The Study On Snail Helms

I was tasked with this recent dilemma - how are item stats distributed, is it normal frequency from minimum to maximum, or is there a curve? The admins weren't particularly helpful in answering it, so I have decided to do a case study. The most common item I currently get, grinding or looting chests, is the snail helmet. So, I am collecting data on these, for the health stats. If you get a snail helm from grinding or looting, please identify it and post a screenshot/tell me the health bonus and health regen. I am using these two stats for my investigation. Also, it is important that you don't choose one with specifically good stats- this has to be random.

Example: Hey, I got 2 snail helms! the first is 700 hp, 230 regen, and the second is 840 hp, and 170 regen.

Thank you for your time :)

---

EDIT: I've collected all 50! I graphed the results here. Red line is HP bonus, and Blue line is HP Regen bonus. Black marks represent averages.

HP: 28% of helms were above average value.
Regen: 38% of helms were above average value.

Both are around what the expected range was (30%). SO, it seems that @Nyam was right =P

 

There's a base number you can find in the Item guide at wynncraft.com/help, and the range is 0.3-1.3 * the base number.

Let's say Steamjet walkers have a base of 20% walk speed. That means it can get anywhere from 6% to 26%.

 

I know that. I want to know the frequency of the value of each stat. You would expect average values to be more common than mimum values, right? That's what I'm testing.

 

It's completely and utterly random.

 

I think I might know how this works, kinda.

There used to be a glitch where items with certain characters (like é) broke. This breaking could also be triggered temporarily on other items too by right-clicking a merchant, and would stay in effect for all items in your inventory until a few seconds after you closed the merchant GUI. This glitch was most well-known for allowing people to see what items are before they're identified (although that was kinda useless-ish since most towns with merchants have IDers anyway), but if it happened to an already-identified item, it converted the IDs into a long string of purple text, which shows a few other things. [Github link, with pictures] (This glitch was fixed sometime around patch 7 don't ban me pls)

From this, we can see how identifying stuff works: For each identification an item gets, a roll between 30% and 130% is chosen, which is multiplied by the base value. We also know that this value is then always rounded up (as opposed to being rounded to the nearest whole value, which was what happened before Gavel), since items with base identifications of +7 can get +10. It also means that identifications are (probably) determined upon identifying the item, although that's kinda irrelevant.

For example, Speaker has a base XP Bonus of +21%. If someone finds a Speaker, identifies it and its XP bonus gets a roll of 84%, it will get +18% XP, because the base value of 21 is multiplied by 84% (or 0.84), giving a result of 17.64, which rounds up to 18%. If another Speaker gets a 130% roll on its XP bonus, it will get +28% XP since 21*1.3 = 27.3, which rounds up to 28%. Speaker is also a perfect example of proof that the value always rounds up, since it's a known fact that Speaker has max 28% XP and this wouldn't be possible if 27.3 rounded to 27 instead of 28. If you actually work out the values of each roll, you can see that you pretty much have the same chance of getting ID values, apart from maximum and minimum values, which are often rarer (some more than others) due to the fact that the percentage ranges which round to those values are cut off by the maximum and minimum rolls of 30% and 130%.

Spoiler: Math

XP bonus rolls on Speaker (base is +21%)

+7% XP = 30-33% roll (~3.96% chance)
+8% XP = 34-38% roll (~4.95% chance)
+9% XP = 39-42% roll (~3.96% chance)
+10% XP = 43-47% roll (~4.95% chance)
+11% XP = 48-52% roll (~4.95% chance)
+12% XP = 53-57% roll (~4.95% chance)
+13% XP = 58-61% roll (~3.96% chance)
+14% XP = 62-66% roll (~4.95% chance)
+15% XP = 67-71% roll (~4.95% chance)
+16% XP = 72-76% roll (~4.95% chance)
+17% XP = 77-80% roll (~3.96% chance)
+18% XP = 81-85% roll (~4.95% chance)
+19% XP = 86-90% roll (~4.95% chance)
+20% XP = 91-95% roll (~4.95% chance)
+21% XP = 96-100% roll (~4.95% chance)
+22% XP = 101-104% roll (~3.96% chance)
+23% XP = 105-109% roll (~4.95% chance)
+24% XP = 110-114% roll (~4.95% chance)
+25% XP = 115-119% roll (~4.95% chance)
+26% XP = 120-123% roll (~3.96% chance)
+27% XP = 124-128% roll (~4.95% chance)
+28% XP = 129-130% roll (~1.98% chance)

Spoiler: More math

30% roll: 21*0.3 = 6.3 -> rounds up to +7% (Minimum)
31% roll: 21*0.31 = 6.51 -> rounds up to +7%
32% roll: 21*0.32 = 6.72 -> rounds up to +7%
33% roll: 21*0.33 = 6.93 -> rounds up to +7%
34% roll: 21*0.34 = 7.14 -> rounds up to +8%
35% roll: 21*0.35 = 7.35 -> rounds up to +8%
36% roll: 21*0.36 = 7.56 -> rounds up to +8%
37% roll: 21*0.37 = 7.77 -> rounds up to +8%
38% roll: 21*0.38 = 7.98 -> rounds up to +8%
39% roll: 21*0.39 = 8.19 -> rounds up to +9%
40% roll: 21*0.4 = 8.4 -> rounds up to +9%
41% roll: 21*0.41 = 8.61 -> rounds up to +9%
42% roll: 21*0.42 = 8.82 -> rounds up to +9%
43% roll: 21*0.43 = 9.03 -> rounds up to +10%
44% roll: 21*0.44 = 9.24 -> rounds up to +10%
45% roll: 21*0.45 = 9.45 -> rounds up to +10%
46% roll: 21*0.46 = 9.66 -> rounds up to +10%
47% roll: 21*0.47 = 9.87 -> rounds up to +10%
48% roll: 21*0.48 = 10.08 -> rounds up to +11%
49% roll: 21*0.49 = 10.29 -> rounds up to +11%
50% roll: 21*0.5 = 10.5 -> rounds up to +11%
51% roll: 21*0.51 = 10.71 -> rounds up to +11%
52% roll: 21*0.52 = 10.92 -> rounds up to +11%
53% roll: 21*0.53 = 11.13 -> rounds up to +12%
54% roll: 21*0.54 = 11.34 -> rounds up to +12%
55% roll: 21*0.55 = 11.55 -> rounds up to +12%
56% roll: 21*0.56 = 11.76 -> rounds up to +12%
57% roll: 21*0.57 = 11.97 -> rounds up to +12%
58% roll: 21*0.58 = 12.18 -> rounds up to +13%
59% roll: 21*0.59 = 12.39 -> rounds up to +13%
60% roll: 21*0.6 = 12.6 -> rounds up to +13%
61% roll: 21*0.61 = 12.81 -> rounds up to +13%
62% roll: 21*0.62 = 13.02 -> rounds up to +14%
63% roll: 21*0.63 = 13.23 -> rounds up to +14%
64% roll: 21*0.64 = 13.44 -> rounds up to +14%
65% roll: 21*0.65 = 13.65 -> rounds up to +14%
66% roll: 21*0.66 = 13.86 -> rounds up to +14%
67% roll: 21*0.67 = 14.07 -> rounds up to +15%
68% roll: 21*0.68 = 14.28 -> rounds up to +15%
69% roll: 21*0.69 = 14.49 -> rounds up to +15%
70% roll: 21*0.7 = 14.7 -> rounds up to +15%
71% roll: 21*0.71 = 14.91 -> rounds up to +15%
72% roll: 21*0.72 = 15.12 -> rounds up to +16%
73% roll: 21*0.73 = 15.33 -> rounds up to +16%
74% roll: 21*0.74 = 15.54 -> rounds up to +16%
75% roll: 21*0.75 = 15.75 -> rounds up to +16%
76% roll: 21*0.76 = 15.96 -> rounds up to +16%
77% roll: 21*0.77 = 16.17 -> rounds up to +17%
78% roll: 21*0.78 = 16.38 -> rounds up to +17%
79% roll: 21*0.79 = 16.59 -> rounds up to +17%
80% roll: 21*0.8 = 16.8 -> rounds up to +17% (Average)
81% roll: 21*0.81 = 17.01 -> rounds up to +18%
82% roll: 21*0.82 = 17.22 -> rounds up to +18%
83% roll: 21*0.83 = 17.43 -> rounds up to +18%
84% roll: 21*0.84 = 17.64 -> rounds up to +18%
85% roll: 21*0.85 = 17.85 -> rounds up to +18%
86% roll: 21*0.86 = 18.06 -> rounds up to +19%
87% roll: 21*0.87 = 18.27 -> rounds up to +19%
88% roll: 21*0.88 = 18.48 -> rounds up to +19%
89% roll: 21*0.89 = 18.69 -> rounds up to +19%
90% roll: 21*0.9 = 18.9 -> rounds up to +19%
91% roll: 21*0.91 = 19.11 -> rounds up to +20%
92% roll: 21*0.92 = 19.32 -> rounds up to +20%
93% roll: 21*0.93 = 19.53 -> rounds up to +20%
94% roll: 21*0.94 = 19.74 -> rounds up to +20%
95% roll: 21*0.95 = 19.95 -> rounds up to +20%
96% roll: 21*0.96 = 20.16 -> rounds up to +21%
97% roll: 21*0.97 = 20.37 -> rounds up to +21%
98% roll: 21*0.98 = 20.58 -> rounds up to +21%
99% roll: 21*0.99 = 20.79 -> rounds up to +21%
100% roll: 21*1 = 21 -> (whole numbers don't get rounded) +21% (Base value)
101% roll: 21*1.01 = 21.21 -> rounds up to +22%
102% roll: 21*1.02 = 21.42 -> rounds up to +22%
103% roll: 21*1.03 = 21.63 -> rounds up to +22%
104% roll: 21*1.04 = 21.84 -> rounds up to +22%
105% roll: 21*1.05 = 22.05 -> rounds up to +23%
106% roll: 21*1.06 = 22.26 -> rounds up to +23%
107% roll: 21*1.07 = 22.47 -> rounds up to +23%
108% roll: 21*1.08 = 22.68 -> rounds up to +23%
109% roll: 21*1.09 = 22.89 -> rounds up to +23%
110% roll: 21*1.1 = 23.1 -> rounds up to +24%
111% roll: 21*1.11 = 23.31 -> rounds up to +24%
112% roll: 21*1.12 = 23.52 -> rounds up to +24%
113% roll: 21*1.13 = 23.73 -> rounds up to +24%
114% roll: 21*1.14 = 23.94 -> rounds up to +24%
115% roll: 21*1.15 = 24.15 -> rounds up to +25%
116% roll: 21*1.16 = 24.36 -> rounds up to +25%
117% roll: 21*1.17 = 24.57 -> rounds up to +25%
118% roll: 21*1.18 = 24.78 -> rounds up to +25%
119% roll: 21*1.19 = 24.99 -> rounds up to +25%
120% roll: 21*1.2 = 25.2 -> rounds up to +26%
121% roll: 21*1.21 = 25.41 -> rounds up to +26%
122% roll: 21*1.22 = 25.62 -> rounds up to +26%
123% roll: 21*1.23 = 25.83 -> rounds up to +26%
124% roll: 21*1.24 = 26.04 -> rounds up to +27%
125% roll: 21*1.25 = 26.25 -> rounds up to +27%
126% roll: 21*1.26 = 26.46 -> rounds up to +27%
127% roll: 21*1.27 = 26.67 -> rounds up to +27%
128% roll: 21*1.28 = 26.88 -> rounds up to +27%
129% roll: 21*1.29 = 27.09 -> rounds up to +28%
130% roll: 21*1.3 = 27.3 -> rounds up to +28% (Maximum)

Because of the way this works, it's not possible to get some values when you ID something with a really high base ID. For example, Pure gets base +400% spell damage, and the maximum spell damage it can get is +520%. But because 400*1.29 = 516%, the second-highest possible spell damage on Pure is +516% and not +519%. So, technically speaking, if you have a Pure with +516% spell damage, its spell damage may be considered as being 'one off max'.

This way of storing IDs is also why all items in the server get updated when something gets nerfed/buffed. For example, if you had a Return to Ether with a 130% roll, giving it +33% walk speed back when the base value was 25, it would stay at max walk speed (+17%) when that got nerfed to base 13. Sometimes, because of how rolls work, an item might change from having a maximum ID to having the same ID at one off max or the reverse. If you had a Return to Ether with a 125% roll and +32% walk speed, its walk speed would actually become the maximum of 17% after the nerf because the roll stays the same, but with the new base walk speed, it rounds up to the maximum. (So if you're trying to buy a Return to Ether with more than the post-nerf maximum walk speed, you won't be able to, as they get updated and no longer exist.)

From my personal experience, the 30 to 130% roll is completely random, although you could argue otherwise and it's kinda hard to assume so without any evidence. I get a metric ton of Awakenings and Demon's Wills when I lootroute, so I'll collect some of those, ID them and then graph the IDs. I'll edit this post when I find more information.

Edit: Just realised that Awakening has really low base IDs, so I've started collecting Demon's Wills instead so that the graph is less bland.

Spoiler: First 64 Demon's Wills' life steal rolls graphed

Almost thought I saw a pattern at the lower end here but then 101-110% ruined everything, so now I'm not sure what happened there. More data coming soon™

TL;DR: IDs probably have pretty much equal chances of happening. In some cases, minimums and maximums are slightly (or not so slightly, depending on the item) rarer than other IDs.

Why am I writing these kind of things as replies and not threads

 

*enthusiastic clapping*

 

I got one with +1040 hp and 260 regen

 

This is amazing! Thank you so much! That's exactly what I wanted to test. Yet, I still feel like it should be changed a bit, where it is more likely to get average than extreme maxima/minima.

 

Here's an idea, not as detailed as yours but oh well

0.3-0.4x - 2.5% chance of getting it
0.4-0.5x - 5%
0.5-0.6x - 5%
0.6-0.7x - 7.5%
0.7-0.8x - 10%
0.8-0.9x - 15%
0.9-1.0x - 20%
1.0-1.1x - 20%
1.1-1.2x - 10%
1.2-1.3x - 5%

This makes it so 35% of the time, you will get higher than average. I feel like this is a good distribution to keep good items rare-ish. Abou 1/20 of the time, you would get a really good item, but remember, there is almost a 50% chance of getting one less than 0.9x the base value. And minimum is set so low cause nobody wants to get really really bad stuff (says me with the 14 off minimum hp Leo)

 

health bonus 608, health regen 250
bonus, 952 , regen 170 ,
bonus 624, regen 250

 

wait, is this based on numbers?
And if so, is this all the numbers combined, or individual ID's?
Because if its the item's ID's overall, then the small chance to get the highest and lowest ID's make sense, as there would be only 1 way to get a maxed item, whereas multiple ways to get a mediocre/not maxed item.
Ex. lets say max is a total of 100 distributed through 2 stats. That would mean that both stats have to be 50 out of 50
However, to get a total of 50, there are many combinations, such as 30 + 20 and 21+29.

 

I have sold at least 30 snail helmets in my time ;-;

 

health 288
regen 182

 

If you ID them and then sell them you actually lose money. Fun fact.

 

I believe I profited on almost every one. It was about 60e to id and then sold for 60-150e.

 

I'm pretty sure it takes 160e to ID, not 60. I'll test asap.

 

904hp and 216hp regen

 

584, 254 regen
400, 98 regen

 

He knows that, but he's doing like a survey statistics thing, to find the real average.

 

You just need math. Taking about 10 snail helms doesn't show a 'real' average.