Calculating chance of crafting "Perfects"

• I was hoping to start an in-depth investigation into the chance of crafting 'perfect' pieces of gear. I've browsed all of the theorycrafting forum and significant amounts of general discussion and haven't found one that reveals enough for my tastes. Googling had similar results.

So, what exactly am I talking about? I plan on playing a DH come release (this is largely irrelevant, just using it for an example), and I will be looking into maxing my damage while letting Magic Find and Gold Find take the secondary and tertiary respectively.

Let's look at an example from the Beta:

Journeyman Bindings (http://diablonut.incgamers.com/item/journeyman-bindings)

25-32 Armor
• +12-17 Vitality
• +2 Max Random Magic Properties
Required Level: 11

Ideally, the 'perfect' bracers for my class for this item is the following:

32 Armor
17 Vitality
+ Max Dexterity
+ Max Magic Find

Now i'm interested in the math for the odds of crafting this perfect item for one specific class, a perfect item for any of the classes (replace Max Dexterity with whatever Max stat), and then using that to generalize percentage chance of creation with any variable on gear.

Anyone up for taking a swing at the math?
• Looking at just 1 stat, and assuming things are weighted equally.

25-32 armor
12-17 vitality
+1 Random Magic Property.

Assuming each magic property is weighted the same, regardless of the variance
within said property, then the multiplier here is just the total # of affixes
in the beta. My count from Diablonut is 62. Are certain affixes specific to
certail item slots? Well if it isn't, and any affix can be present on any slot,
then we'd multiply the variance of armor, variance of vitality, the chance of
hitting the random we want(62), and the variance of that affix.

Rank 1 of dexterity on diablonut is +1-8.

1/(7*5*62*8) = 1/17360.

Now adding a second random property:

Rank 1 of Magic find on diablonut is +5-9% Better Chance

1/(7*5*(62*8)*(62*5) = 1/(35*496*310) = 1/5381600

Could this math possible be correct?

I also read in an Affix thread that the full game might have as many as 300 affixes,
this would make the odds even more insane.

I'm guessing affixes must be specific to item slot, which would cut down the largest
multiplier.
• You are almost correct in your calculations (under the assumptions that you have stated, which seem reasonable enough to me).

First of all, the range 25-32 includes 8 integer values, not 7. You made the same error with the range 12-17, which includes 6 values. You did it correctly for the ranges 1-8 Dex and 5-9% MF, which include 8 and 5 different values respectively. This is assuming that the range is a closed interval (includes the endpoints noted), but if it is an open interval then your amount of Dex and MF values is wrong.

Furthermore, when you do the calculation for the chance to get the optimal range if you have 2 random properties you forgot about combinatorics. The chance that you get both of the desired properties (+Dex or +MF in your case) does not depend on the order in which those properties occur. An item with +8 Dex and +9% MF is just as valuable to you as an item with +9% MF and +8 Dex (other order of properties, same values). This means that the chance to get the desired combination of properties is doubled.

The math:
1/62 * 1/8 (chance to get +Dex and +8 out of 1-8 for the first property) * (and) 1/62 * 1/5 (chance to get +MF and +9% for the second property)
+ (or)
1/62 * 1/5 (chance to get +9% MF for the first property) * (and) 1/62 * 1/8 (chance to get +8 Dex for the second property)

This means that in the end your chance for getting the optimal armour becomes:
1/8 * 1/6 * ((1/62 * 1/8 * 1/62 * 1/5) + (1/62 * 1/8 * 1/62 * 1/5)) = 1/8 * 1/6 * 2/153760 = 2/3690240 = 1/1845120

So about 1 in 2 million. Not as bad as what you calculated, but still a hell of a lot of crafting... Take note though that the probability that you craft a "valuable" perfect item is way more than that, because you might also play other classes or like different affixes other than MF.

Very good point about double the chance, and also for fixing the armor/vitality stats.

I think there's a slight miscalculation here:

1/8 * 1/6 * 2/153760 = 2/3690240 = 1/1845120

I think you'll find that 1/8 * 1/6 * 2/153760 = 2/7380480 = 1/3690240

Correct me if i'm missing something though.

I also realized that, as far as I know, the game will not allow you to 'double dip'. So therefore if you have 62 different affixes on the first enchant, you'll only have 61 on the second. With double the chance, the fixed armor/vitality values, and the double dipping, i'm looking at this number now:

2 chances out of / (8 armor variance) * (6 vitality variance) * ((62 affixes) * (8 variance in Dex)) * ((61 remaining affixes) * (5 variance for MF))

2/(8*6*(62*8)*(61*5)) = 2/(8*6*496*305) = 2/7261440 = 1/3630720

So 1 out of a little over 3.5 million crafts will be 100% perfect with two fixed stats (Armor and Vitality) and two randoms, that you need specifically maxed.

Now if we replace the Dex with any of the three stats that add damage (Dex, Int, Strength) we're looking at 4/7261440 = 1/1815360.

These numbers are still pretty outrageous, and I believe the flaw lies in the number of possible affixes. There are 62 on diablonut, but i'm almost positive at this point that those affixes are assigned specific item slots.

Just to prove my point, if you were looking for a perfect in the above stats for any of the three (Dex, Int, or Strength) and decided to craft all 1.8 million, and crafting 1 took approximately 2 seconds (factoring in the time it takes to salvage the failed attempts this may be very optimistic).

It'd take you 42 days. Just to craft them. Not even blizzard is this mean. :-) Now we just need to find the affixes specific to each item slot and take it from there....
• 1/8 * 1/6 * 2/153760 is indeed 1/3690240 (typed 2 instead of 1 and didn't re-check)... And also forgot about the double dipping thing yeah.

Your chance for getting either the Dex, Int or Str version is off though, it's simply 3x the chance to get one specific type (as the chance to get each one is of equal probability). Same thing as when you calculate the chance to get a 1, 2 or 3 on a 6-sided die (3x the individual probability).

But yes, the chance to get that perfect item with very specific affixes is outrageously small. Don't forget though that with several million players, even if each is only crafting one item once, it is expected that -some- people will end up with that perfect item. Just don't expect it to be you.

You also have to remember that we assumed here that your primary stat and MF are the optimal affixes to have, but if Blizzard balances correctly then it should be very, very difficult to determine the actual "best" stat, as these things might vary with for example crit chance (and the fact that survivability is much harder to measure than raw DPS). Don't forget that for example Str adds armour, so it might not give as much +DPS as say a pure DPS affix like +crit chance.
• This may come dangerously close to falling into a new topic, one based around arguing the merits of each affix, but I think it's safe to say that there will be 'winner' stats and 'loser' stats. Some stats that you see on an item and mentally take note of the wasted enchantment. Just off the top of my head these would include:

'Losers':

-Health Regen.
-Pickup gold/health globe range.
-Thorns abilities (I argue this because i plan on playing a class that revolves around avoiding getting hit and staying at ranged)
-Health globe bonus to health.
-Maybe %block and armor...

'Winners':

-Anything that boosts damage, whether it be 'of wounding' with straight damage additions (+2-3), 'of the snake' with added poison damage (+3-6 poison), or a class specific stat, like Dex for DH's, increased attack speed...
-Vitality, more health is always good.
-Magic Find for the ability to find better gear, or for more magical items to salvage to make better gear...
-Gold Find for repair costs, stash size increases, crafting, buying cheap blue gear to salvage to craft...
-Resists

Obviously you will have to balance out your characters stats to maximize survivability, damage done, and MF/GF. As difficulty increases so will your need to boost the first two, rather than the former. The question still remains: "What is the chance of crafting that specific best item that i need?"

I think in order to further answer that question we have to identify which affixes can be placed on which item slots. I've spent some time googling and came up short, so I'll attempt my own tests tonight in the beta and post my results.
• This discussion is still ultimately pointless, as the math (right or wrong) is only applicable if you can say with 100% surety that this will be the pool of mods, and the only pool of mods, available at release. Which you can't.

The plausibility of this mod pool being much larger is very high, which immediately invalidates any theorycrafting calculations that are done here.
• Quote from snared04drummer

This discussion is still ultimately pointless, as the math (right or wrong) is only applicable if you can say with 100% surety that this will be the pool of mods, and the only pool of mods, available at release. Which you can't.

The plausibility of this mod pool being much larger is very high, which immediately invalidates any theorycrafting calculations that are done here.

I understand where you're coming from, it does seem pretty much pointless to get down to specifics. Any specifics I have used prior to this post have been in an attempt to better explain via example. As for the POINT of the thread though, it is to eventually model (based on examples) an equation with variables (variables that will almost certainly change come the full release) to calculate the odds. Whether or not more affixes are added or not, is irrelevant, as long as we are capable of finding the values of the variables an equation can still be theorycrafted to give information for the actual release, as well as the beta.
• I don't know alot of people who does the calculations for the perfect item to spawn and come up with the results with a happy face. In fact I doubt we'll see any 100% perfect (rare) item spawn at all during d3's lifetime. To my knowledge, this hasn't even happened in d2 in a legit way yet (6 100% perf highest AND best mods in best base-item, eth for armor+weapon, non-upped possibly for weapon, elite item for armor and so on).

I think it would be much more interesting to the community to make some kind of compendium for items that we can assume will be "commonly" used, such as high-end crafts. By incorporating all the somewhat useful affixes and allow perhaps only 3-4 of these not necessarily perfect mods to return a useful number, since we all know 10 million crafts isn't necessary to find a useful item.

But as snared04drummer says, this is highly dependant on several missing factors we can't simply know pre-release or, as I suspect, for a long time afterwards.

edit: I should add that I am highly aware of that "perfect" is a misleading term. LLD items will likely spawn that might be perfect for that build and equally "perfect" items for hybrid builds or other strange ideas. I'm speaking about items that would be perfect for the mainstream intent, such as maximum damage output at level 60, or whatever it's going to be.
• This is all assuming it's the same chance for a 1 dexterity to spawn as a let's say 5 dex (hypothetical max).

It could be an equal % chance, such as a 20% chance to reach that max 5 dex. BUT for all we know you have a 90% chance to spawn 1-3 dex, and then an 8% chance for a 4, and a 2% for a 5. (unless Blizzard has stated otherwise, than my apologize)

Just my 2 cents
^ YouTube.Com/IceBleuGaming ! It's a thing! Check it oooout!
• Quote from Snaks42

This is all assuming it's the same chance for a 1 dexterity to spawn as a let's say 5 dex (hypothetical max).

It could be an equal % chance, such as a 20% chance to reach that max 5 dex. BUT for all we know you have a 90% chance to spawn 1-3 dex, and then an 8% chance for a 4, and a 2% for a 5. (unless Blizzard has stated otherwise, than my apologize)

Just my 2 cents

Assumptions are CERTAINLY being made. I think the assumption is logical however. It doesn't seem logical for them to make it any harder to hit that max stat then to hit the lowest stat. As we're starting to see, the amount of combinations alone already make finding the perfect stat fairly rare.

I've noticed that diablonut does in fact house what I assume are correct levels of affixes, and which item slot those affixes can be placed on. The question after that becomes which item levels correspond to which levels of accessible affixes. It doesn't make sense to craft a level 60 piece of armor and have it hit, say, +1 armor. There is going to be a low and a high level of affix(again, logical assumption), and those affixes themselves have a low and a high.

I'm going to put the assumptions to practice tonight. I've saved up some crafting mats over the last two days and plan on creating as many of those example bracers as I can in an attempt to find exactly what level affixes can be attached to them. That should help me get the stats on a percentage fairly easy. Doing an AH search is another great idea for checking this. Just viewing which are for sale and with what stats.

Excited to get home and do more research. :-)
• Quote from Snaks42

This is all assuming it's the same chance for a 1 dexterity to spawn as a let's say 5 dex (hypothetical max).

It could be an equal % chance, such as a 20% chance to reach that max 5 dex. BUT for all we know you have a 90% chance to spawn 1-3 dex, and then an 8% chance for a 4, and a 2% for a 5. (unless Blizzard has stated otherwise, than my apologize)

Just my 2 cents

Stuff like this can be tested with reasonable accuracy by crafting a couple hundred of the same low level item and doing some statistical calculations with the results.

Sadly I don't got beta access, so I can't help there.
• in short:

VERY low chance.
Game Designer - Micro Design
• So!

After some time spent tonight crafting some of the Journeyman Bindings, I have a new perspective on what it's looking like. I made 50 of them, taking notes on each one. These are the enhancements I found:

Dexterity, Str, Int, Vit, MF, Crit, PickUp, Exp, Thorns, Regen, L/Gl, and GF.

Then going through each of the 62 enhancements listed on diablonut, I found that the following are listed as available for Bracers, but I did not find a single one out of 50:

Armor, Damage Reduction [Elemental], Damage to Health, Dexterity + Intelligence, Dexterity + Vitality,
Intelligence + Vitality, Item Value, Maximum Life, Resist All, Resist Arcane, Resist Cold, Resist Fire,
Resist Lightning, Resist Poison, Strength + Dexterity, Strength + Intelligence, Strength + Vitality.

So, 17 listed that I didn't find, 12 found that are also listed. 29 possible enhancements for bracers in total if diablonut is correct.

At 29 possible enhancements, two random per attempt, 50 attempts, it seems ludicrous that I wouldn't have hit one of the 17 solely on chance. This leads me to believe that they must be item level restricted and the journeyman's simply aren't high enough.

Now, back to our original question. What's the percentage chance of hitting some maximum stats? Something else I came to realize was that, especially at this low level, but questionably even higher up, a stat like armor isn't really necessary to max out. Even at low levels 10 armor does not even raise damage reduction by a single %. Negating this, and focusing on the stats of the item, I've found the following for the Journeyman Bindings:

Going for Dex + MF:

2 chances of hitting the two stats I want, 6 possible vitality, 17 Dex, and 10 MF

2/ (6 * (29 * 17) * (28 * 10)) = 2 / ( 6 * 493 * 280) = 2 / 828240 = 1 / 414120.

So, in order to get Max Dex and Max MF on these specific bracers, it's approximately one out of 400,000 crafts.

Now add Max of a damage stat with the MF, not just Dex:

1 / 138040.

Master Equation for finding % Chance of X number of perfect stats:

X = Total number of Random Stats

X / ( (Any total # of fixed stat options) * (Total enhancements available for item * correct enhancements variance) * ( Total enhancement available for item - 1 * correct enhancements variance).

I checked the AH to see if any of these perfect Stat / MF combo's were listed and there were none.
• Yeh Blizz said in a video, I'm sure it's one of Jay's that some affix's will be reserved for later. Jay mentioned resists probably won't show up much until nightmare, as they simply aren't needed much in normal.

So you should just assume crafting at 60, so the total pool will be available

At lower levels, there will be a smaller pool to choose from, so theoretically a higher chance for a perfect combination for your class.

Theoretically higher is still very small though
• I was wondering if crafting always gives a fixed number of random properties or if it gives at most a certain number of them, and if the second holds, what the chance is to get 2 properties instead of just 1.

This is because DiabloNut uses the wording "+2 Max Random Magic Properties", while the wording on the official site is "+2 Random Properties".

http://diablonut.incgamers.com/item/journeyman-bindings
http://eu.battle.net/d3/en/artisan/blacksmith/recipe/journeyman-bindings
• HSSSSSS!!!! Statistics HSSSS!!!!!

Way more variables for the answer to this than I care to think about.
ex.
25-32 armor = 7 posibilities alone
12-17 Vitality = 5 posibilities alone
+2 random magic properties = ungodly large number of posibilities

So for just the armor/Vit combo we are talking 35 posible outcomes. Then you have to find out how many magic properties there are. After that you add in the ranges they cover for the item level.

You might even need a deeper understanding of how the system is designed.
ex.
Say for a level 11 item like in the OP for 1 magic property of magic find there are 2 names. (i.e. wand of "ooo shiny" / wand of "ooo and ahh") lets say the "ooo shiny" is a min level of 1 magic property and "ooo and ahh" is a magic property with a min level of 10. Each of these will have a range. The problem is if the system generates a name to match the stats or stats to match the name. I'm not sure to what degree this changes things mind you, it just seems like another place for the math to get longer.

I was wondering if crafting always gives a fixed number of random properties or if it gives at most a certain number of them, and if the second holds, what the chance is to get 2 properties instead of just 1.

This is because DiabloNut uses the wording "+2 Max Random Magic Properties", while the wording on the official site is "+2 Random Properties".

http://diablonut.inc...neyman-bindings
http://eu.battle.net...neyman-bindings

I can tell you that by now, I must have crafted at least 75 of these +2 enhancement bracers, and never come up with just 1 enhancement. It leads me to believe that the enhances are static.

Also, for those interested in my findings, you can view them here:

• Quote from Dumatrunks

I can tell you that by now, I must have crafted at least 75 of these +2 enhancement bracers, and never come up with just 1 enhancement. It leads me to believe that the enhances are static.

Also, for those interested in my findings, you can view them here: