Good rare drop chance ?

[Axamas]

Considering the number of affix and so the multitude of possible configuration, has someone done the math to evaluate the chance of droping a good rare ; I mean a rare with the most searched affix such as core stat/vit/res all.

Knowing the chance to drop a good rare could help people understand why so many rare drops are crappy.

[kaervek]

I'd imagine the chance to get good mods (ilvl 62/63 mods) is the same as getting ilvl 62/63 items in the first place, quite slim. Then consider you want at least 3 mods ilvl 62 or higher to make a great item and you see why good rares are so rare.

It would be nice to know the exact figures though for item generation like we did in D2, although that probably took a while after release for that infomation to get collated.

[jamesisbest]

People have differing opinions on what is a "good" item. Gear for builds are actually branching out quite a bit since 1.03 and probably will continue to do so. Of course knowing the rates for each affix for each item level would make it easy for you to calculate the odds of finding the stats you desire. Certain mods have higher frequencies on certain item slots, what the exact numbers are I don't know. Though i agree would be great to know the rates on affixes (and if Blizzard has been secretly tweaking them each patch).

[iESCAPISM]

I doubt this is something that can be theorized properly. And if it was, it would mean people would min/max a cookiecutter specc around the most common, strong affixes.

[Ohlmann]

(and if Blizzard has been secretly tweaking them each patch).

What I would like is to have each hour the chance of a specific affix be raised a bit, so that we could see hundred of thousands peoples waking up at 3h AM for 5% more chance to get IAS on their glove.

But it may only be my sadistic tendancies.

[Axamas]

Well let's make some maths just to illustrate my question.

Imagine
- there are 20 possible affix
- that a rare can have 4 affix
- and that you want 3 specific affix on a rare
What odd to get the very one rare that you seek :
Chance is : 1/20 * 1/19 * 1/18 * A3,4 = 0,0035 ; that is you got such an item once every 285 drops. (I hope my maths are correct )

Which can be felt by a player as : drops are craps, so far I've got 284 craps....which is not very rewarding nor addictive.

Comparing D3 to D2 :
- in D2 the drop of good rare (yellow) was very rare ; for the same statistic reason as in D3 (many affix, a short number of valuable combinations)
- but in D2 you also droped unique (gold) and sets (green) with fixed good combination of affix , with a good chance to drop and that doesn't exist in D3.
The thrill in D2 came from gold/green/runes drops never from yellow.
In D3 you have only yellow drops and yellow drops is not rewarding.....and people get disappointed from the game.

My 2 cents...

[DundeeKahn]

Comparing D3 to D2 :
- in D2 the drop of good rare (yellow) was very rare ; for the same statistic reason as in D3 (many affix, a short number of valuable combinations)
- but in D2 you also droped unique (gold) and sets (green) with fixed good combination of affix , with a good chance to drop and that doesn't exist in D3.
The thrill in D2 came from gold/green/runes drops never from yellow.
In D3 you have only yellow drops and yellow drops is not rewarding.....and people get disappointed from the game.

In fact, good rares in D2 were nigh on impossible to get. IIRC, affixes where added to the pool at high levels, but not removed, so you had TC87 ilvl85 rares with "Adds 1-3 cold damage" or "+2 light radius". They fixed that problem in D3 by introducing affix families. This greatly reduced (if not completely removed) the low-end version of mods in top level items. Of course, you still can get bad rolls, bad combinations or both.

D2 was mostly about fixed-stat stuff. Good stuff was rare but "granted" once it dropped. It had a visual cue. The fact that D3 is about a small subset of the yellows (1:~300, by your account, but I've seen more pessimistic estimations in some other topic) may cause the rewards to be harder to spot and evaluate. ("Wait! Is this headpiece even good for a Monk?"*) Also most excelent items still leave room for improvement in less than perfect rolls or fewer than max stats/sockets. This creates opportunity for long therm incremental improvement, but for everlasting insatisfaction as well.

*I sold a Monk-only headpiece for 1.8M after a close friend who had been long farming Inferno act3 ruled it vendor trash. He told me I would be lucky to get 15k for it.

[NReynolds]

What odd to get the very one rare that you seek :
Chance is : 1/20 * 1/19 * 1/18 * A3,4 = 0,0035 ; that is you got such an item once every 285 drops. (I hope my maths are correct )

Yes, I'm that bored; Your math seems spot on.

The situation is improved because rares have a chance to have up to 6 affixes, and when they do, the likelihood of a triple goes up.
The situation goes down because even if you have an ilvl63 item with the affixes you want, they might be of a lower strength (the kind found on an ilvl 58 for example)
The situation is improved in that there are usually several different sets of 3 affixes that different builds and classes want, so you might get a great item for someone else, and use it to get the item you really want.

And if you're a Barbarian like my highest character, you want at least 4 affixes per item. Getting at least +60 all resists on ten items has made playing a Barb fun again, not as much fun as I was having cleaving everything in sight, but frenzy has its own charm. Even though I have a much better weapon, my damage's half of what I had been doing in Hell, when every piece of my armor had near-max strength.

They've promised to improve legendaries and sets with v1.1.0 . What I'm REALLY hoping for would be to change ilvl 62 crafted rares to occasionally (10%-25%) produce an ilvl 63. If that were to happen, then I'd start crafting again.

[zakaluka]

I tried to do some theory on this in the weeks before release. At that time, I had some difficulty defining what a "good rare" is. It was also a bit difficult to guess how affix ranks appear on items. But now, we know about this attribute known as an "exclusion group" for affixes. What an exclusion group does is prevent certain affixes from showing up together.

Exclusions will keep you from calcuating odds for a specific affix pool using the standard rules of permutations without repetition or replacement.

There is a way to do what you're talking about, but it doesn't involve calculation of combinations and permutations. Doing so is still theoretically possible, but it's much more complicated than above posts suggest and it still restricts you to a simple yes/no criteria - what are the odds of turning up the desired affix pool. You can't get much more specific using normal methods. What if you wanted to know about your desired affix pool and all others with comparable defensive value?

The process goes like this:
1) You need a script that emulates the server side item generator. You'd want it to (as closely as possible) mimic the way the game does it. Restrict results arbitrarily, to something narrow: say, bracers dropped from a mlvl 63 mob. Make sure items can come with between 4 and 6 affixes as well, just like in game. Also make sure this script knows how to randomly choose a base item from the pool of items that can drop at mlvl 63 (so that it's actually a representative picture of what happens in game. need those level 53 drops with 4 affixes in the item pool).
2) You need another script that can score each item's offensive and defensive benefit against a stored character profile. Not a lot to be said about this step, except that there's a good bit of arbitrary value assigned to some stats. For instance, barbs score vit much higher than every other class. Self healing effects are subjective. Value of each stat, whether offensive or defensive, depends on class/build.
3) Now you run this process for a very long time, generating say ten million items and scoring them against your character profile. Depending on how much resolution you want at the very high end of item quality you might need considerably more runs, say 10 billion.
4) Save the list sorted by the sum of Offensive and Defensive scores (actually a bit more challenging than you might think to sort 10gb worth of records). Plot item density versus score percentile. The plot is necessary for a cost-benefit analysis of crafting, not really for figuring odds at drop quality.
5) Plug your desired item into the scoring algorithm, and get it to spit out your desired item's score percentile, as compared against the large sample of random items you generated. This would tell you how many drops you need before seeing something comparable.

This isn't really an easy task, to come up with "odds" for an item to drop with "above a certain quality". Any attempt to look at the problem from a permutations/combinations viewpoint will yield both a limited answer and inaccurate results.

My goal with this originally was to try and correlate the values of decent to high quality rares, and that of crafting materials. But after launch, since it's pretty clear to me that crafting is probably always going to be a net loss over time (mats are overpriced), it didn't seem like a useful project anymore. Maybe if there are others out there with interest we could make it a collaborative project. However, the farthest I got was to put one item class's affix table into a perl hash and some random scattered tinkering to re-learn a bit about perl's algorithms/modules/data structures. An SQL dump of an existing datamine's DB would have gotten me considerably farther, I think. Anway, for now that particular project goes on the inactive pile. Something that seemed like a cool idea but just wound up looking too involved to be worth it.

[zakaluka]

To be clear, I can lay out the odds for a chosen optimal affix pool to appear. It still doesn't answer the question, because an item with an optimal affix pool can still get really horrible rolls.

All numbers are presented as "permutations" and "combinations". Shorthand -
25p3: permutation taking 3 affixes from a pool of 25. 25!/22!
6c3: combination taking 3 choices from a pool of 3. 6!/[3!*(6-3)!]
To the game, order is significant. To us, it's not. So I'm writing this up in terms of permutations, but to us humans the combination is what matters. The result should be the same either way, it's just easier for me to think in terms of permutation.

Let's take a look at Bracers. According to diablonut, a pair of Razorspikes can carry 33 different affixes. Combination modifiers aren't differentiated, so that adds 6 more - StrDex, StrVit, StrInt, DexVit, DexInt, IntVit. 7 affixes in the DB are either vestigal or don't actually apply to rares or bracers (%armor, the 4 CC reductions, durability boost, %dmg->health). This leaves 32 actual affixes for the Bracer slot.
Exclusion group A is the combination modifiers, accounting for 6 affixes.
Exclusion group B is the single-resist affixes, accounting for 6 affixes.
Non-excluded affixes: 20 total.

Now you have to map out the cases, to see how many possible items there are.
Case 1: None of the excluded affixes appear. Permutations: 20p6 = 20!/14! = about 28 million.
Case 2: One affix from exclusion group A appears. Permutations: 20p5 * 6 [6 different combo mods] * 6c1 [the combo mod can appear in any of the 6 affix slots] = [20!/15!] * 6^2 = about 67 million.
Case 3: One affix from exclusion group B appears. Permutations: 20p5 * 6 [6 different resist mods] * 6c1 [resist mod can appear in any order, again] = [20!/15!] * 6^2 = about 67 million.
Case 4: One affix from exclusion group A appears, then one from exclusion group B. Permutations: 20p4 * 6 * 6 * 6c2 = [20!/16!] * 6^2 * [6!/(2!*4!)] = about 63 million.
Case 5: One affix from exclusion group B appears, then one from exclusion group A. Permutations: 20p4 * 6 * 6 * 6c2 = [20!/16!] * 6^2 * [6!/(2!*4!)] = about 63 million.

Total affix pool: 287 million permutations.
Notice that if we had treated this without considering exclusions, with 32 attributes choosing 6 we would have 32!/26! permutations or 652 million permutations.

Now suppose we want to know the odds of a random 6-affix bracer having the one affix pool we consider to be optimal. This neglects all possibility of the bracer dropping with fewer than 6 affixes, or at a low level, or just getting poor rolls overall. On the opposite end, we're ignoring the fact that there are many affix combinations you'd be ecstatic to find, not just one. This one affix pool is a combination; the number of permutations that one combination covers is 6! or 720.

So now the odds you have of seeing that affix pool are 720 out of 287 million 6-affix bracers. That's 1 out of 399 thousand.
It's a little more legwork to find odds of getting an optimal pool of 5 affixes on a 6-affix item.
But, the odds of getting your optimal 5 affixes on a 5-affix item are 1 in 120,000
optimal 4 affixes on a 4-affix item: 1 in 29,000

Reducing the size of the desired affix pool has a MUCH larger effect, if you keep the number of available affixes the same. Example: 6 affix item but you want to see the odds of rolling your desired 4 affixes. This has a VERY dramatic effect on the odds. The difference should be about 1 and a half orders of magnitude per "miss" (example: odds of 5 affixes desired from 6 available should be in the range of 1 in 31k, odds of 4 affixes desired from 6 available should be about 1 in 2.3k edit: my figures here were off by quite a bit. One and a half orders of magnitude is about a factor of 33. I did it wrong to begin with, and my guess was off by a little bit. See the sheet linked below). Also the existence of primary stat about quadruples your odds of finding something useful, because a good roll with the wrong primary stat on it is still worth trading.

Edit: Here is the math - someone will undoubtedly criticize how I've approached the "2 misses" case. Keep in mind that you start with 1 *combination* that's pre-specified as "optimal". From here I calculated the *permutations* that could fill those last 2 modifiers. The rest of the math is to figure how many different permutations that original combination covers.

https://docs.google.com/spreadsheet/...W05Q3JmX3RBYXc

Hope it's useful, sorry for hijacking this thread (gone a bit overboard with my input here). Note that if you take the result for "4 of 6 affixes are optimal" and divide by 3 (the number of primary stats) - this will tell you:
Of 6-affix bracers dropped, 1 in 250 have someone's 4 optimal affixes.
Of 5-affix bracers dropped, 1 in 435 have someone's 4 optimal affixes.
Of 4-affix bracers dropped, 1 in 9600 have someone's 4 optimal affixes.
If number of affixes is totally random (even odds of receiving 4 5 or 6 affixes) that'd mean 1 in 480 drops show up with someone's optimal affix pool.
Divide by the number of affix combinations you consider to be pretty good stat combinations.