So, I couldn't quit wondering and decided I wanted to actually do the math on the chances of a mara rolling perf crit, perf CD, perf to any useful skill (not specifically dogs), and high on another useful stat (LOH in this case, but will allow for other main stats, main \ vit, dmg, IAS, or % life as well)
I am assuming that legendaries follow the same prefix \ suffix rules are rares, but I could be incorrect in thinking this, and I am not completely sure what mara's + to each stat would be considered. I am guessing it all counts as one giant suffix, as that is the only way the 3:3 prefix:suffix ratio works.. The skill bonus would be a suffix, and AR is a prefix.
That leave 2 prefix and 1 suffixes for the random rolls. This explains why you do not see Mara's with CC, CD, and Attack speed as well. Those are all prefixes, so it can only have 2 of the 3 (thats also why trifecta items are so rare to begin with. It isn't because you have to roll those 3 out of 6 rolls, as many people think, it is rolling those 3 out of 3 rolls)
This math won't be perfect, as it has been a very long time since I actually did any of this, and I'm sure I'll screw things up, but it should give a decent idea.
First it needs to get the top level crit chance or crit damage prefixes. There are a total of 224 possible prefixs, but 5 are eliminated because of the AR roll it starts with, that a max level ammy can roll, so landing this specific one is 1 in 219, but since either will work it is 2/219. So a 1 in 109.5 chance of rolling the highest suffix for crit damage or crit chance.
Then, the second prefix must be the other (CC if the first was CD, or CD if the first was CC), so 1 in 219 for it to roll that.
Then, to roll the max CC is 1 in 3 (top prefix is 9-10%, but includes 9.5% as well)
To roll 100% CD it is 1 in 34 (66-100% for top prefix)
Now the suffix. There are 410 suffixes, but the skill is there, that will eliminate 300 of them (yes, there are 300 different suffixes for +to skills), so we are left with 110 suffixes. Out of those, I consider LOH, damage (xx-xx), or pure int to be the best. Life % and Int\Vit are prefixes. This LOH is the 2nd tier LOH roll, so I'll equate it to 2nd tier or greater dmg or pure int as well. That is 6 out of 110, or 1 in 18.33 will roll a good suffix with a 2nd tier or better quality.
Then the perfect dogs. It would be unfair to make that just for dogs, so, there are 58 random rolls for skills on a Mara's. Each class has 3 or so that are good for it, and the others are pretty garbage. I can't get an exact number, because I do not know every class and every build well enough to see which skills are great and which would be meh.
So, 15 out of 58. 1 out of 3.8 rolls will have a decent skill.
Then, on average, the roll for perfect is 1 in 7. For some skills it is as much as 1 in 9, and others as low as 1 in 5, so I'll just go down the middle (dogs itself is 1-8).
So, (1/109.5)(1/219)(1/3)(1/34)(1/18.33)(1/3.8)(1/7) = 1 in 1,192,621,151
This item is literally 1 in a billion. Only 1 in 1 billion Mara's that are ID'd will roll perfect CC, perfect CD, a perfect good skill, and a decent last stat.
Even if you completely take the skill itself out of it, and determine how often a Mara will roll perfect CC and perfect CD with a decent 3rd skill roll it is still 1 in 44,835,381. I do not think that many Mara's even exist. I would be surprised if more than a million Mara's had even dropped since 1.04 changed it. Really, by the odds, this item shouldn't exist. He didn't just get lucky that it dropped...the fact that this item like this has dropped for anyone was not even likely. Chances are, no other one will ever drop again
Please, correct my math if I am doing it wrong. It really has been a very long time. And sorry to fill your page with this, but I just nerded out on this hard.
Edit:
So, someone pointed out to me that rare items can roll 6 prefixes or 6 suffixes. It is not limited any more (I am pretty sure it was early in the game...).
But, that is not true for Mara's, and probably other legendaries.
If you do not believe me, go search for a Mara's with CC, CD and any of the following (can leave the amount blank. they just wont roll together). Phys\Fire\Any Resist, Gold Find, Magic Find, Attack Speed, Sockets, or Life %. There are others, but that should be enough to prove it.
This post was edited by Large_Intestine on Nov 9 2012 09:32pm