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# What is the chance of rolling such head?

Discussion in 'Single Player Forum' started by Darkshamangarrosh, Dec 2, 2017.

1. ### DarkshamangarroshDiabloii.Net Member

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?

Also what is the chance of finding a 3 Fire Skills 3 Enchant 3 Fire Mastery orb? Or rolling one?

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2. ### ThomasJohnsenDiabloii.Net Member

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I dug up some old stats, I compiled a looong time ago.
My knowledge is rusty at best atm, but based on the calculations, I did years ago:

Lets first establish the basics of the item:

a) A Succubus Skull has a qlvl of 81 and a magic_lvl of 0.

b) Staffmods are divided into tiers. SM and RS are tier 1 and CE is tier 2. The only items that can spawn staffmods of tier 1 and tier 2 are of an ilvl of 24 or lower, so your shrunken head has an ilvl of no higher than 24.

c) Affix levels are calculated based on the following code:
Code:
```if (ilvl>99) then {ilvl=99}

if (qlvl>ilvl) then {ilvl=qlvl}  *!*

if (magic_lvl>0) then {alvl=ilvl+magic_lvl}
else
{
if (ilvl<99-qlvl/2) then {alvl=ilvl-qlvl/2}
else {alvl=2*ilvl-99}
}

if (alvl>99) then {alvl=99}
```
NOTE: The line marked *!* is important - this ilvl is only used in the computation and not stored (if it was, your item could not spawn).

Iterating through the code with ilvl <= 24 and qlvl = 81, we find an alvl of 63.

---

Which in short means that your Succubus Skull is qlvl 81, alvl 63 and has ilvl <= 24.
Any rare Succubus Skull with those specs has a 1 in 58 chance of spawning the Mojo prefix (+2 Sum) (Affix Calc: https://diablo3.ingame.de/diablodb/affix_index.php?lang=en&version=lod&patch=111)

Let us assume, that you shrunken head has an ilvl of 11 or below, which will yield the highest chance of spawning 2 tier 1 staffmods and 1 tier 2 staffmod. Then 16.7% of all staffmods will spawn as SM, 16.7% will spawn as RS and 4.2% will spawn as CE. Only 10% of those will spawn as +3. And only 10% of any item that can spawn staffmods will spawn 3. So I assume the total chance of spawning a rare Succubus Skull with +2 Sum, +3RS, +3SM, +3CE is:
10% * (16.7% * 10%) * (16.7% * 10%) * (4.2% * 10%) * 1/58 = 0.0000000020195 (roughly 1 in 495 millions).

Any shrunken head with higher ilvl will have significantly lower chance of those staffmods.

--------------------------------------------------------------------------------------------------------------------

Any magic orb with ilvl of 37 or above (which is required to spawn tier 4 staffmods (Enchant) together with tier 6 staffmods (Fire Mastery)) has a 10 in 1069 chance of spawning +3 Fire Skills. 30% or all orbs spawn either 2 or 3 staffmods. Enchant has 4% chance of spawning and only 10% of those spawn +3. Fire Mastery also has a 4% chance of spawning, and again only 10% of those spawn +3. So the odds of getting such an orb would be:
30% * (4% * 10%) * (4% * 10%) * 10/1069 = 0.0000000449017 (roughly 1 in 22 millions).

I assume the chance of rolling one is the same as the chance of finding one.

---------------------------------------------------------------------------------------------------------------------

The calculations may be off by a significant margin, since the staffmod generation model is complex and allows for reiteration. And I may have made errors along the way - not having delved into these stats; or math for that matter; in years. They do however give a general idea about the rarity of such items.

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3. ### okeyDiabloii.Net Member

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4. ### Southpaw8668Diabloii.Net Member

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Whatever the odds are, that head is GORGEOUS! I’ve never even seen such a roll on a rare head, thanks for sharing.

5. ### DaveWDiabloii.Net Member

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Why Ber the head? Its not like you gonna get hit alot as a summoner. A P Diamond or UM would have been better imho.

6. ### ThomasJohnsenDiabloii.Net Member

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@okey:
Well - when an item with staffmods is generated, the following process is followed:

1) The number of staffmods is selected. It can be:
a) 3 staffmods 10% chance
b) 2 staffmods 20% chance
c) 1 staffmod 40% chance
d) 0 staffmods 30% chance

2) A base value is selected based on ilvl and goes through some modifications based on item quality and rng. This yields what is called a tier, and based on it, a random skill of 5 is selected (each tier has 5 spells). If the skill chosen isn't legally able to spawn, step 2 is repeated up to 6 times. The whole process can be decribe more simply by:

Base value selection:
Code:
```                    +-------+-------+-------+-------+-------+-------+
| Tier1 | Tier2 | Tier3 | Tier4 | Tier5 | Tier6 |
+===================+=======+=======+=======+=======+=======+=======+
|  1 <= ilvl <= 11  |  80%  |  20%  |       |       |       |       |
| 12 <= ilvl <= 18  |  30%  |  50%  |  20%  |       |       |       |
| 19 <= ilvl <= 24  |  10%  |  20%  |  50%  |  20%  |       |       |
| 25 <= ilvl <= 36  |       |  10%  |  20%  |  50%  |  20%  |       |
| 37 <= ilvl <= 99  |       |       |  10%  |  20%  |  50%  |  20%  |
+-------------------+-------+-------+-------+-------+-------+-------+
```
Skill selection with regards to necromancer spells:
Code:
```+---------------------+-----+------+-----+-------+-------+-------+-------+-------+
|                     |     |      |     | ilvls | ilvls | ilvls | ilvls | ilvls |
| NECROMANCER SPELL   |  ID | ReqI | Tier|  1-11 | 12-18 | 19-24 | 25-36 | 37-99 |
| (Fail Percentage)   |     |      |     |  (4%) | (10%) |  (4%) |  (2%) |       |
+---------------------+-----+------+-----+-------+-------+-------+-------+-------+
| Amplify Damage      |  66 |      |  1  | 16.7% |  6.7% |  2.1% |       |       |
| Teeth               |  67 |      |  1  | 16.7% |  6.7% |  2.1% |       |       |
| Bone Armor          |  68 |      |  1  | 16.7% |  6.7% |  2.1% |       |       |
| Skeleton Mastery    |  69 |      |  1  | 16.7% |  6.7% |  2.1% |       |       |
| Raise Skeleton      |  70 |      |  1  | 16.7% |  6.7% |  2.1% |       |       |
|                     |     |      |     |       |       |       |       |       |
| Dim Vision          |  71 |      |  2  |  4.2% | 11.1% |  4.2% |  2.0% |       |
| Weaken              |  72 |      |  2  |  4.2% | 11.1% |  4.2% |  2.0% |       |
| Poison Dagger       |  73 | knif |  2  |  ***  |  ***  |  ***  |  ***  |       |
| Corpse Explosion    |  74 |      |  2  |  4.2% | 11.1% |  4.2% |  2.0% |       |
| Clay Golem          |  75 |      |  2  |  4.2% | 11.1% |  4.2% |  2.0% |       |
|                     |     |      |     |       |       |       |       |       |
| Iron Maiden         |  76 |      |  3  |       |  4.4% | 10.4% |  4.1% |   2%  |
| Terror              |  77 |      |  3  |       |  4.4% | 10.4% |  4.1% |   2%  |
| Bone Wall           |  78 |      |  3  |       |  4.4% | 10.4% |  4.1% |   2%  |
| Golem Mastery       |  79 |      |  3  |       |  4.4% | 10.4% |  4.1% |   2%  |
| Raise Skeletal Mage |  80 |      |  3  |       |  4.4% | 10.4% |  4.1% |   2%  |
|                     |     |      |     |       |       |       |       |       |
| Confuse             |  81 |      |  4  |       |       |  4.2% | 10.2% |   4%  |
| Life Tap            |  82 |      |  4  |       |       |  4.2% | 10.2% |   4%  |
| Poison Explosion    |  83 |      |  4  |       |       |  4.2% | 10.2% |   4%  |
| Bone Spear          |  84 |      |  4  |       |       |  4.2% | 10.2% |   4%  |
| Blood Golem         |  85 |      |  4  |       |       |  4.2% | 10.2% |   4%  |
|                     |     |      |     |       |       |       |       |       |
| Attract             |  86 |      |  5  |       |       |       |  4.1% |  10%  |
| Decrepify           |  87 |      |  5  |       |       |       |  4.1% |  10%  |
| Bone Prison         |  ** |      |  5  |       |       |       |  4.1% |  10%  |
| Summon Resist       |  89 |      |  5  |       |       |       |  4.1% |  10%  |
| Iron Golem          |  90 |      |  5  |       |       |       |  4.1% |  10%  |
|                     |     |      |     |       |       |       |       |       |
| Lower Resist        |  91 |      |  6  |       |       |       |       |   4%  |
| Poison Nova         |  92 |      |  6  |       |       |       |       |   4%  |
| Bone Spirit         |  93 |      |  6  |       |       |       |       |   4%  |
| Fire Golem          |  94 |      |  6  |       |       |       |       |   4%  |
| Revive              |  95 |      |  6  |       |       |       |       |   4%  |
+---------------------+-----+------+-----+-------+-------+-------+-------+-------+
```
(You may note that the numbers don't add up to the same values in the 2 tables, which is due to the Poison Dagger spell, that can only legally spawn on 'knif' type items, and thus only spawns in very rare occasions where step 2) fails 6 times).

3) The amount of addition to the skill is selected based on:
a) +3 with 10% chance
b) +2 with 30% chance
c) +1 with 60% chance

---

Any item generated with ilvl 1 would thus spawn 3 staffmods with +3RS, +3SM and +XAD:
(chance of 3 staffmods) * (Chance of +3RS) * (Chance of +3SM) * (Chance of +XAD) =
10% * (16.7% * 10%) * (16.7% * 10%) * (16.7%) = 0.000004657 (roughly 1 in 215 thousand).

Given the tables and the process, calculating the odds of any necromancer head should be manageable.

---

Last edited: Dec 2, 2017
7. ### jiansonzDiabloii.Net Member

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Unless I am missing something, that rare Succubus Skull must have been rerolled with 6 Pskulls by another character (a very low level one) than the one who found it, right?

EDIT: alternatively it's been imbued by a low level character.

8. ### ThomasJohnsenDiabloii.Net Member

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I think it would have to be one of the two. I doubt a Succubus Skull can drop in an area that will yield an ilvl low enough.
If it's an imbue btw, the odds are slightly better than what I've calculated, since the odds of getting +3/+3 are slighly higher (ilvl and ilvl/2 resp is added to the rnd[100]).

9. ### helveteDiabloii.Net Member

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Correct, these items cannot exist for untwinked characters.

If you have a Bloodlord Skull rerolled once with the 3pgem recipe in 1.07, you can in theory roll +3 summoning with three tier 1 or 2 staffmods when brought forward to 1.09+. This would enable the magic only pdr and life suffixes too.

10. ### DarkshamangarroshDiabloii.Net Member

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Yeah im aware of that, I even have your older thread bookmarked

zzz too bad its a 1.07 Bloodlord skull why blizzard...oh why...Imagine all the cool +3 skilltab items such as the 1.07 3 Oak 3 Summoning 3 Grizzly 3 dire wolf Dream Spirit or a 3 Offensive Auras 3 Fanaticism 3 Concentration 3 Might Caddy or a 3 summoning 3 raise skeleton 3 skeleton mastery Unearthed wand

Yeah I own it on the Us East Nl realm..can show it and all....it had to be ...er.....custom rolled(and no, not through Charsifood)but tbh it was quite expensive...I know jsp/item importers(by the way blizzard finally fixed imports like a week ago(yes 15 years later)meaning more imports may not exist anymore) are frowned upon but I thought it should be mentioned ..but it cost roughly 12k-15k(yes thats thousands) hrs when I paid for it (when hrs were 1-1.5 of this fg currency ea)

Last edited: Dec 3, 2017
11. ### okeyDiabloii.Net Member

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Thanks,

12. ### BKCDiabloii.Net Member

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i refuse to waste words in this thread[/edit]