Posted
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The following presented data have been collected in Diablo III v. 1.0.3.10235 - v. 1.0.4.11327.
The doubled drop chance for legendaries in 1.05 have been considered for the calculations.
This post may involve spoilers!
Current collection of data (.xlsx file).
Current computation sheets (.xlsx file).
Changelog (.pdf file).
Personal MF Spreadsheet (.xlsx file)
Personal MF Spreadsheet (.xls file)
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Contents:
1. Introduction
1.1 Description of the presented content
1.2 List of contributors
2. Magic find: The basics
2.1 The drop process of items
2.2 Magic find and gear quality
2.3 Obtaining magic find
2.4 Magic find and group play
2.5 Magic find and followers
2.6 Magic find and nephalem valor
2.7 Magic find and caps
2.8 Magic find and monster power
3. Expanded introduction
3.1 The item-integer identifier
3.2 The paragon leveling system in perspective
3.3 The slot system theory
3.4 The item-drop sequence
4. Supporting Data Analysis (Treasure Creature Farming)
4.1 Description of data collection and current sample size
4.2 Gear class as a function of magic find
4.3 Item level as a function of magic find
4.4 Number of items found as a function of magic find
4.5 Bonus: Treasure creatures spawn type rates
4.6 Treasure bandits and blacksmithing plans
5. Supporting Data Analysis (Elite Farming)
5.1 Description of data collection and current sample size
5.2 Nephalem valor and the guaranteed rare drop
5.3 Gear class as a function of magic find
5.4 Sequenced data for elites
5.5 Test dataset for patch 1.04
6. Computations and Advanced Research
6.1 Short introduction
6.2 Model-system for MF
6.3 Computation for legendary drops vs total item drops
6.4 Computation for #affixes rare items as a function of MF
6.5 The sequenced item slots per monster type
7. Summary / Conclusion
8. Outlook
8.1 Current plans for the project
8.2 Further reading
TL;DR
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Abbreviations:
4A: 4-affix rare item
5A: 5-affix rare item
6A: 6-affix rare item
ATR: attributes
cLvl: character level
D2: Diablo 2
D3: Diablo 3
FS: fortune shrine (or the buff from it)
GC: gear class (being common/magic/rare/set/legendary)
GF: gold find
iLvl: item level
L: legendary
M: magic
MF: magic find
MP: monster power
MPLvl: monster power level
NV: nephalem valor
pLvl: paragon level
R: rare
S: set
TB: treasure bandit
TG: treasure goblin
TS: treasure seeker
TP: treasure pygmy
W: white
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1. Introduction(Top)
The work that is presented in this text is a collaborative effort to understand the underlying mechanics of a popular game-aspect known as magic find. It has been discussed thoroughly over many years for Diablo 2 and since the launch of Diablo 3 many discussions have continued in spite of the fact that much was known about MF from Diablo 2 and a great part was directly extractable for use in Diablo 3. It is, however, also a game mechanic that has received much attention since the launch of Diablo 3 as new questions kept rising; some of which could not be explained by the already known facts from Diablo 2. In addition, since patch 1.04 was implemented, the whole concept of magic find was subject to major changes.
This text originally only included research from treasure monsters in act 2 (aka goblins). Basically, back then I wanted to create a thread that answered most questions about magic find (the basic questions such as “does MF increase iLvl?” and similar). The data I collected from goblins were only meant to back up the statements so that people could see the effect of magic find (MF) from the game itself. It “slowly” caught public interest and a few players started joining the discussions, introducing new questions that could hopefully be answered by the work I had made. The interest did, however, grow exponentially when the thread received a sticky and became frontpage news. Since then more people have joined in on the project to help with data collection, computations and simply asking questions that could help direct the research towards new areas/ways of understanding the mechanic. It quickly initiated new research for elite data and especially the research for the number of affixes found on items as a function of magic find as well as the slot system theory and drop sequencing became highly discussed research topics.
It is important to state that what started as a small one-man project has turned into the (currently) probably biggest collaborative research to understanding the mechanic of magic find and I could never have gotten to the point we are at today without the help of the people contributing to this research.
This thread stands today as a central look-up point for many players; newcomers and old players alike and helps eliminate most questions about magic find that people could potentially ask. The text is pretty long and therefore has an internal linking system back and forth between the sections and the contents list. I hope this will help navigating through the whole project, data and results as it is probably the best I can do to introduce some level of overview. Should you not (for whatever reason) want to read the whole thing (which I understand completely, as it is can be a bit hairy) I hope that the internal referencing system will help you navigating to the points that are of interest to you.
If you are here to read the thread for the first time I hope that you will eventually take the time to read the whole thing, however, if you do read this thread for the first time and you have absolutely no idea how MF (or how to gain it) works I suggest you read through the basics in section 2 before anything else. If you believe you have grasped the principle behind MF, but feel slightly confused when reading the actual research sections I strongly suggest that you read the expanded introduction in section 3 (at least 3.3 and 3.4 are very important sections to understand the rest of the research).
I would like to point out, before going too far into the actual research that English is not my native language and errors, typos or simply horrible grammar may be present in some of the following text. I do my best to eliminate these errors and sentences, but should anything be found that completely destroys the value of understanding what I mean, please point it out to me and I will see what I can do to correct it.
Furthermore please note that we are all human. If I have made a mistake in one of the following sections or errors are found in the datasheet; please correct me on it. Note that changes may also be made to the game which can make these findings misleading should they not be updated.
1.1 Description of the presented content(Top)
I will start out by giving a short description of the content that can be found in this text, as it has grown quite large.
The first part of this post (the subsequent section 2) will introduce the very basics about magic find and also goes into detail about a few theoretical considerations. Most of the subsections found in section 2 will be based on results from Diablo 2, however, known changes have been taken into consideration. It will also be heavily based on official blogs/posts from Blizzard.
Following the basics section is an expanded introduction (section 3) which practically involves some important aspects about magic find that either requires further discussion prior to the subsequent sections or it has evolved directly from our research and is therefore important to clarify before introducing the actual data.
In the second part of this post (section 4) is presented data from goblin farming that supports the theoretical points. I would like to stress that this section was how I initially presented the obvious effect of magic find (in that it increases item rarity, not quantity) and is subject to a smaller sample size than what is presented in section 5 for elite farming. This section stands primarily to illustrate the basics about magic find. I strongly suggest not to make vast conclusions based on section 4 alone.
In the third part of this post (section 5) is presented data from elite farming that supports the theoretical point. This part of the post is currently the primary source of data for our research and by far the biggest sample can be found in this section. It will illustrate a decent-sized sample (error bars included) of what to expect when playing with MF and additionally it will be the basis for the computations made in the later sections (note that the graphs in the charts in this section is based on these computations).
In the fourth part of this post (section 6) is presented computations based on the results found from elite farming. The computations are therefore directly applicable to elite farming, but can not be directly applied to other monster types (such as goblins or bosses) without a few manipulations.
These computations have proven useful in illustrating what to take into account when using probability-math and we now have decent results that helps explain how the number of affixes on items are affected by MF (and the lack thereof).
Note that in this section the advanced research will also be found. By advanced I don't mean high-tech or anything: It is just going deeper into detail compared to the "old-fashioned" rough data collection. This includes a table that illustrates monster types (found in inferno) and what dominates their different item slots. This table actually illustrates/sums up all you need to know when farming different special monster types, but it is only supposed to serve as a guideline - use it with caution.
In the latter part of the post can be found a summary/conclusion which draws the most important lines from the research presented in this post (and thread). Following that is a short outlook that describes the current areas we are focusing our research on as well as a section for further reading.
1.2 List of contributors(Top)
I must emphasize that the research presented in this thread is not collected solely by me. Most of the research from goblin farming is provided by me simply due to the fact that the initial version of this post only covered goblin farming. Over time more and more people wanted to join in and help with collecting data and we have now become quite a group of players. I will therefore make a short list of the people contributing to this thread, serving as a form of credit in addition to when they are mentioned within separate sections.
Note that I will not give credit for being active in the discussion of this thread unless you contribute with major insights.
If I have forgotten you, please let me know!
| Player | Primary work |
| _Depression | Patch 1.04 test data collection |
| Dynomait | Computations |
| Ghouul | Data collection |
| head0r | Data collection |
| HuiTzi | Data collection |
| Kozik | Patch 1.04 test data collection |
| Loroese | Data collection and computations |
| Murskautuminen | Data collection, computations and initiator for the slot system theory |
| Nubtro | Data collection & initiator of drop sequencing research |
| Shurafa | Data collection |
| sny83 | Data collection |
| st0rmie | Patch 1.04 test data collection |
| Timza | Data collection and computations |
| Tziera | Data collection (hardcore) |
| Vomica | Graphical illustration of the paragon system |
| ztking | Data collection, computations, further reading, community-discussion and Q&A |
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2. Magic find: The basics (Top)
The best "official proof" there is to how MF really works is based on the Diablo III Developer "AMAA" transcript in which the question related to this topic can be found here.
Blizzquote
Jay Wilson: The mechanic is exactly the same as Diablo 2, and as you describe it hear. And the loot tables are not more vast than D2 because we don't allow items to drop below level 50 in Inferno.
So let's take together what is known about MF. The following points are based on the fact that the mechanics should work similar to D2 along with the few changes that have been implemented for D3 and are documented via blogs or posts from Blizzard employees.
2.1 The drop process of items (source) (Top)
The process described below is directly extracted from D2: The drop process for D3 is not yet certain, but the below example gives a good understanding of how items are generated in general and it is very likely that the process is similar in D3 if not identical. We do, however, not have any specific data or datamined results that indicate if the order is true - I have included it here because it serves to illustrate newcomers how the game creates items.
At the point of which you kill an enemy or open a chest the game may generate items to reward the player. The properties of the items are generated at this moment, even though they may be unidentified. The game uses a special algorithm for the creation of such items; this can be simplified to the following points:
- At the very first is determined the Treasure Class. The Treasure Class is simply a parameter which determines a subgroup of items (list of Treasure Classes from D2 and description of Treasure Classes).
- The game then makes one (or several) iterations, called "picks". These picks are the parameters that "selects" the choice out of several possibilities. One of the possibilities is "NoDrop" which is dead simple: nothing drops. If the iteration does not select the first item on the list of the Treasure Class then the next one down the list will be consulted, then the next, until an item (or a NoDrop) is selected.
- Monsters have a multiple number of picks, however, most normal monsters only have a single pick. For monsters with multiple picks the possibility of NoDrop may be overruled by the other picks.
- Once an item is selected its' properties are determined. This is where things get hairy: Simple items such as potions and books (e.g. Tome of Blacksmithing) are only found in normal quality, however, items such as weapons, rings and amulets have different qualities such as broken, normal, magic, rare, set and legendary. It is at this step that Magic Find is checked!
- For every item selected an item level is assigned based on a predetermined %table.
- If the rarity check (of point 4) results in an item with a rarity of set or legendary, the game will check the list of all valid item types (determined by their iLvl) and randomly selects one to drop.
- Lastly the item affixes are generated (aka the affix values, not the amount of affixes).
Again, I would like to note that while it is assumed it works in a similar way in D3 it is not known with certainty, so take the above with a grain of salt. It does, however, describe the process or machinery of item-drops even though the order may be different.
2.2 Magic find and gear quality (source) (Top)
MF increases the "quality" of the gear you get, but only in terms of the rarity of the items which means the "item class" (gear class = GC). The item level is not affected by MF nor is the amount of loot dropped.
Basically, MF makes more of the items that drop be magical or better (rare/set/legendary). The exact parameters are not certain, however, it is very common to use the example that
>>If you have 1% chance of getting a rare item from a drop, increasing MF from 0% to 100% will increase the chance to 2% of getting that rare item.<<
It is important to point out that it is never as simple as this, but it serves as an example. The trick is that the above is true, but you need to think around it in terms of probability to get values that can be correctly compared to observed values from the actual game. In addition, items tend to get better on average with larger MF values, but this is a result of items being differentiated based on the number of affixes they have (more will come later to this).
Before proceeding it is important to elaborate what is meant by gear quality.
Gear quality is a widely used term that covers both iLvl, affix rolls and item rarity. When we discuss item quality we usually mean that in terms of item rarity (aka what color the item has and what number of affixes there is on that item). By now it is easy to be confused, as the number of affixes found on an item is affected by MF but the actual stat rolls of these affixes is not. The below table should clarify the difference.
| Difference in items | Item 1 example | Item 2 example | Does MF have an effect |
| Affixes stat rolls | 150STR | 200STR | |
| 150VIT | 210VIT | No | |
| 25% Crit dmg | 30% Crit dmg | ||
| +6% life | +7% life | ||
| Number of affixes | 150STR | 150STR | |
| 150VIT | 150VIT | ||
| 25% Crit dmg | 25% Crit dmg | Yes | |
| +6% life | +6% life | ||
| 7% attack speed |
Or in short: If an item rolls vitality, MF will not scale the vitality roll (such as from 100 to 200), but the more MF you have, the larger the chance there is to get an item with more affixes. The more affixes an item has, the more "shots" it will have to gain attractive affixes.
This example is very raw, but it should help illustrate the effect that MF have (and does not have) when items are being rolled. Further explanations can be found in section 3.1.
It might be worthy to note by now that since patch 1.05 went live, the actual affix rolls (aka if an item rolls 100 vitality or 200+ vitality) will be solely based on the mLvl of the monster that was killed and from which the item dropped. In short: The higher the mLvl you fight against, the better the actual affix rolls (on average).
2.3 Obtaining magic find(Top)
Magic find can be gained by two general methods being either temporary or permanent:
- There are two permanent ways of obtaining MF and the first one is from the Paragon system: Every paragon level you obtain grants your character a 3% bonus to MF (and GF). It is possible to get to a level of 100 granting a total of 300% MF and GF. Paragon levels are gained via XP once your character hits cLvl 60.
It is also possible (for now) to gain MF from item affixes on gear: When you equip gear with MF on it you will gain that percentage as long as you wear the gear (see section 2.5 about gaining MF from followers). I write "for now" in brackets because Blizzard has stated that they want to move away from MF on gear in the future. MF gear will still be valuable at the early paragon levels in order to maximize MF (if you want to be capped - see section 2.7 about MF and caps), however, as you progress in the Paragon system you will eventually be able to swap out MF gear since the paragon levels may provide what you need. - Temporary ways of obtaining MF are from buffs. Buffs can be gained by 1) killing elite packs at cLvl 60 and thereby gain the Nephalem Valor buff (see section 2.6 for a description of NV) or 2) by buffing with a Fortune Shrine. These buffs stacks, however, the fortune shrine buff is very time limited compared to NV. In addition, the NV buff is able to surpass the 300 MF cap while the fortune shrine buff is limited by the cap (see section 2.7 for more).
- Since patch 1.05 it is also possible to gain MF based on the Monster Power level (MPLvl) playing on (see section 2.8 for details).
2.4 Magic find and group play(Top)
Before patch 1.04 MF used to be shared in group play, however, with the patch this has changed and MF will only be applied to yourself no matter if you play in a group or solo.
2.5 Magic find and followers(Top)
It is possible to gear up your follower with MF, however, in D2 followers only had an impact with MF if they landed the killing blow. This is no longer the case for D3: A set percentage of the MF geared onto your follower will be applied to you.
As for now, this percentage is set to 20%. This means that 20% of the MF geared onto your follower will be applied to you. It is uncertain how the system rounds the numbers, however, it is assumed that the total MF on the follower is calculated, multiplied by a factor of 0.2 and at this point rounded (instead of rounding on every gear piece).
This means that adding 20 MF to your followers gear will effectively add 4 MF to you as long as the follower is hired. Note that upon entering cooperative play, the follower will remain in town and the extra MF will therefore not be applied.
2.6 Magic find and nephalem valor(Top)
It is possible to gain MF by getting the nephalem valor (NV) buff. This buff will be applied automatically if your character is level 60 and you (or the group) kill an elite pack. The NV buff applies +15% MF, +15% GF and +15% XP gain, lasts 30 minutes and can be stacked up to 5 times. The timer of the buff will be reset upon applying a new stack (aka at five stacks, by killing a new pack, you just reset the timer of the buff).
There is another bonus from NV that greatly increases its potential regarding farming: Each stack of NV grants an additional item drop for minibosses and act endbosses. These items will have a minimum level of rarity associated with them. There is a similar effect to elite packs, but only at maximum number of NV stacks. The most potent extra drops are:
- If you have 5 stacks of NV and you kill an elite pack, an additional item will drop that is guaranteed being at least a 4-affix rare (yellow).
- If you have 4 stacks of NV and you kill a boss, an additional item will drop that is guaranteed being at least a 4-affix rare.
- If you have 5 stacks of NV and you kill a boss, two additional items will drop that is guaranteed being at least 4-affix rares.
The guaranteed rare for elite packs being activated at 5xNV stacks is also applied to treasure goblins, bandits, seekers and pygmys, however, it is not applied to unique monsters.
For minibosses and act endbosses the first 3 extra drops will be primarily magic quality items (eventually you can see section 6.5 for the effect.
Act endbosses include:
Spoiler
And minibosses include:
Spoiler
2.7 Magic find and caps(Top)
A very common question when it comes to MF is regarding caps. While this should be very simple, it can get a bit messy:
- There is a theoretical cap on MF meaning that - since MF increases your chance of finding a magic, rare or set/legendary item - there is a cap to these chances (source). It is, however, practically impossible to reach this cap!
- Since patch 1.04 there is now a cap to MF. The MF you gain from your gear + your follower + any fortune shrines will stack and is capped at 300 MF. Any stacks of NV will be capable of surpassing this cap, so if you are capped at 300 MF without NV, you will effectively have 375 MF with 5xNV.
- The MF gained from MP "ignores" these limitations, so to speak. The MF gained from MP is added no matter what MF you have equipped, gained from pLvl or the amount of stacks of NV.
- The current cap (patch 1.05) on MF is:
- 300 from gear/followers and/or pLvl
- 75 from NV (5 stacks)
- 250 from MP (MPLvl 10)
--> Grand total of 625 MF
OBS! Do note that Blizzard has stated they wish to move away from MF on gear. It is possible that MF on gear will be completely removed in a later patch.
The following is a list of current max MF% obtainable via gear (not including weapons):
| Gear slot | Max possible MF |
| Helm | 20 |
| Helm socket | 31 |
| Shoulder | 20 |
| Amulet | 45 |
| Gloves | 20 |
| Chest | 20 |
| Bracers | 20 |
| Belt | 20 |
| Rings | 20 (30)* |
| Legs | 20 |
| Boots | 20 |
| Off-hand | 20 |
| - | - |
| Total | 296 (306)* |
* Nagelring can go up to 30, but is unique.
2.8 Magic find and Monster Power(Top)
There's a great blog post about this already, but I just want to make a few things clear related to MF and Monster Power.
It is possible to have Monster Power Level (MPLvl) set to any integer from 0 to 10.
0 means that monster power is "inactive". Anything above 0 gives a certain bonus which can be interpretted from this table. Setting the MPLvl to anything but 0 also means that mLvl will be set to a static level of 63 no matter what act you play.
The magic find you gain from MPLvl stacks above the 300 MF cap (in addition to the NV stacks), meaning that the MF cap in patch 1.05 will be 625. See the section 2.7 above for details.
The bonus item is an extra item you gain whenever you have a drop from monsters (including gold, potions, etc).
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3. Expanded introduction (Top)
In this section will described some of the key ideas and models regarding magic find and some of the underlying mechanics that is either directly related to our research or is a direct result thereof.
I will start out by expanding the understanding of item classifications as well as the understanding of the paragon system, especially by introducing a perspective that can help realize what sort of effort is required to nail level 100. Subsequently will be given two key ideas that have been brought up from two of the contributors to this research. These ideas have been implemented into a model system that can help explain the findings that are shown in the following sections.
Note that the following subsections 3.1-3.4 are based on results that are obtained directly via the game (Diablo 3) and some of the sections are directly results of our research, however, their importance require their key principles to be introduced prior to the actual data.
3.1 The item-integer identifier(Top)
Prior to patch 1.04 it was possible (due to a bug) to break the item-code of every item in the game. The item codes involves a list of key numbers that helps distinguish one item from another: In fact, it was possible to obtain which affixes an item had rolled without even identifying the items. It was aditionally pointed out that the number of affixes could be identified by a certain value found at a certain position in the item-code. This bug was therefore fixed in patch 1.04, however, before the patch was implemented it was found from our research team that the understanding of the mentioned value (or digit) for extracting the number of affixes could be expanded.
What we found was that in the item-code there (always) was a 1-digit integer value which determines the gear class of the loot. From searching through a long list of items it has been found that
| Integer | Item class |
| 9 | Legendary / Set item |
| 8 | 6-affix rare item |
| 7 | 5-affix rare item |
| 6 | 4-affix rare item |
| 5 | 3-affix magic item |
| 4 | 2-affix magic item |
| 3 | 1-affix magic item |
| 2 | Superior common item |
| 1 | Common item, consumable, crafting reagents and tomes, etc. |
| 0 | Inferior item |
The above list describes a proper grouping of items based on their properties and potential. Not once was found an item that varied from the above results.
So when an item is rolled it performs several checks and it start at the top value 9 being legendary / set items (it may be worthwhile clarifying now that set items are equal to legendary items except that they can be coupled to form sets granting extra bonuses - but set items are indeed legendary items). If the roll "hits" (that is, the roll X < Y with Y being small for legendary items and large for lower rarity items) the item will be of legendary rarity, but If the roll misses this item rarity it will proceed to integer 8 which equals 6-affix rare items. Again, if the roll misses at 6-affix rare items it will proceed to 5-affix rare items (integer 7) and so on. Eventually Y will be so large (in fact it will be 1 in some cases) that the roll will not miss that item rarity.
By inspecting large samples with these integer values it was furthermore found that 3-affix magic items seemed impossible to drop from the world (all 3-affix magic items found were, in fact, crafted items). Aditionally it was possible to identify the true number of affixes on items that had confusing affix rolls (as some affixes can roll out double ATR, such as +STR and +VIT from the same affix).
Since patch 1.04 there is no known way of extracting this integer value from items anymore, but it was possible to get decent data prior to the patch that helped research on how MF affects the number of affixes rolled on items.
3.2 The paragon leveling system in perspective(Top)
Presented in another thread on these forums is a chart about the paragon system and the experience required for each level (and bracket). I have requested to include this chart into this text as it puts the whole leveling from level 0 to 100 in a perspective, and the chart has even been refined to involve as much information as possible for this text.
Reposted with permission from Vomica.
From the official introduction to the paragon system it is mentioned that they want to move away from MF on items and the paragon system is ultimately the result they came up with. Quoting Jay Wilson:
Blizzquote
We wanted to find a solution that was not only very forgiving of gear swapping, but one that would ultimately help us slowly and gently move Magic Find off of items in the future. It’s such an intrinsically important stat to the core purpose of playing the game that tying it to gear — which is a customization system in many ways — is ultimately an approach that would continue to cause problems. We need to transition away from it, and do so in a way that doesn’t flip the entire game end-over-end.
In the future this system will therefore most likely be the primary way to obtain MF (not counting in NV) and as a result quite a few people have to make choices with the most common being "what level should I aim for?". This is very difficult question to answer as it will ultimately be a personal opinion, however, the above chart hopefully helps in deciding this without going into too much detail.
A few key points that I want to extract from the chart:
- It will take a LONG time getting to level 100, without a doubt this is probably the only matter that is not debatable.
- Note that approximately 50% of the total experience required to get to level 100 will ultimately put you at ~pLvl 80. The time required getting from 0 to 80 will be approximately the same as getting from 80 to 100 and it is very debatable if getting the last 20 pLvls (and thereby 60 MF) is worth it. Some may definately find it more worthwhile getting 2 characters to pLvl ~80 instead of having one character at ~100. Again, this is a point of view.
- It is very difficult realizing how much time is required getting to max pLvl: People farm different content in different ways and with different levels of +XP gains. I have therefore "normalized" the numbers a bit so it may be easier to understand: Try playing a character to pLvl 10. This requires a total of 136,800,000 XP or ~1.3% of the XP required to get to pLvl 100. If you then want a decent picture of what it would take you in order to get to pLvl 100; imagine doing pLvl 0-10 approximately 75 more times and you will be there.
3.3 The slot system theory(Top)
Big thanks to Murskautuminen and for bringing in this key idea.
The slot system theory is in reality very very simple. Basically, imagine a box. When an item drops, imagine that the game engine picks up an item from the box. The item that drops thereby depends on the box (or slot) that the item is picked from, but not because the items are predetermined from the box; only because a box has a set chance for rolling items within a given gear class.
Take an example (this is purely based on arbitary values): A normal trash monster dies. The game then rolls if the monster drops something (aka it rolls for a Drop vs. a NoDrop). If it hits a drop, then the monster will drop items based on the slots that it is associated with it.
For a normal trash monster this could be 0.05% to hit a legendary, 5% to hit a rare, 20% to hit a magic item, etc.
It is important to understand that the slot system can be thought of in two ways: Either each monster has a slot that is coded into the game code or it simply is applied a slot when it is killed from a predetermined set of slots. Which is the true picture cannot be distinguished at our level of research, but little does it matter. Now you may mention that it is most likely the last example (that there is a predetermined set of slots that simply get applied to monsters) for a very simple reason: Getting 5xNV buff will apply an extra item to elites and two for bosses and therefore this option seems the most reasonable, but it could also simply be coded in such a matter that these slots have a 100% chance to NoDrop when not having NV applied. Either way, there is little value in discussing this matter.
A monster does not need to have a single slot. In fact, several slots have been found to be "activated" from various creatures depending on their types. Let's take the best example: Elite creatures. These monster types have (in inferno) a total of 5 slots that are related to gear. Three of these slots have 100% chance to drop, but their distribution of item rarity varies for each slot. One slot has a 50% chance to drop and also varies in distribution of item rarity from the rest, however, in spite of these differences there is now evidence that gear slot 1 and 4 are close to identical as is the same for gear slot 2 and 3 (more will come in the next section). It is gear slot 3 that has 50% drop chance. The fifth slot is the NV rare slot and is very different from the rest in that it has 100% chance to drop when 5xNV is applied, but doesn't drop if that is not the case. Also, this slot will always be a rare item - when it drops of course.
More research is required to identify these slots (and especially if monsters share slots). Early results from our data indicate that elites and treasure monsters (goblins) share some slots - even the NV rare slot. In addition we have found that bosses have very different slots from every other monster found in the game (except for the NV rare slots).
For now, however, I suggest reading the next section 3.4 as it is a continuation of this section (they interact very nicely with each other).
3.4 The item-drop sequence(Top)
Big thanks to Nubtro and for bringing in this key idea.
This is a continuation of the slot system theory (in some way at least), so if you have not read section 3.3 I suggest doing that first.
The standard way of collecting data has been somewhat expanded by an idea from Nubtro: By recording each monster kill (ofc only those of interest), it was found that not only does monsters have variable item slots, they also drop them in a specific sequence. This was realized by simply recording the kills of certain monsters (using recording software such as fraps or similar) and subsequently view the video in slowmotion or frame-to-frame mode.
What is really interesting about this is not only that it expands the understanding of the slot system, but the fact that drops are sequenced puts the game design on a wholly different level.
The item-drop sequence is an interesting point to the research of MF even though it may not seem to be clear why: The item-drop process itself should indeed not be affected by MF, however, if the drop sequence has some level of structure (aka not randomly sequenced) then it might be possible that MF needs to be explained in more detail to bring forth the larger picture. It should become clear when the data from Nubtro has been presented.
Over a total of 349 elite kills it was found that the drop sequence could be generalized to a list having.
- Gear drop #1
- Gear drop #2
- Tome drop
- Gold drop #1
- Gold drop #2
- Gold drop #3
- Gold drop #4
- Gear drop #3
- Gem
- Potion
- Gold drop #5
- Gold drop #6
- Gold drop #7
- Gold drop #8
- Gear drop #4
- NV drop
- Globe of Health drop
| Sequence number | Drop (#) | Guaranteed? | Average distribution |
| 1 | Gear (1) | Yes | Mostly blue, some yellow |
| 2 | Gear (2) | Yes | Mostly white, some blues (1-affix dominates) |
| 3 | Tome / NoDrop | No | - |
| 4 | Gear (3) / NoDrop | No | Mostly white, some blues |
| 5 | Gem / NoDrop | No | - |
| 6 | Potion / NoDrop | No | - |
| 7 | Gear (4) | Yes | Mostly blue, some yellow (same as Gear (1)) |
| 8 | Gear (NV) | See --> | Requires 5xNV buffs - guaranteed yellow |
Note that from the above table the minimum found items were always 3 and maximum 4. The gear drop that is sometimes missing is Gear (3) which is usually a white item.
The fact that drops are sequenced means that we are now able to distinguish different slots from another using this method (meaning that the theory that is presented in section 3.3 can be investigated by collecting "sequenced data").
One of the very interesting points are, again, that gear slot 1 and 4 (which drops as #1 and #4 in the sequence) are slots that never drop less than magic items, while gear slot 2 and 3 mostly drops white items with rare items being quite... well, rare. This has great importance to the efficiency of MF in that it works on the base drop %'s and it does so on each gear slot separately and independently: Therefore, gear slot 2 and 3 will rarely drop rare items and being even at ~350 MF it is very likely to see drops from elite packs consisting of 3 rares and 2 white items.
- - -
4. Supporting Data Analysis (Treasure Creature Farming)
4.1 Description of data collection and current sample size(Top)
I will start out with gobling farming as it is from here the initial idea for the project initiated (see section 5 for elite farming). It is only in this set of data that item level has been investigated. I will be using this section as a brief introduction to MF by eliminating the most common questions regarding the (lack of) effect of MF on iLvl and quantity.
I will give a short description of the procedure I used to collect the data that can be found in the analysis. I have simply farmed treasure creatures with varying values of MF on my gear.
Just for making it clear, it is these guys who helped me collect the large amounts of data:
After each kill on a treasure creature (either goblin (TG), bandit (TB), seeker (TS) or pygmy (TP)), the following information from the items dropped were noted:
- Total number of drops (except potions).
- Number of gear of white/magic/rare/set/legendary rarity.
- Number of Tomes of Secret, gems and plans/designs.
- The iLvl of the items dropped within their respective gear rarity range (only a subset of the data inlucdes information on iLvl).
From those I killed I have collected data points of varying magic find. Additional data is added to my data points and/or new data points by contribution(s). It requires many creatures to assemble just one data point (a lot of items are required in order for the point to be somewhat precise), so the charts are still weak predictionwise, but they should be quite precise.
4.2 Gear class as a function of magic find(Top)
I will start out with the most important results: Testing the class of gear (white/magic/rare/set/legendary) as a function of MF. The items are only including those dropped upon death and since grey-class items (broken/cracked etc.) were not found once such have not been included.
The data results are (the values are the % of total items found):
| MF | W (%) | M (%) | R (%) | S (% ) | L (%) | Sample size |
| 0 | 32.49 | 57.67 | 9.84 | 0.00 | 0.00 | 437 items |
| 30 | 32.12 | 56.26 | 11.62 | 0.00 | 0.00 | 439 items |
| 60 | 31.49 | 54.99 | 13.53 | 0.00 | 0.00 | 451 items |
| 76 | 31.27 | 54.58 | 14.14 | 0.00 | 0.00 | 502 items |
| 150 | 30.30 | 51.30 | 18.40 | 0.00 | 0.00 | 462 items |
| 234 | 26.28 | 44.54 | 29.06 | 0.00 | 0.11 | 898 items |
| 252 | 25.71 | 42.27 | 31.72 | 0.00 | 0.30 | 1346 items* |
| 270 | 23.17 | 40.83 | 36.01 | 0.00 | 0.00 | 436 items |
| 290 | 22.20 | 39.36 | 38.22 | 0.00 | 0.23 | 437 items |
* Thanks to head0r for contributing with 459 items.
Note that Tziera has also been performing some research regarding goblin farming in inferno hardcore. The sample size is very small, but preluminary results from him are: 34 goblins killed, 50W (~29.4%), 72M (~41.9%) and 48R (~28.2%). 5xNV applied.
The values are rounded to the second decimal.
The amounts of items found being set and legendary items are extremely low compared to the amount of white/magic/rare items found. It is therefore only those three gear classes I will base the charts on.
Below is a chart with seven data points of which the % of total gear found for GC of common (white), magic and rare is displayed. This chart should help illustrate the effect of magic find on the class of the obtained gear.
Note: The curve in this chart is only connecting the data-points and is only there to fill out the blank spots.
It should easily be concluded that magic find increases the class of the gear found.
I would like to point out that the sample size is not large enough to state the current nature of MF: The data does not prove the system to be explainable with an exponential formula nor a linear formula. One very interesting point is that at approximately 225 MF have rares been found to be just as common as white items.
4.3 Item level as a function of magic find(Top)
A smaller subset of the data included sampling of iLvl. These data have been collected them into the chart below. If magic find increases the iLvl of the items found, then it would should be clearly visble by a stair-like appearence at each iLvl mark.
The sample size for the below chart is 3,137 items.
Note that the relative distribution of iLvl has changed since data collection (see hotfix); they reflect the old distribution (can be found in this blog).
4.4 Number of items found as a function of magic find(Top)
The data of total items dropped on average per goblin as a function of MF is collected in the table below.
| MF | Total gear dropped | Total kills | Average gear per kill |
| 0 | 437 | 100 | 4.370 |
| 30 | 439 | 100 | 4.390 |
| 60 | 451 | 100 | 4.510 |
| 76 | 502 | 110 | 4.564 |
| 150 | 462 | 100 | 4.620 |
| 234 | 898 | 200 | 4.490 |
| 252 | 1346 | 300 | 4.487 |
| 270 | 436 | 100 | 4.360 |
| 290 | 437 | 100 | 4.370 |
The sample size is not the largest, but I honestly think it's large enough to illustrate that magic find does not increase the number of items found.
An extra interesting point is that treasure creatures seems to be affected by the guaranteed rare drop: Over the 148 treasure creatures that have been killed with 5xNV the average amount of items per creature was found to be 5.527. In the above chart this value (without NV) is clearly stable around 4.500. Additional evidence is that not a single creature dropped less than 1 rare item when the NV buff was applied for the kill.
The data presented by Tziera also indicates this to be true in hardcore difficulty.
4.5 Bonus: treasure creatures spawn type rates(Top)
As a little bonus I can also present the relative spawnrate of treasure creatures. A total of 1281 creatures were found of which 325 were TG (25.4%), 315 were TB (24.6%), 317 were TS (24.7%) and 324 were TP (25.3%). It's fairly safe to presume the spawnrate is 25% for each type.
4.6 Treasure bandits and blacksmithing plans(Top)
While I do not have enough data to conclude anything about this (yet), it does seem like treasure bandits have become very pleased with dropping blacksmithing plans!
I am not sure if MF has an effect on them and it would require an enormous sample size to conclude such. Until now I will just list the plans collected.
Off the 315 treasure bandits that was killed, the following plans dropped:
- Exalted Flesh Ripper
- Exalted Pallium
- Exalted Phantom Bow
- Exalted Piercer
- Exalted Slag Hammer
- Exalted Sovereign Helm
- Exalted Fine Pallium (x2)
- Exalted Fine Slag Hammer (x2)
- Exalted Fine Sovereign Greaves
- Exalted Fine Strike Wand (TP)
- Exalted Fine Golden Talon (TG)
- - -
5. Supporting Data Analysis (Elite Farming)
5.1 Description of data collection and current sample size(Top)
The data collected for this part of the project involves killing elite packs with varying levels of MF and stacks of NV while recording the drops for each pack.
In case anyone is confused on the terminology; an elite pack is a pack of monsters with increased difficulty. They can either be champion packs (aka each monster in the pack has the same extra affixes) or rare packs (aka a single monster in the pack is the "leader" having full affixes while minions of the pack only have a subset). The drops from the elite pack is made when the last champion die or when the pack leader of a rare pack dies. The other champions/minions counts as normal monsters.
Current sample size is 6,972 elites and almost 30,000 items. Most of this data is accomplished by contributions from other players and credit is given in the sections where their data has been included.
5.2 Nephalem Valor and the guaranteed rare drop(Top)
One thing that has become certain from elite farming is that the guaranteed rare drop is an additional item that will be added to the drops - it is not one of the baseline dropping items that will be of rare quality. This should be clearly visible when looking at the below table (note that MF does not increase amount of items dropped which was illustrated in section 4.4).
| Total MF | Stacks of NV | Total Elite Packs | Total Items Dropped | Average #Items / Elite Pack |
| 0 | 0 | 503 | 1799 | 3.577 |
| 0 | 0 | 250 | 867 | 3.468 |
| 0 | 0 | 254 | 907 | 3.571 |
| 200 | 0 | 400 | 1392 | 3.480 |
| 75 | 5 | 400 | 1795 | 4.488 |
| 200 | 5 | 500 | 2245 | 4.490 |
| 200 | 5 | 399 | 1801 | 4.514 |
| 267 | 5 | 534 | 2425 | 4.541 |
| 300 | 5 | 600 | 2700 | 4.500 |
| 369 | 5 | 203 | 918 | 4.522 |
| 400 | 5 | 200 | 887 | 4.435 |
Note that without the NV buff the total number of items found per elite pack is either 3 or 4, while this value is 4 or 5 with the NV buff applied. This means that an elite pack drops a minimum of 3 items with an additional item having approximately 50% dropchance and if 5 stacks of NV is effective on the kill, an extra item (which is guaranteed to be rare) will additionally be dropped.
There is one interesting question that is currently unanswered: Is it possible that MF can have an effect on the guaranteed rare drop so it may be a set or legendary item instead? It will be very difficult reaching such a conclusion, however, it has been found that the guaranteed rare drop can be rolled as a legendary item rather than the rare quality (evidence - .jpg, screenshot).
This means that the roll is set to hit with 100% certainty at the 4-affix rare quality level so that an item with at least 4-affix rare quality will always drop, but there is still a chance of rolling the legendary quality or 6- or 5-affix rare quality. As a reminder, the rolling process goes
Legendary
--> 6-affix rare
-----> 5-affix rare
--------> 4-affix rare
If it does not hit legendary, 6A or 5A, then it will at least be 4A.
If it is assumed, however, that the legendary droprate is improved by MF in general, then it will directly follow that the guaranteed rare drop also is. We have a very small sample that also indicates this to be true (as it will have an effect on affix distribution on rare items, see section 6.4).
5.3 Gear class as a function of magic find(Top)
Thanks to contributions from quite a few players we now have quite a few well-established data points:
| Total MF | #NV | W (%) | M (%) | R (%) | S (%) | L (%) | Sample Size | Act | Credit |
| 0 | 0 | 37.63 | 52.20 | 10.12 | 0.06 | 0.00 | 1799 items | 1 & 2 | Timza |
| 0 | 0 | 35.18 | 53.98 | 10.84 | 0.00 | 0.00 | 867 items | 1* | Cyeron |
| 0 | 0 | 37.71 | 52.48 | 9.81 | 0.00 | 0.00 | 907 items | 1* | Murskautuminen |
| 0 | 0 | 36.29 | 54.18 | 9.53 | 0.00 | 0.00 | 1196 | 1* | Nubtro |
| 200 | 0 | 30.96 | 41.67 | 27.23 | 0.07 | 0.07 | 1392 items | 1 | Timza |
| 75 | 5 | - | - | ~36.11 | - | - | ~900 items** | 1 | Loroese |
| 75 | 5 | 26.30 | 38.89 | 34.76 | 0.06 | 0.00 | 1795 items | 1 | Cyeron |
| 151 | 5 | - | - | ~40.55 | - | - | ~905 items** | 1 | Loroese |
| 200 | 5 | 24.50 | 30.87 | 44.50 | 0.00 | 0.13 | 2245 items | 1 | Cyeron |
| 200 | 5 | 24.71 | 32.04 | 43.14 | 0.00 | 0.11 | 1801 items | 1 | Timza |
| 230 | 5 | - | - | ~45.94 | - | - | ~936 items** | 1 | Loroese |
| 238 | 5 | 25.22 | 30.42 | 44.14 | 0.00 | 0.22 | 904 items | 2 | HuiTzi |
| 267 | 5 | 23.74 | 29.76 | 46.34 | 0.04 | 0.12 | 5699 items | 2 | Sny83 |
| 300 | 5 | 23.19 | 27.48 | 49.11 | 0.00 | 0.22 | 2700 items | 1 | Cyeron |
| 369 | 5 | 22.55 | 26.03 | 51.20 | 0.00 | 0.22 | 918 items | 2 | Nubtro |
| 400 | 5 | 20.30 | 24.98 | 54.72 | 0.00 | 0.00 | 1389 items*** | 1 | Shurafa |
* Data was collected entirely in Warrior's Rest.
** The number has been calculated backwards (assuming 4.5 rares per elite pack on average), so use the data points with caution!
*** Note that the lack of legendary/set items may be due to the lower sample size (1 set piece + 1 legendary was found while collecting the NV buff).
This data is currently graphed as:
The dots with associated error bars are experimental data. The graphs are computed from a model-system and is not experimental data - See section 6.2 for details.
One thing that is currently of interest is how MF works on the base items dropping from elites; as the guaranteed drop is an additional item added to the baseline drops (see section 5.2), it can be interesting knowing how well MF works on the baseline drops alone. The guaranteed rare is applied per pack so the rare items column and the total gear column can be substracted items corresponding to the total amount of elite packs killed for each entry with 5xNV applied, giving the following data.
| Total MF | #NV | W (%) | M (%) | R (%) | S (%) | L (%) | Sample Size | Act | Credit |
| 0 | 0 | 37.63 | 52.20 | 10.12 | 0.06 | 0.00 | 1799 items | 1 & 2 | Timza |
| 0 | 0 | 35.18 | 53.98 | 10.84 | 0.00 | 0.00 | 867 items | 1* | Cyeron |
| 0 | 0 | 37.71 | 52.48 | 9.81 | 0.00 | 0.00 | 907 items | 1* | Murskautuminen |
| 0 | 0 | 36.29 | 54.18 | 9.53 | 0.00 | 0.00 | 1196 | 1* | Nubtro |
| 200 | 0 | 30.96 | 41.67 | 27.23 | 0.07 | 0.07 | 1392 items | 1 | Timza |
| 75 | 5 | - | - | ~17.86 | - | - | ~700 items** | 1 | Loroese |
| 75 | 5 | 33.84 | 50.04 | 16.06 | 0.07 | 0.00 | 1395 items | 1 | Cyeron |
| 151 | 5 | - | - | ~23.60 | - | - | ~704 items** | 1 | Loroese |
| 200 | 5 | 31.52 | 39.71 | 28.60 | 0.00 | 0.17 | 1745 items | 1 | Cyeron |
| 200 | 5 | 31.74 | 41.16 | 26.96 | 0.00 | 0.14 | 1402 items | 1 | Timza |
| 230 | 5 | - | - | ~30.49 | - | - | ~728 items** | 1 | Loroese |
| 238 | 5 | 32.39 | 39.06 | 28.27 | 0.00 | 0.28 | 704 items | 2 | HuiTzi |
| 267 | 5 | 30.51 | 38.25 | 31.03 | 0.05 | 0.16 | 4434 items | 2 | Sny83 |
| 300 | 5 | 29.81 | 35.33 | 34.57 | 0.00 | 0.29 | 2100 items | 1 | Cyeron |
| 369 | 5 | 28.95 | 33.34 | 37.34 | 0.00 | 0.28 | 715 items | 2 | Nubtro |
| 400 | 5 | 26.21 | 32.25 | 41.54 | 0.00 | 0.00 | 1076 items*** | 1 | Shurafa |
OBS - The guaranteed rare drops have been removed from these data.
*, **, *** See the notes for the table above this one.
This data is currently graphed as (OBS! Note that the NV guaranteed rare has been removed from this data):
The dots with associated error bars are experimental data. The graphs are computed from a model-system and is not experimental data - See section 6.2 for details.
Two interesting observations: At ~250 MF will rare items be just as common as white items and at ~325 MF will rare items be just as common as magic items. This is only applied to the baseline drops and the NV rare is therefore not included in these values.
5.4 Sequenced data for elites(Top)
The data is a bit small for this research, however, it is enough to point out something close to the true distribution of item-qualities/gear-classes per item slot. If you are unfamiliar with this kind of data I suggest reading section 3.4.
In the datatable below, each entry is written in a form of X-Y-Z-V. These numbers represent the items found of White-Magic-Rare-Legendary/Set items respectively for the given gear slot.
| MF (#NV) | Gear slot 1 | Gear slot 2 | Gear slot 3 | Gear slot 4 | Gear slot NV | Sample size | Credit |
| 0 (0) | 0-296-54-0 | 308-40-2-0 | 131-23-1-0 | 0-292-57-0 | NA | 1204 items | Nubtro |
| 0 (0) | 0-126-28-0 | 133-19-1-1 | 47-14-1-0 | 0-131-23-0 | NA | 524 items | Murskautuminen |
| 75 (5) | 0-283-117-0 | 313-83-3-1 | 159-33-3-0 | 0-299-101-0 | 0-0-400-0 | 1395 items | Cyeron |
| 313 (5) | 0-58-69-0 | 93-33-1-0 | 43-20-2-0 | 0-46-81-0 | 0-0-126-1 | 446 items | Ghouul |
It is a little difficult to illustrate this pattern in a table so I have graphed the slots and their relative distribution of items for the three MF situations above - that is, farming with 0 MF and farming with 75 or 313 (including 5xNV). The graphs are:
It should immidiately become obvious that applying the NV buff gives the extra rare item in addition to the rest and that MF is primarily only effective on gear slot 1 and 4. The effect of MF on gear slot 2 and 3 primarily results in a boost towards more magic items and going as high as 313 MF, white items is still the dominant rarity for these gear slots.
This could help explain why it is so difficult for people with high MF values to find 5x rare items from one elite pack (and even 4x rare items will be quite rare too).
5.5 Test dataset for patch 1.04(Top)
In this section will be included a short test that has been made to check if the data presented elsewhere in this thread (of which most has been collected pre-patch 1.04) can be directly applied to patch 1.04 of Diablo 3. The reason why this is getting its own section is because patch 1.04 introduced the paragon system and involved many changes regarding how to obtain magic find. Since no words came out that the whole mechanic of MF would change, we were concerned that the new cap would involve normalization of the drops which then would be detectable at the baseline droprates for monsters.
We therefore settled to test if any changes were made to elites' base drop %'s of item rarity, as any changes to these %'s would ultimately effect everything else we had collected prior to the patch. This is the data we collected:
Sequenced data:
Pre-patch 1.04: total kills = 503
Post-patch 1.04: total kills = 780
Data combined:
| Slot (patch) | %W | %M | %R | %L |
| 1 (1.03) | 0.00 | 83.73 | 16.27 | 0.00 |
| 1 (1.04) | 0.00 | 83.72 | 16.28 | 0.00 |
| - | ||||
| 2 (1.03) | 87.50 | 11.71 | 0.59 | 0.20 |
| 2 (1.04) | 81.79 | 16.67 | 1.54 | 0.00 |
| - | ||||
| 3 (1.03) | 82.03 | 17.05 | 0.92 | 0.00 |
| 3 (1.04) | 78.24 | 20.39 | 1.38 | 0.00 |
| - | ||||
| 4 (1.03) | 0.00 | 84.10 | 15.90 | 0.00 |
| 4 (1.04) | 0.00 | 85.26 | 14.74 | 0.00 |
Graphical display:
And the data overall is:
MF = 0, NV = 0
| Situation | Total elites | %W | %M | %R | %L |
| Before patch 1.04 | 1356 | 36.86 | 53.07 | 10.04 | 0.02 |
| After patch 1.04 | 949 | 35.01 | 55.31 | 9.68 | 0.00 |
I feel confident in concluding that nothing regarding the gear slots base drop %'s have changed in patch 1.04. If anything has, then it is likely there is a slight shift towards more magic items for gear slot 2 and 3, but it could simply be due to the level of error for the samples.
- - -
6. Computations and Advanced Research
6.1 Short introduction(Top)
This section involves some of the more elaborate research made in respect of magic find, loot quality and even the item-drop process. The section is not "advanced" in the meaning that you need a master degree to understand it, however, the findings and computations presented here goes slightly more into detail about the actual game mechanics involving MF and farming and some math is involved.
I will give a short introduction abut what can be found within this section: We will start out with some computations that shows the diminishing returns effective on rare items found as a function of MF and how the results scale with our observed values. From that point on are made a few computations that describe the effect of MF when the NV buff is applied and computations regarding the amount of affixes on items as a function of MF (and NV).
Following the computations will be presented some of the recent research that Nubtro has initiated in terms of the actual drop sequence. The research in this field is still quite new, but the findings are already very interesting.
6.2 Model-system for MF(Top)
The results from this section was used for the charts in section 5.3.
A special thanks to ztking for providing additional insight related to this model.
Before going too much into detail regarding this computation it is important to understand a very important difference in the drop chances: Nominal and real values (in correlation with ztkings work - see section 8.3 - real values can also be called resultant values). Made short a nominal value can be regarded as de facto while the real (or resultant) values are usually average measurements.
Related to the research presented here, a nominal chance is the base chance that an item rarity has to hit when the roll lands on that tier. The real (or resultant) chances are what we observe based on the hits. An example to illustrate this could be the following: Imagine an arbitary item-slot having the nominal chances of 1% for legendary items, 40% for rare items and 100% for magic items. This means that if the roll misses the legendary item rarity and subsequently the rare items rarity, it will always end up being a magic item (because it has 100% nominal chance which equals a 100% chance to hit that tier). However, the real (or resultant) chances (which is what we observe) will not be 100% magic items. Calculated in terms of probability the relative real (or resultant) value distribution will be:
Legendary = 1%
Rares = (1 - P(L_hiit)) * 40% = (1 - 0.01) * 40% = 39.6%
Magic = (1 - P(L_hit)) * (1 - P(R_hit)) * 100% = (1 - 0.01) * (1 - 0.40) * 100% = 59.4%
Because each item rarity tier is dependant on each of the above tiers rolling misses (except for legendary items).
So now that this is in to place things get slightly more complicated, because in fact rare items have three subclasses depending on their number of affixes; same goes for magic items (which is technically two because 3-affix magic items are crafted-only) and in some way common (white) items also have two. To elaborate I will include the item-integer list from section 3.1 again.
| Item integer | Also abbreviated | Item class |
| 9 | L | Legendary / Set item |
| 8 | 6A | 6-affix rare item |
| 7 | 5A | 5-affix rare item |
| 6 | 4A | 4-affix rare item |
| 5 | 3A | 3-affix magic item |
| 4 | 2A | 2-affix magic item |
| 3 | 1A | 1-affix magic item |
| 2 | sW | Superior common item |
| 1 | W | Common item, consumable, crafting reagents and tomes, etc. |
| 0 | Inf | Inferior item |
So, for each item slot being rolled in this game that slot will have a set value of nominal chances for each item-integer. Take for instance some arbitary values based on the first item slot from elite packs:
| IItem rarity | Nominal chance | Real (or resultant) chance |
| L | 0.0010 | 0.0010 |
| 6A | 0.0165 | 0.0165 |
| 5A | 0.0400 | 0.0393 |
| 4A | 0.1150 | 0.1085 |
| 3A | 0.0000 | 0.0000 |
| 2A | 1.0000 | 0.8352 |
| 1A | 1.0000 | 0.0000 |
| sW | 1.0000 | 0.0000 |
| W | 1.0000 | 0.0000 |
| Inf | 1.0000 | 0.0000 |
Rounded to the fourth decimal.
Note in the table above that since the P(2A_hit) = 1, every item with a rarity lower-tiered than 2A (such as 1A, sW, W and Inf) will not be found. But, just because P(2A_hit) = 1 does not mean that all the items found will be 2A-items! This is a very important difference.
So, now that this is expanded to the whole set of "item tiers", it gets a little bit more complicated: Magic find is involved in these chances, but only in the nominal chances! (note: The real - or resultant - chances are derived from the nominal chances so all in all MF affects both).
This means that for e.g. legendary items from the example above the true scenario is actually equal to
Nominal chance = Base chance * (1 + (X/100))
Of which the
Base chance = nominal chance at 0 MF.
X = MF %
Taking the above table again and manipulating the nominal chances by applying 200 MF (which means each chance is multiplied by (1 + (200/100)) = 3) gives the following result:
| IItem rarity | Nominal chance @ 200 MF | Real (or resultant) chance |
| L | 0.0030 | 0.0030 |
| 6A | 0.0495 | 0.0494 |
| 5A | 0.1200 | 0.1139 |
| 4A | 0.3450 | 0.2881 |
| 3A | 0.0000 | 0.0000 |
| 2A | 1.0000 | 0.5470 |
| 1A | 1.0000 | 0.0000 |
| sW | 1.0000 | 0.0000 |
| W | 1.0000 | 0.0000 |
| Inf | 1.0000 | 0.0000 |
Note that nominal chances can only be 1 ≥ Y ≥ 0. For this reason the P(2A_hit) = 1 even though it was that with 0 MF as well.
Expanding this it is possible to create a model-system for how MF affects loot distribution. For this it would therefore require a large sample testing at 0 MF (which we have a decent sample for) and from there backtrack the nominal chances. Since our data only provides precision we are limited to using it to create a model-system that is based on arbitary values somehow related to experimental results and see how the model system fits the data.
Doing this is slightly more time-consuming and will not be discussed here. Instead the results for all 5 elite drop slots and their respective arbitary nominal chances is given in the table below. For making it slightly easier to (and perhaps also more useful) the inferior items have been completely removed and superior white items and normal white items have been grouped together (indicated by cW). Furthermore 3-affix magic items (3A) have been removed simply because they don't drop.
| IItem rarity | Slot 1 | Slot 2 | Slot 3 | Slot 4 | Slot 5 |
| L | 0.0010 | 0.0010 | 0.0010 | 0.0010 | 0.0010 |
| 6A | 0.0165 | 0.0010 | 0.0010 | 0.0165 | 0.0200 |
| 5A | 0.0400 | 0.0020 | 0.0020 | 0.0400 | 0.0500 |
| 4A | 0.1150 | 0.0040 | 0.0040 | 0.1150 | 1.0000 |
| 2A | 1.0000 | 0.0450 | 0.0450 | 1.0000 | 1.0000 |
| 1A | 1.0000 | 0.0200* | 0.0200* | 1.0000 | 1.0000 |
| cW | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| - | |||||
| Item-slot droprate | 100% | 100% | 50% | 100% | Requires 5xNV |
* There is a catch to these two slots in that they drop items called "magic+" items (which are items such as rings and amulets) which does not have any white item equivalents. For clarity this is not included here, but an explanation is given below.
The overall results from this model-system has already been applied in section 5.3 being the actual graphs in the charts while the dots resemble the gathered data. For this reasion illustrations for this model-system will not be included in this section.
For those interested in an elaborate explanation about the magic+ items: There are certain item types which have no white item equivalents. These items include amulets, rings, sources, quivers, mojos, and the enchantress/scoundrel/templar special items. These items will always be magic or better and will therefore have a nominal chance for P(1A_hit) that is very different from other items in gear slot 2&3 (gear slot 1&4 are not of interest here as white items can't drop from these slots). In fact, P(1A_hit) = 100% for these specific items.
From research regarding item-type distribution (lead by ztking) it was found that these magic+ item types consist of approximately 6-8% of all items. An average value is approximately 7.3%. For this model I decided to go forward with the number 7.5% as an arbitary value. So if we note that item slot 2 and 3 are identical and they can be separated into a "normal" slot and a "magic+" slot, we have the following distribution:
| IItem rarity | Slot 2&3 normal | Slot 2&3 magic+ | |||
| L | 0.0010 | 0.0010 | |||
| 6A | 0.0010 | 0.0010 | |||
| 5A | 0.0020 | 0.0020 | |||
| 4A | 0.0040 | 0.0040 | |||
| 2A | 0.0450 | 0.0450 | |||
| 1A | 0.0200 | 1.0000 | |||
| cW | 1.0000 | 1.0000 | |||
| - | |||||
| droprate | 92.5% | 7.5% |
This can be calculated by treating normal gear 2&3 as a single slot with 1.3875 drops on average (92.5% of 1.5 drops) and in addition treating magic+ gear 2&3 as another slot with 0.1125 drops on average (7.5% of 1.5 drops). It is important to note that magic+ gear is not another gear slot - it is simply a way to manipulate the model for easier computations.
* * * * * * * * * *
Note that based on this model-system I have created a small spreadsheet that can be used to visualize what you should be finding when farming.
Remember that this is a model! It should be used with caution as it is based on mechanisms we expect being true and arbitary values for the various P(X_hit). We can say, however, that the model fits our experimental data very well.
The sheets can be downloaded for different versions of excel.
Spreadsheet (.xlsx file)
Spreadsheet (.xls file)
Feedback and corrections are of course welcome.
<Known issues>
- The extra item drop gained from MPLvl only affects gear drops from trash monsters.
* * * * * * * * * *
6.3 Computation for legendary drops vs total item drops(Top)
Expanding the scope slightly from section 6.2 (you do not need to have read it for this section though), this section will involve another computation that is more related to longer farming runs and the chances of finding legendary items.
This section is based on the following assumptions:
- The base drop chance of legendary items is equal for all drop-slots and can be explained by the formula [ Y = 1/1000 * (1 + MF/100) ] for various MF levels (Y = nominal drop chance).
- Over longer farming runs the items that drops are independant on each other and can be described by a binomial distribution.
So, what can a binomial distribution help with for this matter?
A binomial distribution illustrates that for a set number (N) of subsequently performed, but indepedent tries, the chance of having exactly Y number of successes (which here is a legendary item dropping) with a chance of success being Z (which is 1/1000 at 0 MF) is given by a value X. This value can be calculated from the non-accumulated binomial distribution.
This means that we can use the binomial distribution to calculate the chance of finding exactly X amount of legendary items over N dropslots.
It can, however, be manipulated to give another result: If we calculate the chance of not finding a single legendary item, then 1 minus this chance will equal the chance of finding at least 1 legendary item based on a set amount (N) of dropslots.
This can be calculated over a set amount of dropslots and variable MF (since the chance of success depends on MF). The chart given below illustrates the results with variable intervals of MF starting from 0 and going to max MX (625).
For comparison, an approximately full clear of act 3 will result in approximately 500 items dropping. Note that this is a very rough comparison, but serves to illustrate a common standpoint.
Bringing it all together: What MF does is bringing you to the plateau that is closing in on 100% chance with less total items collected. Put another way you will on average find legendary items more frequently (or with lower time intervals in between), but this result shouldn't be something new by now. The chart does, however, illustrate quite a big difference between farming with 0 MF and 75 MF while the difference is smaller at larger MF values (but definately notable).
It is important to clarify that it is not possible to reach a definitive 100% chance even though it may seem so from the above chart. A 100% chance would imply that collecting X items you would always have found 1 legendary and that will not be the case.
6.4 Number of affixes on rare items as a function of MF(Top)
Note that this computation includes the estimates from section 6.2 and is subject to being updated when section 6.2 is
Based on the assumptions presented in section 6.2 we have been looking a little bit into the probability calculations to provide an estimate for the effect of magic find on the number of affixes found on rare items. The calculation sheets are linked at the top of this post.
This computation is based on the assumption that the rolls are independant and going stepwise from:
- Legendary
- 6-affix rare
- 5-affix rare
- 4-affix rare
First is calculated the P(item is [quality]) for each situation.
P(Item is L) = 1 - P(L_miss)
P(Item is 6A) = P(L_miss) * ( 1 - P(6A_miss) )
P(item is 5A) = P(L_miss) * P(6A_miss) * ( 1 - P(5A_miss) )
P(Item is 4A) = P(L_miss) * P(6A_miss) * P(5A_miss) * ( 1 - P(4A_miss) )
Graph (values are given in %'s):
If we then neglet the option for hitting a legendary (the chance is only 0.5% at 400 MF), we can estimate how the #affix distribution may be like as a function of MF. This is performed by making a new column having
P(Item is rare) = P(Item is 6A) + P(Item is 5A) + P(Item is 4A)
And present the P(Item is #A) in terms of P(Item is rare). This will provide an approximated % of the #affixes distributions of rare items as a function of MF. The graph below illustrates the results.
Note that the relative increase per point of MF is extremely small.
Interesting values from 0 MF to 1000 MF are:
| MF | %6A | %5A | %4A |
| 0 | 10.28 | 30.52 | 59.21 |
| 250 | 11.02 | 31.89 | 57.09 |
| 400 | 11.50 | 32.78 | 55.72 |
| 1000 | 13.80 | 36.84 | 49.36 |
Note that being at 400 MF there is a very vague difference compared to 0 MF and 400 is (at this moment) very close to the max value of currently obtainable MF. The biggest difference is seen in the decreasing distribution of 4A rare items. We have to go to 1000 MF to get 3%-points higher distribution of 6-affix rares and being around 250 MF (which should be a common position of MF for a farmer using MF gear) there is barely any difference at all for every #affixes compared to 0 MF.
Do note that the above only considers the relative distribution of #affixes on rare items - it does not include the fact that more rare items will be collected in total (see the first graph in this section; it includes this effect). Put another way: You will find more rare items with more MF and those rare items will have a chance to roll out 4A, 5A and 6A, but the relative distribution of 4A, 5A and 6A are not changing by significant amounts by increasing MF.
A quick test performed in Warrior's Rest A1 has been performed. The data combined are:
| MF | stacks NV | 4-affix rare items | 5-affix rare items | 6-affix rare items | Total rare items |
| 0 | 0 | 59 | 26 | 9 | 94 |
| 230 | 0 | 95 | 48 | 16 | 159 |
| In % | |||||
| 0 | 0 | 62.77% | 27.66% | 9.57% | 100% |
| 230 | 0 | 59.75% | 30.19% | 10.06% | 100% |
Involving the NV rare
In addition to the data for affixes as a function of MF, Timza has been looking into the number of affixes depending on using NV or not when farming. He has sampled a total of 400 elites at 200 MF with no NV and 399 elites at 200 MF with 5xNV included. He noted the distribution of affixes by using the integer-identifier value described in section 3.1. The sample is considerably large and the results for rare items are
| MF | #NV | R(4A) (% of total gear) | R(5A) (% of total gear) | R(6A) (% of total gear) |
| 200 | 0 | 16.88 | 7.26 | 3.09 |
| 200 | 5 | 31.98 | 7.66 | 3.50 |
The above table seems to be rather equal in terms of how #affixes are distributed in spite of 4A rares increasing drastically. This suggests (since the values are %'s of total items) that for the NV rare item the chance of hitting a 4A is simply set to 100% instead of having another item with a completely new distribution set. Do note that this "set at 100% for 4A" does not mean the NV rare will always be a 4-affix rare item; it only means that it will never be less than a 4-affix rare: The "100%" is the P(4A_hit) for the NV rare, but the roll still have to go though legendary/set item, 6A and 5A rare.
If we then make a computation that takes the sample from Timza, calculates the expected #affix rare items at 200 MF and removes these from the NV sample it will leave us with only the NV rares left. If the NV rare has a hit of 100% chance at 4A, then the distribution of 4A rares (in % of total rares) will be equal to (neglecting the legendary chance):
100% - 3.09% - 7.26% = 89.66%
The computation provides us with the following numbers:
| MF (#NV) | Situation | R(4A) (in % of total R) | R(5A) (in % of total R) | R(6A) (in % of total R) |
| 200 (5) | Non-NV rares removed | 85.75 | 9.24 | 5.01 |
| 200 (5) | Expected if 4A=100% hit | 89.66 | 7.26 | 3.09 |
The fact that the % of R(4A) is lower than the expected and the two other (R(5A) and R(6A)) are higher can maybe result from the fact that another item is added to the item pool from the NV buff and this can also roll out higher than 4A. However, the above computation indicates that it is very likely for the NV rare to simply have a 100% to hit on the 4-affix rare.
Another sample performed with only 5xNV (therefore 75 MF applied by default) gives the following distribution for the # of affixes on the NV rare items:
Total items: 400
6-affix rare items: 12 (3.00%)
5-affix rare items: 27 (6.75%)
4-affix rare items: 361 (90.25%)
It is therefore very reasonable to conclude that the NV rare simply has a limit put at P(4A_hit) = 100%. This is a quite important fact, as it will mean MF will be more effective towards the relative distribution of 4A/5A/6A compared to the other gear slots. A computation based on the assumption that the NV gear slot is simply identical to gear slot 1 or 4 with the exception that P(4A_hit) = 100% gives the following result:
This is quite a different picture from the other situation; it is not a vast difference compared to going from minimum MF (75 in this case due to 5xNV being required) to maximum MF (375), however, it is at least more noticable compared to the other gear slots.
Based on the data contributed by Gigahurts and combined with my own sample we should be able to see this difference (collected at high MF values); note that his sample is small in size so take these percentages lightly, but it does seem to be a trend (these rare items are only NV rares!):
| MF (#NV) | R(4A) (in % of total R) | R(5A) (in % of total R) | R(6A) (in % of total R) | Sample size |
| 75 (5) calculated | 93.09 | 5.16 | 1.75 | - |
| 75 (5) collected | 90.25 | 6.75 | 3.00 | 400 items |
| - | ||||
| 308 (5) calculated | 84.18 | 11.74 | 4.08 | - |
| 308 (5) collected | 75.96 | 19.23 | 4.81 | 104 items |
| - | ||||
| 328 (5) calculated | 83.43 | 12.29 | 4.28 | - |
| 328 (5) collected | 69.92 | 23.58 | 6.50 | 123 items |
Again, note that hese are only the NV rares.
The sample size presented in the above table is certainly not the largest, however, it is the only one we have as it has become difficult to distinguish the number of affixes on rare items since patch 1.04. The computation assumes that the chance of rolling rare items from the NV rare slot is the same as slot1 and 4 from elite packs, however, it is possible there is a difference in the nominal chances.
In any case, the overall conclusion from this section is that MF is more effective towards the distribution of affixes on rare items on the NV rare than the other rare drop slots, but to what extent is currently unknown.
6.5 The sequenced item slots per monster type(Top)
Note that this section is a work in progress and subject to changes.
Based on the drop sequence that was presented in section 3.4 we have developped a table that should help illustrate the item slots that are associated to different monster types and in what sequence they drop.
Because wer are taking so much information and ultimately shrinking it down to such a small table, it will without a doubt be practically impossible to extract everything else found in this thread directly from it. It will, however, serve as a very simple model to explain some of the key features about monster types and their item slots as well as understanding the overall efficiency of magic find.
This is still a work in progress, however, the following is a table that illustrates the monster type and which slot types are applied in a given sequence. The slot types illustrates the predominant distribution at 0 MF or as close to 0 as possible, e.g. M/R indicates magic items being the dominant and R items being somewhat found decently. Note that the first type (the one that is dominant) is the least item rarity found - for example, from M/R slots you will never find white items.
Code to understanding the table:
W/M = White items dominate, magic items common (below white rarity not found)
M = Magic items dominate, rare items occasionally (below magic rarity not found)
M/R = Magic items dominate, rare items common (below magic rarity not found)
R = These are the NV-rare slots (below rare not found)
T = Tome of secrets
G = Gem
| Slot | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| Elite packs | M/R | W/M | T | W/M | G | M/R | R | - | - | - | - | - | - |
| Treasure Goblin | M/R | W/M | T | W/M | G | M/R | R | M/R | - | - | - | - | - |
| Treasure Bandit | M/R | W/M | T | W/M | G | M/R | R | M/R | T | T | T | - | - |
| Treasure Seeker | M/R | W/M | T | W/M | G | M/R | R | G | G | G | - | - | - |
| Treasure Pygmy | M/R | W/M | T | W/M | G | M/R | R | M/R | - | - | - | - | - |
| Miniboss | W/M | M | M | T | M | M | M/R | R | R | T | - | - | - |
| Act endbosses | W/M | W/M | M | M | T | W/M | M | M | M | M/R | R | R | T |
For elite packs and treasure goblins, bandits, seekers or pygmys it is slot #7 that gets activated with 5xNV stacks, slot #4 has 50% drop chance while slot #1, #2 and #6 (plus slot #8 for treasure monsters) all have 100% drop chance. The specific drop chance for slot #3 and #9-11 for bandits and seekers have not been determined.
For minibosses slot #1, #2 and #3 have a 100% drop chance. Slot #5-10 gets activated one by one (starting with #5) for each stack of NV active.
For act endbosses slot #1-4 and #6 have a 100% drop chance while slot #7 has ~50% drop chance. Slot #8-12 gets activated one by one (starting with #8) for each stack of NV active.
- - -
7. Summary / Conclusion(Top)
Bringing all the pieces together provides us with:
- Magic find increases the class ("item-color" or rarity) of the gear found.
- Magic find will - on average - increase the number of possible affixes on items because this is directly related to the item class which in turn is affected by MF.
- Magic find does not increase the number of items found (aka not effective on quantity).
- Magic find does not increase the iLvl of the gear found.
- The guaranteed rare drop from Nephalem Valor is an additional drop and it is possible to roll a legendary instead of rare.
- The guaranteed rare drop from Nephalem Valor is applied to goblins as well.
- The effect that MF has on increasing the number of possible affixes on rare items appears to be minimal and close to neglible for the standard elite drops. It does, however, appear to have a prominent effect on the NV rare drop.
- Whether or not magic find affects the affix rolls themselves (aka not how many affixes you get, but how good the affix values turn out) is not investigated here, but there is no reason as of to suspect that magic find would increase the actual stat rolls. As of patch 1.05, Blizzard has also stated that these rolls will depend on the mLvl of the monster that the item dropped from.
- The items drop in a predetermined sequence with each item dropped coming from a "slot". These slots have different chances to roll out a rare item, but only one of them (out of 4 gear slots without NV) seem to have the possibility to hit a NoDrop. The research mentioned here is very early, but is an important aspect if a complete picture of average drops is to be computed.
- The items dropping from elite packs appear to be divided into "slots" that drop in a specific sequence. An elite pack has 4 of these slots and if 5xNV is effective a fifth is added. These slots have different base chances to roll out different item rarities: Gear slot 1 and 4 seem to be identical and have a base dropchance of around 10% for rare items, gear slot 2 and 3 seem to be related but have a very small chance to roll a rare item and in addition, gear slot 3 has a 50% chance to hit a NoDrop. Gear slot 5 (the NV slot) is always at least a 4-affix rare item.
- - -
8. Outlook
I hope that this post will eventually be so well constructed that it will serve as a central point where most of the mathematics and regarding MF, its efficiency and its mechanic will be gathered.
8.1 Current plans for the project(Top)
Sadly I have had to stop updating this project as my work is demanding more time. For this reason the post will no longer receive any major updates from my part, but some minor updates may be filled in now and then (such as corrections to the spreadsheet).
8.2 Further reading(Top)
This thread initially was meant to eliminate most common questions from the public, however, there are also some who have taken this research to another level and made posts based on what we have presented in this text. In this final part of the post I will therefore include links that could be of interest.
ztking has written a compendium of MF mechanics and FAQ on the offical forums. His work focuses on a more guide-related style, while this thread here only focuses on crunching numbers and testing systems.
If you are interested in the mechanic of magic find or have any questions regarding it or anything related to it, you should take a look.
Other useful links:
Diablo Wiki on magic find
Game guide - items and equipment
- - -
TL;DR: Suck it up and go read the summary.
- - -
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