Health of banner items

[Lodz]

Hi
I want to collect all data about banner health. Here are my data (41 level).

Direct link to big image: https://www.angrybirdsnest.com/wp-content/uploads/album/66572/b-ABE-v4.png

thanks to: @tigerussell, @killerkea, @dr_ishmael, @kerravon

When you get new item please write its health, stars, your level and element (top, flag or emblem) and league
example: Top; Gold; **; 4862; 41

Topic

[t_russell]

Top;Diamond;Set;5865;41
Top;Diamond;***;5738;41
Top;Diamond;**;5610;41
Top;Diamond;*;5483;41
Top;Diamond; ;5355;41
Top;Platinum;***;5355;41
Top;Platinum;*;5117;41
Top;Gold;***;4973;41
Top;Gold;**;4862;41
Top;Gold;*;4752;41
Top;Gold; ;4641;41
Banner;Diamond;Set;5865;41
Banner;Platinum;Set;5670;41
Banner;Diamond;**;5610;41
Banner;Gold;Set;5474;41
Banner;Platinum; ;5355;41
Emblem;Platinum;***;2248;41
Emblem;Platinum;**;2151;41
Emblem;Platinum;*;2102;41
Emblem;Platinum; ;2053;41
Emblem;Gold;***;2053;41
Emblem;Gold;**;2008;41
Emblem;Gold;*;1964;41
Emblem;Gold; ;1919;41

This is all the info I have that I would consider reliable, The only thing I have scrapped from the arena was the green rags I started with but I just don’t remember what the star levels were for all this other crap I have lying around.

[KillerKea]

I think you are missing a column. Apparently wheel spins can have a higher maximum and a lower minimum than items from the pig machine. For example, I have wood emblems that are 1122, 1339, 1403, 1434 and 1466. All of these are level 41 items. The biggest and lowest number are from wheel spins.

Maybe you should specify that you are only collecting data for level 41 items right now. Gold 3* emblem is 2008. I’ll post more later when I have more time.

[dr_ishmael]

Tops and flags scale exactly by 10% per league, i.e. Stone league items are 10% stronger than Wood league, and Diamond items are 50% stronger than Wood. So here’s that table:

level 41 Top/Flag
   Wood  Stone  Silver  Gold  Platinum  Diamond
0  3570   3927    4284  4641      4998     5355
1  3655   4021    4386  4752      5117     5483
2  3740   4114    4488  4862      5236     5610
3  3825   4208    4590  4973      5355     5738
4  3910   4301    4692  5083      5474     5865

Emblems aren’t as easy to figure out – they scale by approximately 13% per league, but it’s not exact. Here’s as much as I know, combined with the data in this thread:

level 41 Emblem
   Wood  Stone  Silver  Gold  Platinum  Diamond
0  1339   1517    1696  1874      2053  
1  1371   1553    1736  1919      2102  
2  1403   1590    1777  1964      2151  
3  1434   1626    1817  2008            
4  1466   1662    1857  2053      2248  

“4-star” items, as @killerkea pointed out, are only available from the reward wheels.

[KerrAvon]

@lodz and @dr_ishmael I can add three more items to your emblem table.
Wood, 4-star, 1466
Silver, 4-star, 1857
Gold, 0-star, 1874

Some of my items from the rewards wheel are 3-star and some are 4-star. Is there a pattern to this or is it just a random prize on the wheel?

[dr_ishmael]

@kerravon Numbers added. I haven’t paid too much attention to the wheel prizes, so I can’t help there.

[TomC]

@dr_ishmael Do you have stats for set tops/flags in relation to that table?

[dr_ishmael]

@tomc You already posted the complete stats for set items, I didn’t feel I needed to repost it. The margin between set items and non-set items decreases at higher leagues, to the point that Diamond set items are equal to Diamond 4-star items (5865), so it’s a non-linear relationship.

[TomC]

@dr_ishmael Ah interesting, thanks for the info!

[KillerKea]

Silver 1 star emblem is 1736.

My starting level 41 wood emblem is 1122 and my starting top and flags were both 3086 so the equipment you start with is weaker than what you get from the wheel spin or pig machine. All my wheel spins items have been either 3 or 4 star.

[dr_ishmael]

@killerkea Added 1736 to the table.

Starter items seem to be “special” in that they don’t fit into the standard spectrum at all. My second account has seen items from levels 32 – 36, which covers the range where the level 41 starter stats should appear, but they don’t.

Wood League 2* stats

Level  Emblem  Top/Flag
   32     984      2625
   33    1080      2880
   34    1110      2960
   35    1140      3040
   36    1170      3120

[KillerKea]

@lodz Thanks for making the table. After seeing it I can now tell you the formulae they are using so you can complete every spot of your table to within 1 because sometimes they truncate a number and sometimes they round a number. Everything is derived from the zero star wood item.

For tops/flags you get a 10% bonus for each league higher than wood and a 1/42 bonus for each star.

For emblems you get a 2/15 bonus or 13.33% for each league above wood and a 1/42 bonus for each star.

Therefore your missing numbers for the platinum emblems are
2232, 2284, 2338, 2391, 2444

The set items increase by only 4% per league above wood.

[dr_ishmael]

@killerkea 1/42 works for level ~41 items, but not for lower levels. This is my dataset for level 30-43 tops/flags (pegged @ 2* as usual), with one point missing at level 38, filled in by my best guess.

Level   Stat  Diff
   30   2475	
   31   2550    75
   32   2625    75
   33   2880   255
   34   2960    80
   35   3040    80
   36   3120    80
   37   3400   280
   38  (3485)  (85)
   39   3570    85  (level 41 0*)
   40   3655    85  (level 41 1*)
   41   3740    85  (level 41 2*)
   42   3825    85  (level 41 3*)
   43   3910    85  (level 41 4*)

The best guess I can make is that it’s some combination of step functions, but the different durations of each static value (80 for 3 levels, but 85 for 6 levels) don’t fit with that idea very well, either.

Since I’m talking low-level stats… @kerravon, do you have any additional data for really-low-level items? You gave me some data on tops/flags over here, but not emblems, and I’m sure you’ve acquired more items since then.

[Lodz]

I completed table. Purple values are not confirmed. This values refer 41 level players.

@killerkea
10% bonus for each league higher is only average value. When i compare values it seems to be 12% 11% 9% 9% and 8% between leagues.

[dr_ishmael]

@lodz It’s cumulative and calculated against Wood League, not incremental against the previous league.

• Stone = 110% * Wood
• Silver = 120% * Wood
• Gold = 130% * Wood
• Platinum = 140% * Wood
• Diamond = 150% * Wood

That’s for tops/flags, of course; emblems would be 113.33%, 126.66%, etc.

[KillerKea]

Since people still don’t understand the formulae I’ll break it down further and give some examples on how to use it.

Base = zero star wood item
Base for level 41 wood top/flag = 3570
Base for level 41 wood set item = 4888
Base for level 41 wood emblem = 1339

Top/Flag Multiplier
Wood = 1.0
Stone = 1.1
Silver = 1.2
Gold = 1.3
Platinum = 1.4
Diamond = 1.5

Set item Multiplier
Wood = 1.00
Stone = 1.04
Silver = 1.08
Gold = 1.12
Platinum = 1.16
Diamond = 1.20

Emblem Multiplier
Wood = 15/15
Stone = 17/15
Silver = 19/15
Gold = 21/15
Platinum = 23/15
Diamond = 25/15

Star Multiplier
0-star = 42/42
1-star = 43/42
2-star = 44/42
3-star = 45/42
4-star = 46/42

To calculate the value of an item you use this

Base of item type * multiplier for item type * multiplier for # of stars

Therefore a 3 star platinum flag would be

3570 * 1.4 * 45/42 = 5355

A 1 star silver emblem would be

1339 * 19/15 * 43/42 = 1736.45 rounded or truncated it still comes out to be 1736

A Stone set item would be

4888 * 1.04 = 5083.52

In this case the number appears to be truncated instead of rounded since the actual number is 5083 however the 4888 number is probably derived from another number so it might actually be something like 4887.7 and 4887.7 * 1.04 = 5083.2)

@dr_ishmael
I only saw data for level 41 items and that was the original intent of this post. I didn’t have any data for lower level items and to be honest I’m not really interested in lower level items because you never stay that level for long and I have no desire to start over, but feel free to expand on my formulae for the lower level items. If you can collect 2-3 data points for 0 star wood items of different levels, then I can calculate the formula they use to determine the value of items as they increase in level and find out what the base for a zero star level 1 wood item is which is like patient zero, but I’m sure you are capable of doing that too.

Since you said 1/42 doesn’t work for non level 41 items, then collect some data points for a specific level and you can use algebra like I did to figure out what the bonus actually is. Maybe the formula they are using the for bonus is something like 1/(level + 1).

[dr_ishmael]

@killerkea Did you look at the list of values I posted? It’s not a simple linear progression. (If it were, I would have already “used algebra” to solve for the linear terms.) 1/42 probably won’t work with higher levels whenever Rovio raises the level cap.

[KillerKea]

@dr_ishmael I meant to ask you how you can have level 43 data when the max level for everyone is currently 41. I figured your data must be inaccurate. If it is non-linear like your data suggests, then you’re going to need a lot more than 2-3 data points to figure out the formula they are using for different levels because it doesn’t look like a curve either. It looks like there are steps, but you need to know when those steps are and how much of an increase for each step. Good luck collecting the data.

[dr_ishmael]

@killerkea I’ve explained this multiple times – star progression is level progression. On the normal GPM, 2* items have identical stats to the 2* crafted items at the same level, so I peg the 2* item to the level. A 3* item at a given level is identical to a 2* item at the next higher level; a 1* item is the same as 2* at the previous level.

Thus: A 0*item is level - 2, 1* is level - 1, 3* is level + 1, 4* (arena reward wheel only) is level + 2. A level 41 4* item is equivalent to a level 43 2* item, and that’s how I treat them in my data.

Also, I know how to do statistical analysis, so please stop treating me like a sixth grader.

[KillerKea]

@dr_ishmael Items I can craft often have very different values. For example, I can craft a Cobalt Saber, Cheese Hammer and Feather Lance for Red. Those do damage of 230, 208 and 219. The GPM items with the same picture are Sparkle Saber, Aromatic Hammer and Annoying Lance and their values do not match the crafted ones so I think your chart is flawed. The data you have seems to indicate that as well.

It is best to use 0* items as the base from which to calculate the final value.

[dr_ishmael]

@killerkea I’ll take this to PMs so we don’t derail this thread any further. If anyone’s interested, just head over here.

[KerrAvon]

@dr_ishmael As always I haven’t been keeping track of when I picked up my items. So they are from levels 12 to 16.

Tops/Flags
Wood 681, 715, 825, 960
Stone 847, 908, 1056, 1122
Silver 924, 1152, 1224, 1296
Gold 1248, 1326, 1404, 1482, 1690
Platinum 1428, 1512, 1596, 1820, 1911
Diamond 1710

Set items
Wood 1275
Stone 1326
Silver 1539
Gold 1596, 1820

Emblems
Wood 248, 383
Stone 408, 434, 459
Silver 456, 542
Gold 504, 536, 567, 599, 683
Platinum 748
Diamond 675, 713

[dr_ishmael]

@killerkea I forgot to say, thank you for figuring out the fractions for the emblem scaling – the fifteenths are working very well. You spurred me into doing some more analysis (that I’d already done but forgot about), and I just figured out how that somewhat odd fraction comes about!

What I had done was to compare the emblem stats to the top/flag stats at the same level/star combinations, but for some reason I must have dismissed the results as inconclusive. However, I looked at that anew and (re?)discovered that emblems are always 3/8 as powerful as tops/flags.

The fifteenths come in when we get to the per-league bonuses. For tops/flags, each league adds 1/10 to the Wood league stat. For emblems, they get 1/20 (5%) of the Wood top/flag stat per league – not, in actuality, a fraction of their own base stat. If you put the fractions together, however, you have 1/20 divided by 3/8, or 1/20 * 8/3 = 8/60 = 2/15.

QED: KillerKea got the right scaling factors without going through the tortuous mathematics. :) He also got it right when he said “the [emblem] number is probably derived from another number” – it’s derived from the top/flag number!

@kerravon Great numbers, thanks! But if you could pleeeeeease record your level and the number of stars on the next arena item you get (tomorrow’s free GAPM roll?), I would be ecstatic. I’ve got your numbers all tabulated into pseudo-levels (i.e. I’ve aligned them across leagues), but I can’t combine them with my other data until I know at least one of them for certain.

[KerrAvon]

@dr_ishmael The Top from Gold league with a value of 1482 is level 15, 3-star. I’ll make sure I have pen and paper handy to record the stats of the next items I get.

I am not planning to increase my level soon. I was just collecting snoutlings to buy Mastery at the Dojo and so have gone up levels. But most classes are at Mastery 5 now, which I am happy with. There is nowhere to go from Diamond league, so we should be able to get some good stats over the next few weeks for Diamond league at level 16.

[KerrAvon]

@dr_ishmael by the progression in my gold tops/flags I would suggest the first 4 are level 15 0,1,2 and 3 star items, with an increment of 78. The last may be a level 15 or 16 4-star item (it was from the reward wheel). I suggest the same for my emblems, in this case with increments of 31-32. The last may also be a level 15 or 16 4-star item (also from reward wheel). I am pretty sure these were still level 15 items, as I have only recently (I believe when I was in the platinum league) moved to level 16. So this would suggest something odd has happened with 4 star items.

[dr_ishmael]

@kerravon That data point allowed me to peg your entire dataset – and you’re absolutely right! Your gold items, both tops/flags and emblems, are levels 13 through 17 @ 2*, with no gaps (that’s equivalent to 0* through 4* @ level 15).

I’ve also solved the pattern for top/flag Wood league stats, from which everything else is calculated per @killerkea’s and my summaries above. Unfortunately, I haven’t been able to devise a formula to represent it, so I’ll just have to describe it.

For a certain number of levels (on a pattern of 6/6/4/4), the base stat is increased by a static amount. This amount is always a multiple of 5, and it increases by 5 for each segment of the pattern. On the last level of each segment, a bonus increase is applied; this bonus is equal to 5 * (level + 3).

Actually, it’s probably better to just make a table:

Wood League top/flag item base stats @ 2*
(subtract 2 from the level to get a 0* progression)

Stats flagged with ### have been recorded directly by myself or @kerravon
  (or were derived from a stat reported at a higher league)

Level   Delta   Bonus   Stat
   -3                      0
   -2      45             45
   -1      45             90
    0      45            135
    1      45            180
    2      45            225
    3      45      30    300
    4      50            350
    5      50            400
    6      50            450
    7      50            500
    8      50            550
    9      50      60    660
   10      55            715 ###
   11      55            770 ###
   12      55            825 ###
   13      55      80    960 ###
   14      60           1020 ###
   15      60           1080 ###
   16      60           1140 ###
   17      60      100  1300 ###
   18      65           1365 ###
   19      65           1430
   20      65           1495
   21      65           1560
   22      65           1625
   23      65      130  1820
   24      70           1890 ###
   25      70           1960 ###
   26      70           2030 ###
   27      70           2100 ###
   28      70           2170
   29      70      160  2400
   30      75           2475 ###
   31      75           2550 ###
   32      75           2625 ###
   33      75      180  2880 ###
   34      80           2960 ###
   35      80           3040 ###
   36      80           3120 ###
   37      80      200  3400 ###
   38      85           3485
   39      85           3570 ###
   40      85           3655 ###
   41      85           3740 ###
   42      85           3825 ###
   43      85           3910 ###

This progression fits all known data points. The fact that it goes to 0 at a level of -3 fits with other formulae I’ve derived for bird base stats and crafted item stats, which are both linear with respect to (level+3) and thus also give 0 at level -3.

The only thing missing is a bonus of 230 at level 43 (aka the 4-star reward wheel items at level 41). For some reason these items are only 85 points stronger than level 42 items, when the pattern says they should be 230 + 85 = 315 points stronger. One explanation is that Rovio didn’t want there to be a huge stat gap between the most-powerful items and the second-most-powerful items, so they deliberately omitted the bonus for now. When they raise the level cap, they’ll probably add it back.

Now we can calculate the health of any banner item given its level, stars, and league. Whoo!