IF and only IF our item can have 7 random properties and the range of them are 120, the probability of getting a perfect roll should be around 75k/1?
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01052012, 13:06 #1
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Chance to Roll a Perfect Axe of Mighty from Hell

01052012, 13:20 #2
Re: Chance to Roll a Perfect Axe of Mighty from Hell
Here's the thing, how interesting is it really if you have to confine yourself to those variables? We already know the numbers are ranging much higher than 120, so the probability of crafting a perfect rare (never going to happen in the lifetime of D3) is much, much, much lower.
So, I reiterate. How useful is it really?

02052012, 15:33 #3
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Re: Chance to Roll a Perfect Axe of Mighty from Hell
Also, if you mean every property has that variance, and you don't care which properties appear, that still will be a chance of 1:20^7 of an absolutely perfect roll. Which is more than one to a billion against.

06052012, 14:12 #4
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 May 2012
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Re: Chance to Roll a Perfect Axe of Mighty from Hell
You should be asking yourself what are the odds of finding or crafting a GOOD rare.
First off, affix values aren't completely random. If the game rolls %ED, and the maximum %ED modifier is 50%, it's not like you get a random linear roll from 150 on that mod. %ED is broken into 7 ranks. I: 1015 II: 1620 III: 2125 IV: 2630 V: 3135 VI: 3640 VII: 4150. But even which rank from 17 you get probably isn't completely random.
The game chooses a rank for the modifier first (and we're not 100% sure how it does this). Then it rolls the modifier (probably random in the allowed range for chosen rank). Very early on before the official D3 site and forums were ever released, Bashiok hinted that they want to limit the number of "garbage" affix rolls you get. For instance, they don't like seeing a very high potential rare drop (say a rare off Lister in a5 Hell), even getting the right affixes on it, but then having too many of them roll very low values resulting in a garbage item. So it's a good bet that there's a hidden probability table for which rank affix you get, putting some pressure on the quality of affixes. That's something we can't even account for right now.
Now if you want to examine how likely it will be to get a "good" item, make an arbitrary point of reference. Which affixes would I need, and at what quality, to be about onpar with a legendary? The answer is (I've examined it very thoroughly) that you need either:
(A) 3 of the strongest 6 DPS affixes, including the Min/Max damage affix (elementaldamage affix, which can also be physical damage) at a high quality. Other 2 can be moderate quality. This means that actually a blue world drop bow has the potential to beat out a windforce, but not by much and that'd be a pretty damn lucky roll.
(B) 4 of the strongest 6 DPS affixes. If you get 4, they don't all have to be perfect rolls. If those 4 affixes include ElementalDamage, and the other 3 wind up a reasonable quality, your crafted rare bow can outDPS a windforce by more than 30%. On the flip side one possible combo without it falls a bit short so that evens out the odds a bit.
Strongest 6 DPS affixes seem to be:
ElementalDamage
+%Enhanced Damage
Haste (% attacks per second)
Kings (raw bonus to APS)
Critical Damage (although this one needs at least some crit rate on other items to support it)
+Primary stat (although I'm not 100% sure how this one functions related to DPS, so I didn't include it much in comparisons. It could contribute flat +damage per budget, or %ED, %crit is probably in there as well)
Most other DPSboosting stats that can show up on weapons aren't nearly as good.
Now you have to examine (1) the odds of getting the affixes you want and then (2) the odds of getting a favorable roll on those affixes. It's easier to examine craftables than drops, because you know how many affixes you'll be getting (can't even speculate on probabilities for inferno level drops).
(1) isn't particularly hard to examine, and you'd be surprised. The odds are fairly good. Chances of [a] or [b] happening as above are about 1 in 125 crafts on the 6affix craftables, better on high level world drops if you're actually likely to get 6 or 7 affixes. You still don't know the odds for a good roll.
(2) Getting a good modifier roll is something we simply don't have the information to explain. Even if ranking affixes favors higher ranks (crossing my fingers bashiok) it could reduce the odds of that 1 in 125 item actually being good by another factor of 10 (1 in 1300 6affix crafts compete with legendary). If affix ranks DON'T have a gradient of probability on them (completely randomized) then you'd have to see that same affix combo at least 100 times (on an affix with linear groupings, but see below: most aren't quite linear) before getting something good (1 in 13,000 6affix crafts compete with legendary, or worse by as much as a factor of 100).
If d3 chooses affix ranks randomly, some affixes will actually favor low quality rolls, which would make me very sad!! See the ElementalDamage affix, which will be central for a good weapon roll, and notice that it scales more than linearly with rank: http://www.d3inferno.com/affixes/group_ElementDmg.html  If rankings are random, of all the times that affix shows up, only 1/14th of its appearances will be at 50% of max or better. You will have to find JUST elementaldamage about 30 times before that ONE affix gets a moderately good stat (75% of max or better). That'd have very bad implications for odds at rolling decent random stats.
Here's hoping the affixes have a ranking gradient.
Need more data.
Last edited by zakaluka; 06052012 at 15:50.

06052012, 15:24 #5
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 May 2012
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Re: Chance to Roll a Perfect Axe of Mighty from Hell
I didn't much answer the original question, though.
To get an optimal affix pool (all 6 high ranking DPS affixes at once) you'd have to collect 23 million 6 or 7affix world drop rares. I'm using Wands as a reference point for that example, which have 53 possible affix groups. If your weapon has more affix groups, your odds get slightly worse. If your weapon has fewer affix groups, your odds get slightly better.
Now what are the odds of a favorable roll on all 6 affixes at once?
If affix rankings are random and we set our requirement to be that all mods roll 75% of max,
EleDmg is 1 in 30
CritDmg is about 1 in 10
Rest are about 1 in 5
1 in 5^4*10*30 or 1 in 200,000 of these "perfect affix pool" items get good rolls across the board
If affix rankings are chosen on a gradient, for comparison assume about 1 in 3 chance of a good roll.
1 in 3^6 or about 1 in 700 of these "perfect affix pool" items get good rolls across the board.
Very best case 1 in 16 billion inferno rares meet your standards of "perfect". That's if affix ranks are chosen on a gradient, rather than being completely random. This weapon should have a DPS tooltip on the order of 1200 DPS.
Let us say, the very best rares in existence at any time will definitely be worth something. Probably not tradeable securely with the means available to us ingame.
Last edited by zakaluka; 06052012 at 15:55.

06052012, 23:07 #6
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 May 2012
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Re: Chance to Roll a Perfect Axe of Mighty from Hell
There's something wrong with this, I hadn't done the permutations correctly for 7affix rares.
So resummarizing this:
 There are 6 high value DPS affixes that should massively outperform all others.
 A rare with the 1 best DPS affix and any other 2 DPS affixes should be capable of more DPS than a legendary, if the affixes get good rolls (explained above).
 A rare with any 4 DPS affixes and reasonably good rolls should surpass most legendaries, even if the 4 affixes don't get maximum rank.
Of 6affix rares (dropped or crafted):
1 in 23 million will get all 6 best affixes. (Almost guaranteed good roll)
1 in 80 thousand will get 5 of them (Almost guaranteed good roll)
1 in 1400 gets 4 (Reasonable odds of a good roll)
1 in 70 gets 3 (Poor odds of a good roll)
Of 7affix rares (dropped only I believe??)
1 in 3.3 million get all 6
1 in 24k get 5
1 in 650 will get 4
1 in 45 get 3
Thinking about how to use this to relate the value of crafting mats to the value of rares....

08052012, 16:56 #7
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 Mar 2012
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Re: Chance to Roll a Perfect Axe of Mighty from Hell
I enjoyed reading your ruminations on this and as you said we need more info on how affixes are picked to really calculate the numbers. Particularly rank bias, it would be disgusting to craft an exalted grand whatever and get +12 arcane damage as one of the affixes. Should pick this topic up again after release when the mechanics become more clear.
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