Golden Pig Machine

[dr_ishmael]

Just got a Ballista on my alt account this morning (thanks to @partshade’s tip), so filled in the level 34 weapon stat for Bomb/Blues – 374.

@kerravon Thanks for your data!

I’ve placed the “unknown” values into the table and attempted linear approximations on all of the series. I’d like to ask for a double-check on a couple points, just in case there were any data-entry errors among all those numbers:

• @partshade Chuck weapon level 37
• @kerravon Red weapon level 32
• @burbman Chuck offhand level 33

Unfortunately, only a couple of the series appear to fit a completely linear formula. On most, the calculated values come out high on one point and low on a different point. This implies that there are multiple steps to the calculation with rounding happening at different points, rather than a single step with a single rounding at the end, which is how base stats and normal item stats work.

One possibility is that this calculation starts with the 0* crafted item stat and adds a scaled offset to it, so I tried subtracting the 0* stat from our values here. These offsets are still linear, but I still can’t get exact formulas.

[Angry Johnny]

Here are some more numbers if you need them:

Weapon
Red: 276 228
Chuck: 400 332 322
Matilda: 276 228 216 204
Bomb: 442 250 202
Blues: 442 364

Offhand
Red: 1394 636
Chuck: 704 580
Matilda: 1077 889 866 818
Bomb: 1118 924
Blues: 884 730

Sorry that I have no more, I usually recycle duplicate Set Items.

[dr_ishmael]

@angryjohnny More numbers are always good! Although most of yours were already in the table, there were a couple new ones. I’m pretty sure you have at least one typo, too – the maximum Attack for Red/Matilda weapons is currently 276, not 279. But that’s an easy typo to make on the numpad. ;) Also, could you re-check Chuck’s 580? I bet that’s a typo of 520. And Matilda’s 866 is 1 off from being linear with the rest of her offhand data, could it actually be 865?

To anyone else wishing to contribute – please check against DA TABLE (linking again for convenience) for the numbers we already know.

[Angry Johnny]

@dr_ishmael Yes, sorry. Red’s 279 was suppose to be 276 but the others are actually accurate.

Here are the screenshots to prove it:

[dr_ishmael]

@angryjohnny Thanks for checking. @burbman, that 580 clears up the point that I had asked you to double-check, so you’re off the hook. :P

[Angry Johnny]

@dr_ishmael I have just done some experimentation with the Set Item weapons and a calculation that seems to work for me is:

Red/Matilda
Base Value = 30
Multiplier = 6

Chuck
Base Value = 46
Multiplier = 8.6

Bomb/Blues
Base Value = 52
Multiplier = 9.6

With these numbers and the calculation:
Rounded((Strength of Weapon – Base Value) / Multiplier)
you get the Levels of the Set Item weapons in the document.

Make note that this is just some experimentation so it could be completely wrong.

[MVNLA2]

@partshade — Forgot to log out of Rovio account last night, so did this morning before playing golf. Got the ad when I got back.

[KerrAvon]

@dr_ishmael I just checked through all of the numbers I provided and can confirm they are correct as per values in my game.

[Anonymous]

@mvnla2 @dr_ishmael Glad my tip worked so well! Nobody would of ever thought that Rovio account had a connection with video ads huh?

@dr_ishmael Tonight I can double check on my stats. Will report as soon as possible.

[Anonymous]

@dr_ishmael Just checked ALL my stats and they are correct. Also just got a level 41 Golden Bullet today for Bomb with 1118 health.

[dr_ishmael]

@partshade @kerravon Thanks for checking!

@angryjohnny That’s almost what I’m going for, but I don’t want to just derive the level from the stat value, I want to be able to calculate the stat from the level. Try re-calculating the Attack values with your parameters, i.e. Stat = Round(Multiplier * Level + Base Value). There are errors all over the place.

[KerrAvon]

@dr_ishmael It is very strange indeed. My first thought was to base the calculations on what you have discovered previously using the multiplier of level+3 and a base value.

This was not even close, so instead I tried a multiplier of level+5. In this case the calculated values were very close to the reported values. But some calculated values were very slightly out. If you plot the data on a graph then the estimated curve and the reported values pretty much line up. The data looks linear.

The simplest example is with Red’s/Matilda’s attack. The base value is 6, the multiplier is level+5, and most points match exactly – except level 28 (197 instead of 198) and level 32 (221 instead of 222).

I hope you have had more luck or some further insight.

I should also add here, since you have included items from below level 30, I have a level 28 weapon for Matilda at strength 197. This was not in my original list.

[dr_ishmael]

@kerravon Yep, I’d noticed the apparent level+5 offset as well. Your new number there is interesting – it’s only the second data point we have for Red/Matilda weapons at an even-numbered level, and both of them deviate from the formula. I have a third one, actually, at an even lower level – L24 is 173, which also deviates.

I wonder if every even-numbered level is like this, and the pattern is “+5 at even levels, +7 at odd levels.” I know patterns like this are significant, but it’s been 10 years since I took a statistics class so I can’t remember what they mean.

[MVNLA2]

What about a non-integer multiplier or offset?

[dr_ishmael]

@mvnla2 In regards to Red/Matilda weapons, this type of pattern is impossible to reproduce with a simple linear formula, regardless of the precision of the parameters. The calculation has to have multiple steps in order to produce a pattern like that.

(If the pattern only changed by 1 each step, i.e. from +5 to +6, then that would indicate that the factor is 5.5. But it changes by 2 each step, from +5 to +7.)

For the other series – when you have both positive and negative deviations, no amount of precision will help.

[Eric2203]

@dr_ishmael

3 more data points you didn’t have on your spreadsheet yet:

Red – Offhand – 818
Chuck – Weapon – 374
Matilda – Offhand – 1054

[dr_ishmael]

@eric2203 Thanks, added!

[Eric2203]

@dr_ishmael @angryjohnny @mvnla2

I don’t think the formula is as simple as Strength=Ax+B where x is the level, A is the multiplier and B is the offset. I’ll attempt to describe why I’m stating that…

You can see the progression isn’t linear. For example, let’s use Chuck’s weapon strength. @dr_ishmael tells us that he has 3 known data points: level 29 – 296, level 37 – 364, level 41 – 400. 41-29=12 and 400-296=104. A potential multiplier could be 104/12=8.667. The offset works out to 45 in that case. Problem is, at level 37, which is our other known data point, this falls apart: 37*8.667+45=365.7.

What this tells me is that the offset is also a function of the level. So the formula is probably more like Strength=Ax+Bx (x being the level).

But… that’s not right either: Ax+Bx is the same as (A+B)*x. We’re back to a linear formula, which I’ve just said is incorrect. So long story short, I came up with the following formula:

Strength=Ax+B/(100-x)

That also comes from the fact that the offset seems to be inversely proportional to the level. That’s why I have something like this: B/(100-x).

Forgive me for not explaining this more clearly, but at the end of the day, it seems to almost work. Using Chuck’s known data points for weapon strength in @dr_ishmael’s spreadsheet, I came up with the following values for A and B:

Strength=7.18*x + 6236/(100-x) where x is the level.

This “almost” works for every level. If I plug this into Excel, I get the following:

Level Strength (Chuck)
1 70.17779293
2 77.99888736
3 85.83323648
4 93.6812545
5 101.5433731
6 109.4200422
7 117.3117313
8 125.2189301
9 133.1421499
10 141.0819248
11 149.0388128
12 157.0133973
13 165.0062886
14 173.0181251
15 181.0495757
16 189.1013407
17 197.1741545
18 205.2687872
19 213.3860467
20 221.5267817
21 229.6918837
22 237.8822897
23 246.0989857
24 254.3430094
25 262.615454
26 270.9174717
27 279.2502777
28 287.6151549
29 296.0134585
30 304.446621
31 312.916158
32 321.4236743
33 329.9708704
34 338.55955
35 347.1916277
36 355.8691377
37 364.5942435
38 373.3692482
39 382.1966058
40 391.0789339
41 400.0190276

It’s slightly off compared to the data from @dr_ishmael, but it’s very close! And the value for level 33 seems totally wrong (332). Looks like @angryjohnny provided that data point. You sure about that one, @angryjohnny?

I haven’t done the other birds and I haven’t done off-hands either. If someone could take a look at this and see if that makes sense, I’d appreciate it.

I do have one problem with what I just did: I don’t see a programmer at Rovio picking the values I calculated out of thin air. There must be some reasoning behind them. These values may themselves be derived from something else within the game. Who knows…

[MVNLA2]

I haven’t been paying a lot of attention to the numbers, but people must have some of the “same” set items obtained at the same level. Are they the same? Is it possible that the value depends on the mastery of your bird as well as your level?

[Anonymous]

@mvnla2 Likely not. Mastery was added after the Set Items and when I change my bird from Veteran to Elite in the old version I didn’t see any change.

[KerrAvon]

There are a number of data points that are in more than one players data sets. The values are not dependent on mastery. The value of 332 has been provided by three people and I believe is correct.

I think it would be really useful if others added their own set item values, even if the exp levels when they were obtained are not known.

[Eric2203]

@kerravon You’re right. I hadn’t gone back to the previous page initially. Now that I have, I see you also provided that value. So did @burbman.

It’s weird how that one is off from the rest. Guess that throws my values off. I know it’s not linear though, so there’s gotta be something else we’re missing.

[KerrAvon]

@eric2203 Sorry, but I believe your curve deviates from the actual data, particularly at the lower experience levels. This formula will also have issues when you get close to an experience level of 100.

If you plot the equation for red’s/matilda’s weapons

attack value = (experience level + 5) x 6,

with attack value as y-axis and experience level as x-axis, then you have a straight line which would cross the y-axis at 30.

You can overlay the actual recorded values onto this straight line. All of the actual recorded values match the curve exactly except for those from levels 24, 28, and 32, which are all exactly a value of 1 below the value on the curve. The actual recorded points seem to fit this straight line (linear) curve.

You can do the same with the curves for the rest of the set weapons and offhand items. I don’t known the ins and outs of this forum to upload my graphs from excel, but the rest of the curves seem to fit straight lines.

I have used red’s/matilda’s weapon as an example, because it has a simple factor of 6. For all the rest of the curves, this factor is estimated with one or two decimal places. For example, the value I have for chuck’s weapon is 8.7. In this case there is one recorded point (the level 33 item) that seem to deviate from the curve by a value of approx. 1.

It is odd that some values deviate from the curves. It may be they have an unusual way of calculating values for set items – rather than just applying the equation. For example, as @dr_ishmael has suggested for red’s weapon, by alternating between +5 and +7 for even and odd experience levels. Overall this would give an average factor of 6.

If we want to see the patterns, which appear to be unique for each set item (although Red’s and Matilda’s weapons are the same, as well as Blues’ and Bomb’s weapons), then we will need a lot more actual data points.

[dr_ishmael]

@eric2203 Everything else I’ve investigated in this game has relatively simple linear scaling, and I don’t expect the set items to be different enough that they need an inverse factor. What I meant by a “multiple-step calculation” is that there are multiple points where intermediary results are rounded, which introduces a variance that makes the final results deviate from a strict linear formula.

An example of this that I’ve actually worked out is the Wealthy Rogue’s health. (I’ve been tracking pig stats in all the castles since level 17 on my alt account; WR appears in the Cobalt castle.) I was able to approximate WR’s health with a linear formula, except that every 8 levels starting from 20 I’d be high by 1, and every 8 levels starting from 22 I’d be low by 1. This annoyed the hell out of me… until I finally realized that WR’s health was always exactly half of the Big Boss’s health. Now, BB I could calculate exactly with the formula Health = Bround(74.75 * (Level+3)). All I had to do was add a second rounding step to it as Health = Bround(0.5 * Bround(74.75 * (Level+3))), and I now had the WR’s health calculated exactly at all levels.

(Bround = banker’s rounding function, i.e. “round to even” as I’ve described previously.)

That was actually the first thing I tried to do for set item stats, but it doesn’t appear to work for this case. Another possible multi-step form is adding the rounded results from two separate linear formulas – that’s why I had attempted to work it out as an offset from the standard item values. Just now I tried an offset from the base bird stats. Nothing is working out, though.

[MVNLA2]

As far as I’ve seen so far, the values are no more than + or – 1 from perfectly linear after rounding to the nearest integer. What if we assume the Rovio programmers take undue delight in sending people like us on wild goose chases? They could have a look-up table for the set item values, and either intentionally or unintentionally increased/decreased some by 1.