195(185+10)=1980)
19 - 205 -- (1980+205(195+10)=2185)
20 - 215 -- (2185+215(205+10)=2400)
I don't know if there is a special mathematical formula for what is going on here, so if anyone does, go ahead and post it if you want to. |
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| Yamikuronue Posts: 1288
Location: Mottonsborough
Magus Age: 116 years old
| Message #15666 Posted: Oct 25, 2008, 6:02 am |
| It's possible your findings ARE the formula. The more data I collect, the more patterns I see - a lot about this game that seems semi-random is actually just a simple yet unintuitive pattern, like being an easily derived number times a fraction of some sort to make it seem rather arbitrary. It's just obfuscated enough to make it worth doing the research to find out, I've discovered ^_^ |
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ApathyPosts: 108 Location: Last Alvia Dawning Magus Age: 108 years old Clan: ARROW | Message #15685 Posted: Oct 25, 2008, 9:46 am |
Formula:
Y = resource per hour
X = building level.
Y = 5X * (X+4)
Simple as that.
EDIT: It was actually simplified to this from the above data. Read on for mathematical explanation.
f(0) = 0
f(1) = f(0) + (10*1) + 15 = 25
f(2) = f(1) + (10*2) + 15 = 60
f(3) = f(2) + (10*3) + 15 = 105
substitute f(1) into f(2), f(2) into f(3)
f(3) = f(0) + (10*(1+2+3)) + 15*3 = 105
since f(0) = 0 therefore formula is
f(x) = 10*(1+2+3...+x) + 15*x
arithmetic series formula:
1+2+3...+x = x*(x+1)/2
***(wiki it to see the logical explanation, or see note near bottom of post)
f(x) = 10*x*(x+1)/2 + 15*x
factor out x:
f(x) = x*(x+1)*5 + 15)
factoring further:
f(x) = 5x*(x+1+3) = 5x * (x+4)
Tadaa.
***explanation of arithmetic series***
Imagine this:
0+1+2+3+4+5+6+7+8+9 = ?
1+2+3+4+5+6+7+8 = ?
Well, you could add it up one by one, but how about rearranging them this way?
0+9 + 1+8 + 2+7 + 3+6 + 5+4
total is:
9 + 9 + 9 + 9 + 9 = 45
There were 10 numbers which formed 5 pairs, and the pairs totaled the highest number.
1+8 + 2+7 + 3+6 + 4+5
9 + 9 + 9 + 9 = 36
There were 8 numbers which formed 4 pairs, and the pairs totaled the highest number.
Just be sure to pair each number up. If there is one number left over, put 0 in to make things easier, or just pair up every number except the odd one out and add that back at the end.
By the way, this method only works if each number is increased by 1. Wikipedia "arithmetic progression" if you want to know the algebraic formulas for more complex progressions.
It's easier to explain using a picture for those not too well versed in algebra:
0|
1|-
2|--
3|---
4|----
5|-----
6|------
7|-------
8|--------
9|---------
rearranged by cutting off the top part of the triangle, then putting it back on to make a rectangle:
0+9|---------|
1+8|--------|-
2+7|-------|--
3+6|------|---
4+5|-----|----
Let's say that the area of the triangle is the total amount of dashes. The formula to find the area of a triangle is base * height / 2, which would be 9 * (9+1) / 2 = 45.
For the rectangle, it was made by cutting the triangle at the halfway point, then putting it back on. There were 10 numbers, so the halfway point is 5. The width of the rectangle was made by pairing up the lowest number with the highest one, so that would be 9. The area would be 9*5 = 45.
Remember, 0 has to be included otherwise the triangle would have a flat top instead of a pointed one, and that would not be a true triangle.Last Edited: Oct 25, 2008, 12:14 pm |
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masterslugPosts: 619 Location: Shuul Magus Age: 124 years old Clan: OTAKU | Message #15776 Posted: Oct 26, 2008, 8:10 am |
| ouch...I think I've sprained my brain |
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| Sconibulus Posts: 664
Location: Shuul
Magus Age: 116 years old
| Message #15785 Posted: Oct 26, 2008, 3:06 pm |
5X*(X+4) doesn't work, what we have here is, if I can type it at all correctly,
n
E (10X+5) +5=Y
0 |
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| FatherCoyne Posts: 332
Location: Mallow
Magus Age: 116 years old
Real Name: Kevin Coyne
Email: KCoyne@umail.ucsb.edu
| Message #15787 Posted: Oct 26, 2008, 3:16 pm |
| Dude, Sconi, he just spent a page and a half explaining why those are the same for any positive integer. You're going to pick him apart for missing lvl 0? |
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| Sconibulus Posts: 664
Location: Shuul
Magus Age: 116 years old
| Message #15791 Posted: Oct 26, 2008, 4:02 pm |
| Indeed I am, because I'm a horrible person. That and Level 0 was giving me hell when I was calculating it myself : () ) |
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ApathyPosts: 108 Location: Last Alvia Dawning Magus Age: 108 years old Clan: ARROW | Message #15869 Posted: Oct 27, 2008, 6:05 am |
Guess we won't know the formula for sure unless Kep decides to post the rates for Lv 0.
Anyway, whatever works, works. Right? :P |
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| Yamikuronue Posts: 1288
Location: Mottonsborough
Magus Age: 116 years old
| Message #15878 Posted: Oct 27, 2008, 7:21 am |
Level 0 is 10. When you first join the game you have level 0 in everything, not yet built, and you get 10/hr.
(I remember when widdle Dilty was that young... they grow up so fast... *sniffle*)Last Edited: Oct 27, 2008, 7:22 am |
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