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yes, when you take into account roll quality the scaling value does get worse. you are correct sir. BUT, that effect is just going to apply itself as a coeffecient against the scaling values i calculated. i used the values in the spreadsheet that dont account for roll quality so we'd have to apply the same coeffecient to the scaling value i calculated from the spreadsheet as well. this means that both our values are going to increase but stay in the same proportions. it doesn't have any effect on the argument. with your goal of 0.25, both of our scaling values are given coeffecients of 0.25^3/0.25^4=1/0.25=4. i used the case from going from 3 to 4 affixes but you can see by the math that going up by one desirable affix will always add a quality scaling coeffecient equal to 1/0.25=4. either way, your particular goals calculated, nor the roll quality expectations matter. the point of the original post directed at you was to simply state that the set width of desirable crafts is waaay to wide due to subjectiveness to use anyone's personal goals/expectations as reference/approximation/evidence/whatever. my counter example was meant to prove just that. 

Agree 100%
That's where the 1H level reduction weapons I've sold comes in to play. Like I said in one of the previous posts (can't remember and too lazy to check, our posts are all long lol) I've at least broke even from what I can tell, if not gained a small net amount since the patch. And so I ask you again. Is this close? Can you point to me if I have erred in my understanding of you? 1. This is true, and from my experience (contrary to what most people think, I'd wager) the bottleneck material ISN'T DE, but tomes of secrets. 2. This is true and untrue depending on runs and whether you find anything worth value. Most days are around breaking even though. 3. Something to look forward to is a bonus afterthought. The primary reason in crafting gametogame as I mentioned was time efficiency in terms of making upgrades asap and using them for as much time as possible. This isn't possible if you wait to craft until you have XX / XXX amount of materials. 4. This ISN'T true, as I also mentioned in one of my posts. (repeating that post) Since the patch I've found two, crafted two, and AH purchased EIGHT upgrades.
Edited by gotaplanstan#1369 on 4/20/2013 9:38 PM PDT


You're right, I should have said X + Y instead of X + 2 ... :P As for me, I'm sitting on almost 3 billion gold. I don't have issues with deciding whether I can afford to craft! ;) 

Too bad you can't throw your money at vendors and get DEs back XD


@INJEKT
so,.. Okay, so I'll readily admit that combinatorics is not my strong suit (even though I was forced to take some courses in combinatorics & optimization way back when I was in university). Rather than me sit here and try to understand how you pulled those numbers together, let me ask you this. Does your calculation of possible rolls take into account the possibility of doublecounting combinations? And does it take into account combinations amongst your desireable affixes that you actually don't want? Please allow me to illustrate my thinking here. For example, if your pool of desirable affixes on gloves (this is the simplest case) is ChC, ChD, IAS, Vit, AR, SR, Dex/Vit (I'm only counting 7 so far)... and you are looking to count the combinations of the ones that have 4 out of those 7, then I would proceed counting them in this fashion: (ChC, ChD, IAS, Vit) and (not AR, SR, dex/vit in the remaining slot) (ChC, ChD, IAS, dex/vit) and (not AR, SR, vit in the remaining slot) (ChC, ChD, IAS, AR) and (not SR, dex/vit, vit in the remaining slot) (ChC, ChD, IAS, SR) and (not AR, dex/vit, vit in the remaining slot) (ChC, ChD, Vit, AR) and (not IAS, dex/vit, SR in the remaining slot) [for my TR monk] etc... Because amongst those 7 desired affixes in a glove, I have no desire for a combo like (Vit, dex/vit, AR, SR) even though they are all in the pool of desirable affixes. or even (IAS, Vit, Dex/Vit, AR) etc... And the reason I would ensure that the fifth affix is not one of the remaining 3 is to ensure that you don't double count (even though it would be truly desirable)... like (ChC, ChD, IAS, Vit) and (AR) (ChC, ChD, IAS, AR) and (Vit) From what I can ascertain, I am not sure if your mathematical equation takes this kind of thinking into account. If not, then your method may produce a pool of desirable affix combinations may be overinflated each step of the way. Which is why I like what Mandlebarb's spreadsheet, because he lists each combination he wants to calculate the possible combinations, and I am assuming (he has not specified otherwise) that he has accounted for the possibility of duplication. It may be overly specific, but it accounts for actual playing situations that math (on a representational level) cannot really do on its own. For these reasons, I have a feeling that the process is a bit more complicated than you project it to be. (btw, I think this is where the site http://www.mathsisfun.com/combinatorics/combinationspermutationscalculator.html is extremely valuable, because you can actually plug in each of these scenarios that I listed above and it can actually count out number of combinations based on the conditions you give. For these purposes, it's the best tool I've found that is readily accessible to the masses)
Edited by Nameless#1537 on 4/21/2013 6:17 AM PDT


Maybe we should just drop it (and if you've already suggest this, I'm sorry for missing it) and agree to disagree despite both of our experiences (factually and non) not agreeing with each other. A bunch of things: (1) I've been on every night this week. No idea where the hell you've been. :P (2) I agree that it is likely about time for us to drop one part of the conversation about when to craft (for now). I think that the discussion may have gone beyond it's course of usefulness (for now) and time to start engaging on another angle of attack on this topic which is the other half of my thread title (not just strategy, but crafting odds) which leads to my main focus these days: (3) How do crafting odds impact our decision to craft or what to craft? For me, this is a fascinating topic because (as many have stated before), the odds of finding an upgrade to your existing piece for the average monk who is crafting is actually relatively high in the beginning. But once you craft that upgrade (even if not GG material), one needs to consider the question of the odds of crafting an upgrade to your already upgraded piece (and not just the enormous potential for what it could be) in your decision of how much you will continue to craft said slot vs. shift focus and focus on another slot vs. saving gold for your next item. I believe that the law of diminishing returns absolutely applies to crafting, so we need to consider the question of when are we throwing good money after bad (something that TexaStranger alluded to in an earlier post). It is ideas like that that would inform my decision to stop crafting ammys for the foreseeable future (if ever at all) and instead concentrate on areas that are more likely to give me an upgrade. My situation with the ammy is pretty cut & dry, but not as much if you have a good craft but not a great one (something that TexaStranger has said a prior post). It's not a question of whether to craft (we all agree we absolutely should on some level) but a question of how much to craft or what slot to focus on. It's not a question of hoarding DEs etc, but a pragmatic question of saving gold for your next AH purchase because each craft does have a gold cost that does not seem like much if you do just one, but does add up when you do it in volume (whether it is spread in small chunks done more frequently or saved up for one big crafting session every now and then) as it is something that me and others have been discussing as well.
Edited by Nameless#1537 on 4/21/2013 6:51 AM PDT


A bunch of things: 1. Few different things... a. MH beta b. NBA playoffs (yesterday and today) c. gsl + gstl d. bl2 2. Fair enough. 3. There's a point where finding upgrades becomes near impossible though, since drops for your character are not tailored to it. (I love this feature about MH, and I think I've seen Blizzard hint and possibly doing it in the future with D3 too, can't remember though) 4. Well that part is just common sense and knowing which item upgrades to prioritize. 5. That's exactly the reason I've been waiting on amulets until I'm done with other slots. Despite needing/wanting an upgrade (dps wise, and with some combination of vit/life%/ar) it's not a very high priority atm. 6. Unless you do what I've suggested (talked about doing, myself) by using up all your materials, and then focusing on both. I'm not quite sure why you're mostly still arguing for the separation of the two things. There's no reason you can't be doing both. 

(deleted)
Edited by Nameless#1537 on 4/21/2013 12:01 PM PDT


I'm not sure why you're not responding in a by post basis. You're basically twisting what I've said in different posts (by taking clips from multiple posts of mine), putting them all into one post, just to support your argument. I suppose I can go through it, and show what I've meant and how it is correct, but that will take time and honestly I'd rather be doing other things right now. Maybe I'll do it later though.
You said you wanted to drop it, and yet you continue to respond with arguments. Not sure what you're trying to prove at this point? 

You said you wanted to drop it, and yet you continue to respond with arguments. Not sure what you're trying to prove at this point? Fine. I admit that I can be a little obsessive. Let's leave this one alone. I'll delete my last post and move on. Not worth continuing down that path anyway.
Edited by Nameless#1537 on 4/21/2013 12:05 PM PDT


Does your calculation of possible rolls take into account the possibility of doublecounting combinations? Each affix can only roll once in my considerations. And does it take into account combinations amongst your desireable affixes that you actually don't want? No. In my considerations there is no subset of desirable affixes that are unwanted. my example is 'the other side of the coin' to yours. where your reference was strict in conditions of sets of affixes rolled and mainly offensively based, mine was loose and neutralalthough, still a reasonable objective! From what I can ascertain, I am not sure if your mathematical equation takes this kind of thinking into account. If not, then your method may produce a pool of desirable affix combinations may be overinflated each step of the way. subjective. depends on the crafters current amulet. if you already have an amulet with the 3 'best' affixes, then obviously the set of desirable affixes is reduced when trying to roll an additional affix. however, if your current amulet has (what you consider) the exact 3 worst (but still desirable) affixes, then any subset of 4 affixes in the set of desirable affixes is better. Which is why I like what Mandlebarb's spreadsheet, because he lists each combination he wants to calculate the possible combinations, and I am assuming (he has not specified otherwise) that he has accounted for the possibility of duplication. his numbers were computed, not calculated, and thus his numbers are expected to be off if he only rolled 10,000,000 amulets with a possibility of 36C5=376992ways. if i compare against his sum probability of 3C2 (chc,chd,ias), i would say he might have a bug in his computation code, or just rolled a deviated set of 10,000,000. the correct result is (3C2)*(33C3)/(36C5) = 0.04341. his result was 0.0466. For these reasons, I have a feeling that the process is a bit more complicated than you project it to be. the process to calculate the odds given any set of desirable affixes and any set of their conditions in creating a desired amulet is complicated. it would be a struggle for me to create an algorithm to do so. however, that algorithm is irrelevant in this argument. all that was needed to be shown was that there was a subset of desired affixes, with any set of conditions on those affixes, that would produce a desired amulet, for anyone who might craft it, that had a much different scaling value of odds crafting from 3>4 affixes than the reference you provided. whether i reduced the conditions to simplify the math or not is irrelevant. i still produced a result. (btw, I think this is where the site http://www.mathsisfun.com/combinatorics/combinationspermutationscalculator.html is extremely valuable, because you can actually plug in each of these scenarios that I listed above and it can actually count out number of combinations based on the conditions you give. For these purposes, it's the best tool I've found that is readily accessible to the masses) you are correct. that tool can calculate the odds for crafted amulets where the conditions are equal to my examples (any subset of a set of desired affixes). anything more complex it can't do. feel free to verify my math. :P and lastly, Okay, so I'll readily admit that combinatorics is not my strong suit (even though I was forced to take some courses in combinatorics & optimization way back when I was in university). to which i must ask, why are you arguing which you don't understand? 

First off...
#1 I didn't say I do not understand. I did my undergrad in math (took courses in C&O & stats, probability, etc) & computers, but it is not something I've touched since that time (my career path has taken a very dramatic change and I am in the field of psychotherapy) and so it's not that I am completely without knowledge or understanding. My statement is an acknowledgement that this area is not my strong suit. My purpose of the thread is to learn, and put some ideas together. In the process of learning is to ask critical questions from which I come to a better understanding. It is not to blindly accept what people tell me without thought or question. I am not trying to pick a fight with you, I am asking questions to help clarify understanding. In the process of this Q&A exchange, I have learned that your computations, while legitimate and useful, are not necessarily wholly applicable to the average player who is reading this thread. In my post, I asked some questions that provided a very specific context based on a players' experience. I will quote my original post and contrast it with something you have written. For example, if your pool of desirable affixes on gloves (this is the simplest case) is ChC, ChD, IAS, Vit, AR, SR, Dex/Vit (I'm only counting 7 so far)... and you are looking to count the combinations of the ones that have 4 out of those 7, then I would proceed counting them in this fashion: No. In my considerations there is no subset of desirable affixes that are unwanted. my example is 'the other side of the coin' to yours. where your reference was strict in conditions of sets of affixes rolled and mainly offensively based, mine was loose and neutralalthough, still a reasonable objective! And so is it reasonable to assume that in you providing the other side of the coin, that the truth likely lies somewhere in between your results and what Mandlebarb put together? Whereas his is too strict in your books, your approach could also be seen as too loose for many players. The thing is that for the average player, the amulet and gloves are seen primarily as DPS slots so the neutral approach would make little sense in those two slots specifically. No player in their right mind would consider a glove with (Vit, dex/vit, AR, SR) (and one other random affix) an acceptable craft even on a glove or an amulet if all of those affixes on their own are considered desirable. Furthermore, one could argue that if you already have a glove with ChC, ChD, Vit (and 2 other junk affixes), rolling a ChD, Vit, dex/vit, AR and one other junk affix would not be considered an upgrade even if there are more desirable affixes in the roll. So with each upgrade crafted, the requirements for an upgrade in the next craft become much more restrictive  also subjective to each player and the combination of affixes that they have already rolled on their toon. There are likely, in fact, tonnes of combinations amongst the 7C4 (35) combinations of affixes that would be undesired when it comes to crafting gloves or amulets (I'd estimate more than half of those combinations would likely be discarded if not more leaving only a handful to consider). So in Mandlebarb's approach, it is to eliminate all of those scenarios to scale down the number of possible desirable combinations of desirable affixes. I would believe that, based on that argument alone, I would still gravitate towards Mandlebarb's results with the strong caveat that his results are subjective and be more restrictive than some other players and results may vary according to the expectations of the player. However we are splitting hairs, we both agree that there is a significant leap in the crafting odds as you jump from 3 desired affixes to 4. We may not agree on how big the jump is, but that is subjective and once there is a subjective variable introduced into the equation, the shortcomings of solely relying on algorithms and general mathematical computations are exposed and these models become less practical (but still useful). At some point, user input into the process would add a lot of value to the computations which is why that little pet project I was referring to earlier, will require some time and effort to put together if, for no other reason, than to satisfy personal curiosity.
Edited by Nameless#1537 on 4/22/2013 10:02 PM PDT


One more thing here. IIRC, Mandlebarb's computations are also based on affix weightings placed on each affix that he believes to be applied in Blizz's RNG affix generators that was input into MATLAB to generate the results based on 10M amulets rolled. I am not sure how true that is (the affix weighting), but if that is the case, it could account for the difference between his numbers and yours, where yours assumes equal weighting on each affix. I don't know if it's a bug, but perhaps a deliberate setting that he placed based on some assumptions. In any case, the purpose of this exercise is not to find exact numbers, but a methodology that will yield approximations that are good enough for the purpose of decision making in this game.
Edited by Nameless#1537 on 4/22/2013 12:17 PM PDT


Bump.
Front two pages have been completely redone with brand new material with case studies etc to consider. Please feel free to read, as the information there is, I believe, very relevant to most players in the game. 

The affix weights were worked out by Mandlebarb and me a while ago. Pretty much logging 3000 rare amulets worth of data. Also since Todd always spends billions buying unid legendaries (mainly mempo's and IK chests) I was able to get a pretty large sample size there for single affix probabilities that helped provide greater evidence since the amulet data probabilities are a lot more complicated to work out. All the work is linked in the pdf document:
https://docs.google.com/file/d/0B0gMgiAJ3WsmN3lJWVFfVnJlVTQ/edit?usp=sharing I've gone through most of the work with some math people and they said that assuming that there is no sampling bias it looks like the work is correct. The affix weight is a very important element for determining the probabilities and really cannot be ignored. The only reason why your numbers came close to the simulation is that Crit chance and damage appear slightly more frequently than even probabilities whereas IAS appears MUCH less frequently so they balance out a bit in that particular case. 

I have a bunch of questions for you in this regard. I'm wondering about how to apply affix weighting to probability calculations. Let's say you have a list of affix weightings and you are able to boil it down to some kind of normalized figure (do I have the right terminology) around 1 (where an affix weighting of 1 indicates that the affix is considered average weight, while something like 0.90 is one that shows that it is less likely and 1.1 shows that it is more likely, then would you apply affix weighting in this manner: P(affix 1, affix 2, affix 3, affix 4) * affix 1 weight * affix 2 weight * affix 3 weight * affix 4 weight = affix weight adjusted P(affix 1, affix 2, affix 3, affix 4). Would something like this make sense? And is there some kind of a source document that provides affix weighting for all affixes across slots for crafting purposes? I think the document that you provided only explores it in the case of amulets. Further, is there a place that lists all of the affixes that can roll on BoA crafted items on a per slot basis? I have seen lists for 1.0.4 and 1.0.5 affixes, but not sure if anything has changed for 1.0.7. If there is, can someone link me there, because I can't seem to locate it at the moment. 

Chazhang  beautiful work. Really really great analysis. Best I've seen anywhere.
One question  perhaps I missed this, but was the sample for the study rare amulets or on boa crafts only? I ask because anecdotally, it seems there may be some kind of favorable weighting given to desirable affixes for boa items since there is no worry about overheating the economy; other than perhaps by making them so lax that people too quickly craft desirable items and crafting ceases to be the valuable and highly necessary goldsink that it is. By the way, since we've never met, my name is a total misnomer. I'm not a math whiz by any means. 

@Nameless
That approach works as an estimation, but it isn't 100% accurate. I used that as one of the equations for the estimating it, the actual way of solving it would be do to the nested combinatorics. The more the weight differs from 1 the more off it will be; the more affixes you roll for, the more off it will be. The best way to check the affixes is to go to something like d3own.com and find what the minimum possible rolls are then count the number of affixes from that minimum to the maximum 63 roll. Normally it's all 5163 rolls, but sometimes thats not the case. @Simplemath It was for both. The major analysis was for rare amulets since I could get a very large sample size for that and get myself a reliable sample mean. Then with a smaller sample of BoA items I can compare the results of those vs the rare amulet mean to determine if they're different or not. The reason why people tend to feel like they're getting better amulets from BoA is because of 2 factors. Firstly, you always get 6 affixes (1 static and 5 random), whereas rares range from 46 affixes. If you were to calculate the probability of rolling bifecta given 4, 5 or 6 affixes, you'll see it increases quite a lot from one category to the next. Secondly, the rare amulets are a max ilvl of 62 whereas the crafted BoA are 63 so they roll much better stats on average. Even if the weights aren't actually different, rolling a ilvl 62 min + min/max roll will be around the same average damage as an ilvl 63 min/max roll meaning the latter has an extra affix to roll something else. The same is true for primary stats since they stack. 

Okay, so I finally put some numbers together in terms of probabilities and expected costs to craft upgrades for each BoA slot. All in accordance to available affixes, and from that, picking the kinds of combinations that would interest most monks. The results are posted in post #3:
http://us.battle.net/d3/en/forum/topic/8517952016?page=1#3 Hope you find this useful. I might bump this during the week for the weekday warriors amongst us. 
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