Warning: only for statistic goeroes
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.
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
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:
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.