Talk about items.

[rc009]

This isn't about items you've found unless you have found items people say here.
I wanted to create this so people could talk about items they want to find and if its possible
and maybe if your good at math what are the odds of finding it. Ive been looking at a list of
prefixes and suffixes for items.
When look at this list i was thinking about the best items and what came to mind is
Kings war bow of slaughter is that even possible?
Or maybe even arch-angels staff of wizardry that would be awesome.

[--Pete]

Hi,

For all your gear questions, there's probably an answer in Jarulf's guide.

Kings war bow of slaughter is that even possible?

Neither Kings nor Slaughter can be on bows (Jarulf's section3.4). Besides, that wouldn't be a good bow anyway. Speed is much more important and gives you much better damage per second.

Or maybe even arch-angels staff of wizardry that would be awesome.

Pretty good item, pretty common(just use the entrance to the cats to shop Adria), and my personal favorite for a mage because of its looks and the casting animation (you do know that a mage in CD needs absolutely nothing in the way of gear, don't you?)

Now, a good item of corruption, or the TFoS, those are items to be sought. Or even Woody's Bent Staff of Disease.;)

--Pete

[Nystul]

Besides, that wouldn't be a good bow anyway. Speed is much more important and gives you much better damage per second.

For argument's sake, you are giving swifty bows too much credit here. They would never beat a mythical king's LWB of slaughter in damage per second, and the extra speed is not as useful from a stun or be stunned standpoint as with a melee weapon (other than PvP I suppose). Even in the Real World of Diablo where bows of slaughter don't exist, getting enough damage to stun enemies is enough of a challenge to developing rogues to put swiftness behind raw damage for a long time.

[LennyLen]

Kings war bow of slaughter is that even possible?

Sounds like a job for LICK.

/shameless plug

[FireIceTalon]

For argument's sake, you are giving swifty bows too much credit here. They would never beat a mythical king's LWB of slaughter in damage per second, and the extra speed is not as useful from a stun or be stunned standpoint as with a melee weapon (other than PvP I suppose). Even in the Real World of Diablo where bows of slaughter don't exist, getting enough damage to stun enemies is enough of a challenge to developing rogues to put swiftness behind raw damage for a long time.

Um, as a huge advocate of rogue playing (Ive lvled 4 of these gals to 50), i have to disagree for the most part.

Swiftness bows are just SICK. For a low lvl rogue, yes, raw damage would be more important then damage per second, but you are only low lvl for so long :)

Only place to go is up. And for mid-high lvl rogues, swiftness is clearly superior to raw damage for a number of reasons. Even if the raw damage is less, the the increased damage per unit of time for outweighs this factor, especially in nightmare and hell mode. Not to mention the fact that swiftness bows can stun multiple enemies at once. And against enemies that have super fast hit recovery like Balrogs, swiftness is indespensible on a bow. If im playing a high ac casting rogue, Emerald Heavens would be my bow of choice, in any other situation I would use my Massive Swiftness.

and for PvP, its a no brainer. Swiftness bows are hands down the way to go, though FireIce will occaisonally pull out the Merciless Burning for fun.

[Nystul]

Massive LWB of Swiftness rough estimate weapon damage: 7.5 * 2.1 = 15.75. Since there are truncations involved, I'll round to 15.5.
Mythical King's LWB of Slaughter rough estimate weapon damage: 7.5 * 2.75 + 20 = 40.625. I'll round to 40.

Case 1: Level 30 Rogue, 90 STR, 210 DEX. Base damage = 45.

Estimated damage per shot with swifty: 60.5. Estimated damage per second = 60.5 / 0.30 = 202
Estimated damage per shot with slaughter: 85. Estimated damage per second = 85 / 0.35 = 243

Also note that the mythical rogue will stun level 60 enemies every time, while the swifty rogue will only stun them a minority of the time.

Case 2: Level 50 Rogue, 136 STR, 331 DEX. Base damage = 116.

Per shot with swifty: 131.5. Per second: 438.
Per shot with slaughter: 156. Per second: 446.

[FireIceTalon]

Massive LWB of Swiftness rough estimate weapon damage: 7.5 * 2.1 = 15.75. Since there are truncations involved, I'll round to 15.5.
Mythical King's LWB of Slaughter rough estimate weapon damage: 7.5 * 2.75 + 20 = 40.625. I'll round to 40.

Case 1: Level 30 Rogue, 90 STR, 210 DEX. Base damage = 45.

Estimated damage per shot with swifty: 60.5. Estimated damage per second = 60.5 / 0.30 = 202
Estimated damage per shot with slaughter: 85. Estimated damage per second = 85 / 0.35 = 243

Also note that the mythical rogue will stun level 60 enemies every time, while the swifty rogue will only stun them a minority of the time.

Case 2: Level 50 Rogue, 136 STR, 331 DEX. Base damage = 116.

Per shot with swifty: 131.5. Per second: 438.
Per shot with slaughter: 156. Per second: 446.

Interesting numbers, but its really the Kings Prefix that puts the mythical rogue over the swiftness rogue in this case, so its not exactly a fair comparison.

If you replaced the Massive Swiftness with another mythical bow, a KINGS bow of Swiftness, it would be a much more dominant rogue (especially in PvP) then the one with a Kings Slaughter bow.

There is a reason why Massive Swiftness (or Warriors, Vicious, Brutal Swiift as well) is much more sought then Windforce :)

The swiftness is better for the same reasons that a Kings sword of Haste is better then a Kings Slaughter or Heavens.

[weakwarrior]

Sounds like a job for LICK.

/shameless plug

Some bugs in lick.

I put strange bastard sword into lick and it said I could find it on level 16. I put in axe and it says a boss of level -3 could drop it. When I put in breast plate I get information about the overlord's helm and the gotterdamerung. With gothic plate I get info about the Torn Flesh of Souls.

[LennyLen]

Some bugs in lick.

Yeah, I know. I lost the source code due to a hard drive crash and never got around to writing another version to fix them.

I put strange bastard sword into lick and it said I could find it on level 16

It does that for any qlvl 60 item. There was a reason why, but I've forgotten it.

I put in axe and it says a boss of level -3 could drop it. When I put in breast plate I get information about the overlord's helm and the gotterdamerung. With gothic plate I get info about the Torn Flesh of Souls.

Those are all caused by the same bug, which was caused by the way I parsed the input into prefix, item, and suffix. It occurs when you enter certain base items without any prefixes or suffixes.

I've been saying for years that I'll update LICK, but nobody should hold their breath.;)

[the Langolier]

maybe if your good at math what are the odds of finding it.

Item Rarity Calculator

I made this a long time ago. It's about as accurate as I can figure and should give you a good idea of how rare items are compared to one another. Just for fun calculate a Vulnerable Full Plate Mail of Weakness and compare it to an Obsidian/Zodiac.

[Nystul]

Item Rarity Calculator

I made this a long time ago. It's about as accurate as I can figure and should give you a good idea of how rare items are compared to one another. Just for fun calculate a Vulnerable Full Plate Mail of Weakness and compare it to an Obsidian/Zodiac.

That's nifty. It should go without saying that the best items in Diablo, while plenty hard to get in their own right, are far from the being the most rare. About 10 years ago, someone posted that the rarest item would be an emerald (specific melee weapon) of slaying. According to your calculator, an emerald bastard sword of slaying will show up about once every 2,840,000 games! On the bright side, you only have to get to level 14 and check for Dreadjudge before starting a new game. :D No need to bother with Wirt since even he cannot sell such a combo. At 30 seconds a game, 24 hours a day, it should only take a couple weeks eh?

[weakwarrior]

That's nifty. It should go without saying that the best items in Diablo, while plenty hard to get in their own right, are far from the being the most rare. About 10 years ago, someone posted that the rarest item would be an emerald (specific melee weapon) of slaying. According to your calculator, an emerald bastard sword of slaying will show up about once every 2,840,000 games! On the bright side, you only have to get to level 14 and check for Dreadjudge before starting a new game. :D No need to bother with Wirt since even he cannot sell such a combo. At 30 seconds a game, 24 hours a day, it should only take a couple weeks eh?

I noticed a mistake with the calculator which, I think, would make it take a little longer. The calculator gives the same value for an emerald bastard sword of slaying and an emerald short sword of slaying. However, after the game decides to drop a bastard sword from a unique boss there is a 16% chance of the item being unique; there is no unique short sword. Thus, the chance of magical short sword drop should be higher than a magical (non-unique) bastard sword. Either, the calculator always counts the 16%, even when there is no unique, thus underestimating the probability in the case of the short sword, or it never does, thus overestimating the probability in the case of the bastard sword. Langolier? I´m willing to try 2,840,000 games, but 3,400,000 is just too much.

[the Langolier]

I noticed a mistake with the calculator which, I think, would make it take a little longer. The calculator gives the same value for an emerald bastard sword of slaying and an emerald short sword of slaying. However, after the game decides to drop a bastard sword from a unique boss there is a 16% chance of the item being unique; there is no unique short sword. Thus, the chance of magical short sword drop should be higher than a magical (non-unique) bastard sword. Either, the calculator always counts the 16%, even when there is no unique, thus underestimating the probability in the case of the short sword, or it never does, thus overestimating the probability in the case of the bastard sword. Langolier? I´m willing to try 2,840,000 games, but 3,400,000 is just too much.

Interesting observation. For unique monsters, it always assumes the chance for a unique item is 16%, I never thought to check that there was actually a unique for that base item type as I figured they all were covered. I'll have to work on that.

[weakwarrior]

Interesting observation. For unique monsters, it always assumes the chance for a unique item is 16%, I never thought to check that there was actually a unique for that base item type as I figured they all were covered. I'll have to work on that.

So it´s 2,840,000. Then here we go. Two down - no dreadjudge - 2,839,998 to go (I know - conditional probabilities blah blah).

[weakwarrior]

That's nifty. It should go without saying that the best items in Diablo, while plenty hard to get in their own right, are far from the being the most rare. About 10 years ago, someone posted that the rarest item would be an emerald (specific melee weapon) of slaying. According to your calculator, an emerald bastard sword of slaying will show up about once every 2,840,000 games! On the bright side, you only have to get to level 14 and check for Dreadjudge before starting a new game. :D No need to bother with Wirt since even he cannot sell such a combo. At 30 seconds a game, 24 hours a day, it should only take a couple weeks eh?

An emerald specific shield of the wolf has the same property, although it is a bit easier to find. Why is that? In part it is because there are fewer shields, but the ratio isn't enough to explain the difference in probability.

[Nystul]

If Dreadjudge drops an emerald bastard sword of *something*, there are a lot of suffixes to pick from to get "slaying". If he drops an emerald tower shield of *something*, there are only a few things it can be.

[weakwarrior]

Not that it matters much, but I get a slightly different number than the calculator. Here's my computation

The chances of magistrates on dlvl 14 (and therefore Dreadjudge) is 10%.

There are 67 base items with the bows being 2x as likely which for the sake of probability is the equivalent of adding 8 new items = 75. In addition, bosses can drop rings, amulets, and books. To make these items more common the code has several base items for each: 4 for books, 3 for rings and 2 for amulets, which means another 9 = 84. So the probability of getting a specific weapon (non-bow) is 1/84.

The chance that the item has both a prefix and a suffix is 16.7%.

There are 24 prefixes which can exist on non-bow weapons which are between qlvl 15 and 31. However, + to hit items and + to hit (3), + damage (3), and + both (5) are 2x as likely so we add another 11 so the chance of an emerald prefix is 1/35.

There are 15 possible suffixes which can exist on non-bow weapons which are between qlvl 15 and 31.

When a boss drops something which can have a unique item associated with it there is an 84% chance that it won't be unique.

So, in sum, the chance of an Emerald non-bow (which has a unique item of the same type) of Slaying dropping is 3.18 * 10^-7. The calculator gives 3.52*10^-7.

Can anyone tell me where I went wrong?

[the Langolier]

There are 67 base items with the bows being 2x as likely which for the sake of probability

...

Can anyone tell me where I went wrong?

You had me going for a minute. I appreciate your diligence. I programmed that calculator so long ago I went back through the code that calculates the rarity for unique monsters and saw I forgot to include this if statement for unique monsters:

Code:

if (baseEQ[i].iClass == "Bow") //bows have double chance of being picked
            {
                totalBase++;
            }
            totalBase++;

That would count bows twice as expected. But then I checked Jarulf's guide section 3.8.2, which states, "Bows, however, are actually counted twice if the item is dropped by a normal (non unique or special) monster, and thus have a double chance of being created."

So, bows are not counted twice for unique monsters, meaning the total number of available base items are 76.

[weakwarrior]

I appreciate your diligence.

You appreciate my diligence?! I was careless and was doing it more to see if I understood Jarulf correctly. You, on the other hand, had already done this and had taken the time to check my math. I'm very grateful for your diligence!

[the Langolier]

After going through the calculations I'm sure you can appreciate all the little pieces of information you must collect and keep in mind.

The rarity calculator project actually began with an idea of just posting the rarity of some of the most desirable items (obs/zod, aweseom/stars, etc). I was inspired by some Diablo 2 information I happened across about the source for the best drop probabilities for any unique item. I really thought it would be neat to do the same thing for diablo 1 items. As I started some sample calculations, I found it to be quite tedious. I decided it would be best to write a program that would sort it all out for me.

Before I even started coding, I figured that while I was making a program, I might as well make it calculate for any mlvl I specified. My original plan was for a small C program that would do all the calculations for a single item for all mlvls. That would of course require modifications for every item I wanted to post. Then, if it could do that, why not make a single program that could do the calculations for any item? And if for any item, why not from any enemy? Of course, I figured if I was going to make a program that could do it for any item, I could just publish the program instead of just using it to post the rarity of a few select items.

At that point I was beyond my knowledge of C, so I needed a new language and format to use. I did some research, considered whether or not I wanted it to run in a browser or be a downloadable executable, and eventually settled on using javascript. It was a bit of a lucky guess that allowed for a simple GUI using HTML. I spent a few weeks going through javascript tutorials to learn the language and how the code interacted with the web elements of the DOM.

The first part of the project was designing the form and using javascript to make the drop-down menus behave properly - basically everything that happens before you press 'calculate'. It was fairly easy and gave me the confidence that the whole thing was actually going to work. The next part I did was code the individual functions to calculate the rarity for any single source, starting with normal monsters. Logically the input would be mlvl and the output would be rarity. It took a lot of careful thinking to make sure that the function worked correctly not only for any mlvl, but for any item input. Then there is all the information about item generation in Jarulf's guide that I had to carefully go through several times to make sure I relfected in my code accurately. There's things like affixes with double chances of being chosen, cursed affixes, affix combinations that are not allowed even though they are otherwise valid, etc. Then there are all those little notes like the one I pointed out that make subtle differences.

Once the function for normal monsters was done, it just needed to be copied and slightly modified for the various other sources. The last part I needed to do was tie it all together by combining all of the sources together. Jarulf's guide has much of the information I needed except for one significant factor: monster distribution. He of course lists the probability of a particular monster to appear on a level, but I needed the distribution of them. For example, if a particular enemy spawned with only one other type on the level, it would make up half the level. But if the same enemy spawned with two other types, it would only be about 1/3 of the total number of monsters. What I needed was data for what a statistically average level looked like - basically if you played 10,000 games, added up all enemies of different types that spawned, then divided each by 10,000.

To get the information I needed, I went back to C and had to write a program that used the rules of monster generation. I first tried a systematic approach that would iterate through every possible way the game could generate monsters, count each enemy type, then divide through by the total number of combinations. At the same time I had it tally the probability for them to appear, and it unfortunately did not match Jarulf's guide. In the end, I just had it randomly generate levels thousands of times which worked.

I collected a lot of interesting data through this (unforseen) phase of the project about monster generation. In addition to the monster histogram data that I needed for the calculator, I have data for every dungeon level about how many ways the game can generate a combination of monsters (would include the same monsters generated for a level but picked in a different order), how many of those are unique combinations, and which of those combinations any particular enemy appears in. You'd probably be surprised at the results. For dlvl 1, while there is only one unique combination of enemies (all monsters that can spawn on dlvl 1 always do), there are 720 different ways to generate the level. In other words, the game can pick the same monsters, but in a different order. For dlvl 5, there are 3,505,008 possible ways the game can generate monsters for that level. In total, there are 6,801 unique combinations of spawned monsters! You could play the game for years and literally never see a particular spawn twice. In fact, I am missing data for one level because the total number of combinations is so large that I have yet been able to finish calculating it. My last attempt was over a year ago where I ran the program for 12 hours straight with no results - probably because I ran out of memory (2 GB of RAM). I planned at one point to post the information. Maybe soon I'll compute that final level and do just that...

Finally, the last part of the project was to consolidate the calculations from individual sources over an average game. It goes from item source to source, level by level, difficulty by difficulty, until they are combined for the entire game. Somewhere along the line I also decided to add options for "none" and "any" for a prefix or suffix to open up a lot of possibility for items.

The entire process took me about 3 1/2 months from toying with manual calculations to publishing the calculator, then another half month or so to iron out bugs and revamp the format of the output. I like that it can be used to determine if an item is valid as well as giving you an idea about where it might be found. A jade shield of brilliance is often the choice for arty mages trying to max their mana, but have you ever thought about how hard it would be or where you'd even find one?

Suppose you have a mid-level warrior in nightmare that is getting torn up due to lack of resistances. With your sub-par gear, you can give up the armor slot or a ring slot for an obsidian prefix, no matter the suffix. How hard would it be to find something like that? Well, just combine the probabilities for an obsidian ring or light, medium, heavy armor with our without a suffix - you get 20.5%, just under 1 in 5 games.