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Odds for unique?

Discussion in 'Theorycrafting and Statistics' started by Hrus, Apr 7, 2005.

  1. Hrus

    Hrus IncGamers Member

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    Odds for unique?

    I have a few questions.

    1) Is there a known universal number that represents the percentage of an item being unique (let's say for regular monsters).
    I think that the odds for item being unique (if it can drop from the monster) depends only on your MF, type of monster (regular drop, boss drop, act boss drop, champion drop...) and this universal number.
    But it is probably far more complicated.

    2) Why there is a difference between odds for getting an Astreon's wand and Death Web? (Atma drop calculator). They should be both treated as class-specific items.

    3) Is there a known percentage that those special chests (Lower Kurast, lvl2 Pit) will generate an all-unique drop? I have never seen the unique/set drop from these, but others do.

    I hope stat gurus will answer me :) Thank you.
     
  2. thegiantturtle

    thegiantturtle IncGamers Member

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    1)I don't have any detailed or up to date information, but i know in 1.09 there was no universal "uniqueness" number, more like a specific number for each base type. In general, the lower the item, the higher the chance of it being unique. If Pindleskin dropped both a cap and a Hydra bow, there was a higher chance the cap would be unique than the Hydra bow. That was 1.09 info though, so it may have changed. Someone else probably has better info there.

    2) Neither Death's Web nor Astreon's Iron Ward are class specific. Necro's have class specific heads and paladin's have class specific shields. The difference in drop % might partially be based on a differing "uniqueness" number, but it could also be that they are in different Treasure classes and the base items have a different % chance to drop.

    3) Yes. It's complicated. Thrugg outlined the whole chest dropping process a couple months ago in this thread.


    Hope i helped some

    [EDIT: The post I linked to from Thrugg wasn't the one I thought it was, and you obviously have already seen it cause he was responding to you. I know I've recently seen a breakdown of how the chests decide what type of drop, but for the life of me, I can't find the info. Sorry.]
     
  3. helvete

    helvete IncGamers Member

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    Those two items are "rods" and rods also have 1/3 drop rate. There shouldn't be a difference in drop rate, UNLESS the search was based on the item itself, and one of them has a higher Qlvl than the other. As far as I remember, any monster able to drop Unearthed Wands can drop the unique. Astreons... what was I saying again? ...Can't remember for the life of me... /quote Chocobo Sage
     
  4. Kemist

    Kemist IncGamers Member

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    I have heard of the set/unique drop when LoD first came out, it was everywhere and everyone was doing it.
     
  5. krischan

    krischan Europe Trade Moderator

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    All items which can be worn by a certain class only as well as wands, staves, scepters (also called rods) have 1/3 the normal drop chance in their TC, except assassin items which have 2/3 the normal drop chance.

    To be honest, I don't know why ATMA shows Astreon's and Death's Web with different drop chances. They are in the same TC and caducei and unearthed wands have the same drop chance, but e.g. Baal drops the unique versions of them with slightly different probabilities. It might be some detail in the generation process, although I believe it's a rounding error in ATMA.
     
  6. Thrugg

    Thrugg IncGamers Member

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    There is indeed a base "unique chance". Or rather, there are two, one for normal items and one for class-specifics. In 1.10, these numbers are 400 and 240 (as in 1 in 400 and 1 in 240).

    These are modified by (ilvl - qlvl). If Baal drops an Unearthed Wand, ilvl 99 and qlvl 86, ilvl - qlvl is 13, which improves the unique chance to 1/387.
    Caducei are qlvl 85, so they are improved more to 1/386. This explains the difference.
    Class-specific items do not get the full (ilvl-qlvl) bonus, it is divided by 3 (rounding down). So if Baal drops a Bloodlord Skull, ilvl 99, qlvl 85, difference 14, divide by 3 gives 4, so the odds improve to 1/236.

    The others are correct in observing that Caducei and Unearthed Wands are not class-specific. Being rods, they have the same 1/3 rarity within their TC as class-specifics, but they do not get the better odds of being unique. This is the main reason they are quite so rare compared to other TC87s.

    After the (ilvl-qlvl) adjustment, your MF is applied. Then, the minimum chance cap. Then the bonus for the monster type (eg boss or unique). That gives you the final number.

    These base numbers are in the MPQ files, specifically in itemratio.txt - which you can see in your Atma directory if you want. That lists 3 numbers for each quality, eg "Unique", "UniqueDivisor" and "UniqueMin" which are the base chance, amount to divide (ilvl-qlvl) by, and the min chance cap (x128) respectively. There is a row for each of regular and class spec items, and also for normal and "uber" (exceptional and elite) items - although the normal and uber rows are identical, but a modder could make them different if they wanted. There are also rows for Classic.

    As for superchests, the chances are simple - 2% unique, 4% set, 6% rare, rest magic. They seem much higher than your experience would tell you, but that is because even when a chest drops say unique quality, there is still a pretty high chance you won't get any uniques. And a very high chance you won't get sets, just because so few item types have set versions.
     
  7. Hrus

    Hrus IncGamers Member

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    @Thrugg: unbelievable knowledge.

    I am still not convinced about the superchests. I think I have seen rare drops from these hundred times, but still no sets nor uniques.
     
  8. NEURO_CKY

    NEURO_CKY IncGamers Member

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    Thrugg needs to be on a dii style jeopardy game show..lol. or some other way to make money off of his vast d2 statisttical information. everytime he makes a new post i feel like we need to pass on offering jar around the forum for him!!
    keep up the good work thrugg!!!

    p.s.: your sooo friggin money!!!


    CampKillYourself
     
  9. Hakai_no_Tenshi

    Hakai_no_Tenshi IncGamers Member

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    There is only one truth .. trust ATMA. Everything else is a figment of your imagination ;)

    --T
     
  10. Psychic Watch

    Psychic Watch IncGamers Member

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    Since I still have an interest in the previous patch versions, I'm wondering if the equation in the 1.07 guide at http://www.rpgforums.net/showthread.php?t=126645 applies in the other versions as well:


    I'm mainly curious about a list like this:

    1.00 - 1.06 (Classic): equation

    1.07: Final Modified Chance = (128*Chance - (128*Cx*Chance/1024 ) - X*MF)/128

    1.08: equation

    1.09: equation

    1.10: equation


    It sounds like it might be the same for all, based on Thrugg's info, with only the base 'Chance' different in the itemratio.txt file.
     
  11. Thrugg

    Thrugg IncGamers Member

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    MF was completely (completely) different pre-LoD. There were no treasure classes, no boss bonuses, I don't know how it worked exactly but it was nothing like now.

    The current system has indeed only changed in places since 1.07 came out.

    The information you quote from the 1.07 guide is correct. The base chance back then was 1000 for uniques, 500 for class-specific. The guide mentions the ilvl-qlvl modification.

    The equation is combining two steps. I might as well explain the whole thing in depth...

    Start with your base chance (from itemratio.txt - this chance has changed every patch, was 1000 in 1.07, 800 in 1.08, 500 in 1.09 and now 400 in 1.10).

    Subtract (ilvl-qlvl)/divisor. Divisor is also from itemratio.txt and has changed.

    Multiply by 128. This is just done for extra precision. Instead of storing X and your chance being 1/X, they store 128*X and your chance is 128/(128*X). That is why all the 128s in the equation you quote.

    The next three steps have not always been the same. I will list them, then explain the history.

    A) Apply boss bonus. Each monster has a bonus to finding each quality type called Cx. This is a number between 0 and 1024. Higher is better. It is applied by this equation:
    new chance = chance - (chance * Cx / 1024)
    Effectively that improves the chance by 1024/(1024-Cx). For act bosses, Cx has always been 983, which turns into roughly a 25 times bonus.

    B) Apply MF. The way they have done this changed dramatically early on (because the way they first did it was, to put it mildly, rteraded).
    Originally (1.07) they simply subtracted your MF*X as your equation lists. X was 1/4/9 in norm/NM/Hell respectively.

    If you know a little maths you can see that this results in a curve which starts off really flat and then suddenly curves up steeply (the opposite of what happens now, more or less). For example, if your odds are 1 in 100 and you add 1 MF, you get 1 in 99 - almost the same. If your odds are 1 in 100 and you add 50 MF, you get 1 in 2 - much better. If your odds are 1 in 100 and you add 99 MF then it becomes automatic! This resulted in there being critical values of MF that would always force certain monsters to drop a given quality, set, rare, even unique - though you could only reach the unique critical on Hell bosses. However, the cost of that was that at low levels MF was completely useless.

    In 1.08, they "fixed" this, sorta. They reduced the difficulty bonus to 1/2/3 instead of 1/4/9. Now, you couldn't reach the critical points anymore. But it still sucked at low levels though. So in 1.08, you might as well forget MF altogether.

    In 1.09 they fixed it properly, and it is unchanged in 1.10. MF is now diminished through a formula like
    effective MF = MF * 250 / (MF + 250)
    The 250 value is only for uniques, there are others for set and rare.
    It is then applied by
    new chance = chance * 100 / (100 + effective MF)
    Which means if you have 100 effective MF (which is 167 actual MF), you exactly halve your 1 in "chance" number, ie doubling your chances.

    C) The min chance cap. This was only brought in in 1.09, and has only been working since 1.10. In itemratio.txt is another value for each quality which is a minimum value for your chance number. The idea is that if you have a billion MF they didn't want you to get uniques every drop (even though the diminishing returns actually already achieves this, meh). So here they simply say if the bonuses have reduced your chance below the cap, set it to the cap.

    Unfortunately, when they wrote the caps into 1.09 they forgot about Mr 128. All their caps in that version were the actual cap they wanted when it should have been 128 times the cap. For example, they wanted unique chance to never be better than 1/50, but because of the 128 scaling, putting 50 there meant your odds were never better than 128/50. Not surprisingly.
    They fixed this in 1.10, now the cap for uniques is 6400 (128/6400 = 1/50) as they intended.

    Now, like I said the order changed too.
    In 1.07 and 1.08 it went A then B, giving the equation you quote.
    In 1.09 they added the cap, but the cap was only supposed to affect MF and not rob you of your boss bonus. So since then it has been B then C then A.

    Finally your actual chance is 128/(total chance) as produced by all the steps.

    I'm not going to try to decribe a single equation for 1.10. It is possible but it would be very messy without an equation editor that can handle nested fractions. Also it is important to remember that Diablo is almost entirely done in integer arithmetic. Every division sign you see above is a round-down division. That can make a big difference.

    I know this is a lot to take in all at once. Feel free to ask questions. Also, Doc Tenshi consulted with me at length when writing Atma and I am confident that the chance calculations in there are correct for all 4 versions. There is an issue or two when combining the chances in the more complex TCs, but the individual MF calculations are all good.
     
  12. Hrus

    Hrus IncGamers Member

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    I would be highly interested (and not me alone I think) in complete guide how this works. (proper numbers for uniques,sets,magic etc.) Then it should be stickied or even posted at strategy compendium.
    Again Thrugg: :clap: :clap:
     
  13. Jarulf

    Jarulf IncGamers Member

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    Thrugg,

    1.07 was horribly messed up for MF and completely buggy I would say. Wasn't it the MF that was squared in 1.07? Was it really the number (1,2,3)?? The correction for 1.08 removed that but made the subtraction basically be insignificant. I don't recall the details any more but it should be posted somewere.

    I think ATMA got it all correct though.
     
  14. krischan

    krischan Europe Trade Moderator

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    Yes, I lost my faith. I'm unworthy. Please forgive me :worship: <-- Hey, they finally work again :thumbsup:
     
  15. Psychic Watch

    Psychic Watch IncGamers Member

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    Ok, I follow you on how to calculate each of A and B. I also understand the reasoning for part C, but while trying to work it out for 1.09 and 1.10 I wasn't sure of the exact formula. Is it anything like this?

    Code:
    Base Monster Chance = BaseChance - ( (ilvl - qlvl) / divisor )
    stored BMC (for precision) = BMC*128
    
    
    Part A, boss bonus chance = storedBMC - TRUNC(storedBMC * Cx / 1024)
    
    
    Part B, effective MF chance (...omitted)
    
    
    'messed up' 1.09 cutoff = 50
    
    if (B < cutoff) then (C = cutoff) else (C = B)
    
    
    Final Chance:	TRUNC( (A - C) / 128 )
    
    
    (Since the Excel wasn't pasting nicely I omitted a lot of it).


    Also, for the final combination of A, B, and C in 1.09 and 1.10, I wasn't quite sure about the mechanics of the bolded part (i.e. 'then' == ?) :

     
  16. Bullet-Tooth Tony

    Bullet-Tooth Tony IncGamers Member

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    Thrugg,
    If I got it all correctly, let's try an example:
    I kill Baal and expect an item to be unique:
    1) Base chance = 400;
    2) Apply ilvl-qlvl, 13 for example, so the chance = 387;
    3) Apply bossbonus: 387*(1-983/1024) = 30.6123.
    4) Apply MF. For example, 100% effective (167 actual), which reduces the chance to ~15.297.
    Now, according to your post, this chance for uniques can't be lower than 50, is this correct? This means, that 15.297 (with 167 MF) or 30.6123 (with no MF) turns into 50. If I understood you correctly, there should be no point in wearing MF vs bosses, because your chance for unique should anyway be lower than 50 (30 or 15, doesn't matter), which is set to 50.
    Can you explain, how is this chance cap applied?
     
  17. Thrugg

    Thrugg IncGamers Member

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    PW - yes, the min cap is a simple "if (chance < minchance) then chance = minchance".

    PW and BTT - In 1.09 and 1.10, the calculation order goes
    Apply MF
    Apply cap
    Apply boss bonus
    so that you get the full benefit from the boss bonus. The cap is only to nerf your MF.

    To correct BTT's example, say Baal dropping an Unearthed Wand, when you have 167 MF:

    Base chance = 400
    chance - (ilvl - qlvl)/divisor = 400 - (99-86)/1 = 387
    Multiply for precision: 387 * 128 = 49536
    MF chance = 49536 * 100 / (100 + 100) = 24768
    Compare against unique min cap of 6400, it is higher so no effect
    Boss chance = 24768 - (24768 * 983 / 1024) = 24768 - 23776 = 992
    Final chance is 128/992 = 12.9% (pretty good chance really).

    Does that make it clearer?
     
  18. krischan

    krischan Europe Trade Moderator

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    Just two questions...

    Q1:
    The "apply MF" term 100/(A+100) is nothing else than applying its reciprocal value (A+100)/100 = 1+A/100 to the probability which looks like applying a percentual bonus being A. However, the formula for calculating diminishing returns (e.g. MF*250/(MF+250) for uniques) doesn't work with the MF bonus, but with total MF. So I have to calculate A as follows:

    Add up MF bonuses from equipment
    Add 100
    Apply diminishing returns X*MF/(X+MF) with X=250 for uniques, 500 for sets, 600 for rares and no change (respectively X=infinite) for magicals
    Subtract 100

    Correct ?

    So the example "167 MF = 100 effective MF" would mean having equipment that gives a bonus of 67%.

    Q2:
    Perhaps it's mentioned somewhere in this thread, but where do I find the boss bonus values for all the different kinds of monsters ? For act bosses it's 983...
     
  19. Thrugg

    Thrugg IncGamers Member

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    kris, you apply the diminishing formula directly to your worn MF, you do not add or subtract 100 at any stage (well, except when you apply it to the chance).
    All of the equations I have listed can be re-written in mathematically equivalent ways, however I wrote them in the same form as the code actually calculated them. It can be important when it comes to rounding. Every division is done integer style, rounding down.

    If you have access to TreasureClassEx.txt out of the MPQ, the boss bonuses (strictly speaking, all TCs have them, although the non-boss ones are all zero) are listed in the columns with the obvious names (uniqe, set, rare, magic).
    Act bosses are all 983/983/983/1024 (the 1024 is why they always drop at least magical)
    Act bosses on their quest drop are 993/993/1024/1024 (Andariel is 995/995)
    SUs are 800/800/972/1024
    Uniques and Champions are 800/800/800/1024
    Council members are 650/800/800/1024
    Apart from that there are a bunch of special monsters with personalised patterns (the usual ones, like Summoner/Nihly/Hephasto/Cow King/Countess)
    Oh, and DiabloClone is 1024/0/0/0 :)
     
  20. krischan

    krischan Europe Trade Moderator

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    I guess that's good news for MFers. I have read it in several places that it's different and it seems I got used to it. Anyway, I regard you as the more reliable source and in particular, it's much more logical because the dimishing returns formula will have no effect on a 0% MF bonus then.

    Thanks for that information. As you omitted regular monsters, I guess regular monsters (not being bosses :)) have a boss bonus of 0.

    *Adding thread to subscriptions*
     

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