Help calculate Baal dropchance for specific ring.

[EasyG]

Warning: only for statistic goeroes

Hi,
Im from singleplayer which means Baal is the only possible champion to drop Ilvl99 items. I am interested to find myself a ring with lvl6 firebolt charges and wondered if you could help me calculate how the odds are for this ring to drop.

The assumptions are I play with /players 3 and 200 MF.

The odds for Baal to drop any ring at /players3 according to atma is 1/20. I dont rly know how to calculate the chances for this ring to be magic or rare. so there is the first problem in my calculation.

FCR and firboltcharges are both a suffix, so in order to have them both at 1 ring I need a rare ring with a minimum of 2 suffixes.

Magic rings:
For simplicity, next step I wanted to take is to just look at magic rings, getting the firebolt charges suffix. According to the item generation tutorial I have 75% chance to get a suffix. Now the hard part is to calculate the odds for this suffix to be fireboltcharges, and i will need your help again.

I will tell here how i think it will work. According to the arreat summit, there are 16 main suffixgroups, 1 of them containing the spell charges, but since ive seen items with multiple affixes inside 1 group e.g. fire resist and cold resist, I assume I have to look at the subgroups. There are a huge amount of them, so I will just look at the subgroups that can spawn at rings. This are 23 of them. Assuming all these groups have same rarity (does anyone know if there is a differece in rarity, I feel like seeing some affixes way more often as others), the odds to take the sorc charged skills group would be 1/23. There are 4 different possible skillcharges for sorcs, so the odds to get the firebolt one would be 1/23*1/4=1/92. and so the chance for a magic ring to have thee "of firebolt"suffix would be 3/4*1/92=1/123.

However. I have never seen a rare item with 2 different charged skills at it, so I have the feeling that all charged skills might be in 1 group. In the case of rings, this would be just necro skillcharges and sorc skillcharges. there would be 22 groups and 8 skills in the charges group changing the odds to 1/22*1/8*3/4=1/261

Rare rings

Firebolt lv6 only
Now things get rly interesting. I need to calculate first the odds at 1/2/3 suffixes at 1 rare ring. According to the tutorial rare items get 3-6 affixes with each 50% chance to be suffix with a max of 3 suffixes.

Breaking it down:
1/4 chance at 3 affixes
-1/8 0 suffix >2/64
-3/8 1 suffix >6/64
-3/8 2 suffix >6/64
-1/8 3 suffix >2/64
1/4 chance at 4 affixes
-5/16 1 suffix >5/64
-6/16 2 suffix >6/64
-5/16 3 suffix >5/64
1/4 chance at 5 affixes
-1/2 2 suffix >8/64
-1/2 3 suffix >8/64
1/4 chance at 6 affixes
-1/1 3 suffix >16/64

so in total the chance at an amount of suffixes at a rare ring would be:
0: 2/64
1: 11/64
2: 20/64
3: 31/64

Averagle a ring would have 144/64=2.25 suffixes

So the odds for a rare ring to get "of firebolt" suffix would be 2.25*1/261=1/117 chance. Actually a bit better since not the same 2 suffixgroups can spawn at 1 ring.

conclusion: Assuming all my assumptions are right the odds for a magic ball ring to have firebolts is 1/261 and for a rare ring 1/117. I still dont know the odds for a ring to be magic or rare, but so far it seems like the total dropchance of this suffix would be somewhere around 1/6000. Similar to stormlash.

Both faster cast rate and firebolt lvl6 suffix

The true ring I am aiming for is a rare ring with both the "of firebolt" suffix and the "of apprentice" suffix. This can only spawn at a ring with either 2 or 3 suffixes.
I allrdy calculate the chance to get firebolt suffix is 1/22*1/8=1/176 chance. The apprentice suffix has 1/22 chance.
So a rare ring with 2 suffix will have 2*1/176*1/22= 1/1936 chance to get both suffix
A rare ring with 3 suffix would have 3*1/176*2*1/22=3/1936 chance to get both wanted suffix.

So a rare ring from baal has 20/64*1/1936+31/64*3/1936 chance to get both my wanted suffix. this is around 1/1000 chance.

Assuming 25% of the drops from baal are rare, the odds to drop this ring from baal would be around 0.25*1/20*/1000=1/80.000, twice better odds as tyraels might.

Could someone check all my assumptions/calculations and tell me where/if I went wrong.

[EasyG]

Oops, just read the marrowwalk bug got fixed in 1.11. Thats sad, it gave some interesting builds. Well saves me 80k baalruns

[hubb]

:P

In case you (or anyone else) want to do something like this again, there's a German site with a bunch of calcs that will show you everything you want. You can get Baal's chance to drop a magic/rare ring from here and the odds of that ring having whatever affixes here (click on magic/rare next to "calculate Affix-Chances:" to get there).

PS. Even if the marrowwalk but did still work, the charges would only act as a synergy when you haven't spent points in Firebolt. Which would be pretty hard to pull off as a fire sorc ;D

[EasyG]

Wow that affix ggeneration calculator is awesome! And my calculations were damn close, im proud
The ring was ment for a full trang necro to synergize the skills gained from the setbonus. According to my calculations with moonfall and ring, his fireballs would do around 1500 damage, which is pretty awesome when you dont need to invest a single skillpoint for this.