I'm sure that the OP will welcome any criticism to his model and revise it according to where he feels that the criticism is warranted. He should be used to that as a PhD student. I would like to see his follow-up to the critical response. And we will never get any answers if we are required to blindly applaud attempts based on the amount of effort required in producing them. The correct way to honor a post such as the OPs is constructive criticism.
As for criticism based on the fact that simplifying assumptions have to be made, they are a bit unwarranted. Obviously we can't get a thousand people with the exact same build and gear to farm the same route a thousand times on different torment levels to get the required empirical data. This must be done with a priori logic. The OP equates mob health with time, and assumes that this accounts for the amount of instances to have a chance in a given timeframe (which is the real effect of MF, not the qualitative value of a single mob regardless of how many times you kill him, which is effectively uninteresting). The choice isn't between killing 1 skeleton with 30% more chance or 1 skeleton with 0% more chance, but in whether you want to kill 5 skeletons with 10% chance or 1 with 30% chance in a given minute. And the answer we are looking for is where exactly do the lines go for a hypothetical average character in the world of d3. Travel and loading time must be left as ceteris paribus in this respect. But arriving at general advice shouldn't be impossible. Perhaps it can be looked at relative to damage scaling from items; what does it take to one-shot a mob on normal, and how much more damage can be achieved relative to the percent increase in HP from torment levels relative to magic find? I don't know.
The OPs post can inform this question, but not if the values are wrong and certainly not if they are randomly chosen. We need more.
This man says it best. There are too many factors that can influence everything. My post assumes there is a near static rate in farming each Torment, but, as stated multiple times, one needs to make their own decision at which the highest Torment difficulty they can handle without significant downtime compared to the previous Torment level. However, I have reverted all data to 1.15^N conversion so its all entirely correct based upon the blue post. This man follows the logic upon equating mob HP with time that went into it, but we will 'dumb it down' to the now confirmed 1.15^N that came after I had done this study.
tldr; The graphs are right now. The right graphs were there before. Use logical decisions
I've already spent way too much time on this to even debate all of these posts, but I feel like there are severe reading deficiencies abundant.
Therefore if a monster health increases at a non-linear rate, why not fit a curve to assume Blizzard is interpreting on a basis of time to kill a monster. The resulting DPS to overcome that time to kill a monster was my foundation. But, hey, if we want to go with 1.15^N - that just makes everyone's life simpler
Increasing torment levels makes it more difficult at a non-linear rate (i.e. torment 1 to 2 is easy, but torment 5 to 6 is not),
Look, Galiks. The increase between torment levels is 60%(1.6^N) hp, 45% damage(1.45^N), 40% gold/xp(1.4^N)* and 15%(1.15^N) legendary drops. As you can see they -all- follow the X^N pattern and there is near zero difference between T1->T2 and T5->T6.
*This one is rounded to closest 50%
This is true. And I've had the 1.15^N chart there alongside all of my data. I gave a separate reference that assumed it was based upon a different factor (purely time to kill a monster). In the long run of it all, both approaches yield similar values except at high Torment levels and no differences in drop rates will be seen immediately. My data merely says that if you take samples of legendaries dropping over a long duration of time, they will converge to being affected by these linear coefficients. For the optimist, you consider MF and rifting. For the short term who lives in the present, you do whatever. If you disagree that right information was there all along, and that purely correct information is not there now, then we're at a loss.
I've already spent way too much time on this to even debate all of these posts, but I feel like there are severe reading deficiencies abundant.
For every graph of my interpretation, I presented the standard 1.15^N graph right next to it as a comparison in case mine wasn't right. These are entirely correct.
We assume that the blue poster is indeed confirming the drop rate function so whimsically (probably one of the most well-kept critical pieces of information) and that there isn't additional components to it.
Even if I was/am wrong, why not have an extra piece of information? Mine related defined monster health percentages for varying torment difficulty, and time is the critical component in what makes it worth it to farm a certain difficulty level. Therefore if a monster health increases at a non-linear rate, why not fit a curve to assume Blizzard is interpreting on a basis of time to kill a monster. The resulting DPS to overcome that time to kill a monster was my foundation. But, hey, if we want to go with 1.15^N - that just makes everyone's life simpler. I will remove the left graph of all figures so nobody has to painstakingly look at it.
I assume legendary drop rates is 10% of your current MF. This was confirmed by a blue post I read awhile back and has been generally accepted. This means for 300% MF, you have 30% contributing to your legendaries. This is a 1.3x multiplier. I assume this is multiplied by the rift bonus factor of 1.25 (which can be seen as 250% MF), which is already multiplied by the torment difficulty increase factor.
This is merely a post to compare the legendary drop rate increase factor for rifting and MF. As stated in the post (and of course this is so obvious), don't sacrifice your DPS to an unbearable amount so it's like you're throwing rocks at normal mobs and they aren't falling over. Increasing torment levels makes it more difficult at a non-linear rate (i.e. torment 1 to 2 is easy, but torment 5 to 6 is not), so there should be a fixed value for your gear where you can handle a lower Torment level with MF and the question would be "what gain does this net me?" Say you choose the Torment level below what you can farm in your best, and you slap on 150 MF and you actually end up increasing the drop rate for the same amount of clear time. Simple as that. It comes to several factors, but we're only looking at flat drop rate increase factors here... taking everything into consideration (DPS, monster type, etc.) in varying environments is an overwhelming study.
Galice/Galiks here. Long-time WoW raider (US-Azgalor, now Kil'jaeden), former GM of Rehabilitation Clinic, etc... nerded some stuff out thought I'd share if it helps anyone out.
---------------------------------------
Introduction
The enigma shrouding the drop rate of legendary items in Diablo 3 is a center of debate and mass confusion for the most efficient methods to obtain them. The choice of whether it's worth it to increase the difficulty level for an increase in finding legendary items, and the resulting quantitative gain associated with an increase in difficulty, is still unclear. For example, is it worth the massive time increase to suffer through Torment 6 (t6) monsters for a higher drop rate? Many would say of course not (and it turns out they're right).
It seems obvious that higher difficulty levels are just not worth it as all Torment difficulties drop the same items, but supposedly at a different rate. The aim of this report is to provide a quantitative analysis of the drop rates for torment difficulties, and provide a recommendation in farming through comparing drop rates in and outside of rifts. Additionally, magic find (MF) will be factored into the consideration as an extra factor.
-----------------------
2. Equation Basis http://us.battle.net/d3/en/forum/topic/12413271220?page=13#241 This is 1.15^N as confirmed in this blue post, where N = torment difficulty level.
This was edited. Before there was an equation here that I had manipulated and used this as another reference as comparison to the 1.15^N in case either were right, but alas, 1.15^N was confirmed 3 days ago after I had done any work so only that will be shown. If for whatever reason the previous equation that was here that linked known monster health percent versus difficulty (which also can be thought of as increasing time to kill a mob - a logical way to warrant a drop rate increase), and the blue is just agreeing to release a critical piece of information that has never been released before so whimsically, then that information is no longer public. Your standard 1.15^N formula is shown, as was all along before alongside a separate approach. Nonetheless, the two were similar.
Everything taken into consideration is just looking at the legendary drop rate factor increase for varying parameters. It is in no way explaining the most effective place to farm, as that is left up to the player skill level, gear, speed in clearing, and density/type of monsters/chests in your exclusive rift or outside location. Under the assumption that there is no clear choice/multiple options, these graphs can help lead you in a certain direction.
3. Rifting versus Non-Rifting and Magic Find
Using these values, one can make a comparison against the legendary drop rate factor inside a rift (1.25x multiplier) versus outside of a rift. As one can see below, certain points can be made.
Torment 1 rifting is slightly worse than drop rates from Torment 3 non-rifting.
Torment 2 rifting is slightly worse than Torment 4 non-rifting.
Torment 3 rifting is between Torment 4/Torment 5 non-rifting.
Torment 4 rifting is near Torment 6 non-rifting
More conclusions can be drawn based on self-inquiries.
The question of magic find (MF) and its effectiveness in Reaper of Souls usually ends with 'MF NOT WORTH IT!' Below shows varying MF inside of a rift (assuming MF is multiplicative and legendaries receive 10% of their MF towards legendary drop rates [i.e. 150 MF contributes to 15%] i.e. 1.15*1.25*base_torment_droprate). The plot is shown below.
Wearing no MF inside a Torment 2 rift is slightly less than Torment 4 farming outside of a rift
Wearing 50 MF inside a Torment 2 rift is equivalent to Torment 4 farming outside of a rift
Wearing 150 MF inside a Torment 2 rift is slightly less than Torment 5 farming outside of a rift
Wearing 300 MF inside a Torment 2 rift is almost equivalent to Torment 6 farming outside of a rift
Therefore, as a recommendation for actual possible MF values (Nagelring 50%, Topaz in helm 41%, Cain's set 50%), we can say that for 150 MF farming a Torment 3 rift, we are about the same as Torment 6 outside of rifts. Since Torment 3 speed runs with 150 MF seem much more plausible with the current player/state of the game, this seems to grant the biggest bang for the buck if done consistently and at a proper pace. Comparisons for outside of rift for varying MF are omitted as most interest will likely fall upon the inside-rift scenario due to the 1.25x multiplier (which inherently acts like 250 MF as legendaries receive 10% of the MF value). Nonetheless, other conclusions can be drawn, and these graphs can be used to quantify other questions for varying player skill levels and character capabilities. Choices should be made based upon your own capabilities to optimize speed, location (possible dense area of chests outside rifts), and individual skill.
Battletag is Galice#1533 for questions/inquiries. Galice/Galiks/Galrosh @US-Kil'jaeden (retired for now) Feel free to join my diablo clan <Arch Druid> for a feisty environment and anyone looking for a full-clear heroic WoW guild check out http://www.archdruidguild.com/.
tldr; The graphs are right now. The right graphs were there before. Use logical decisions
---------------------------------------
- Introduction
The enigma shrouding the drop rate of legendary items in Diablo 3 is a center of debate and mass confusion for the most efficient methods to obtain them. The choice of whether it's worth it to increase the difficulty level for an increase in finding legendary items, and the resulting quantitative gain associated with an increase in difficulty, is still unclear. For example, is it worth the massive time increase to suffer through Torment 6 (t6) monsters for a higher drop rate? Many would say of course not (and it turns out they're right).It seems obvious that higher difficulty levels are just not worth it as all Torment difficulties drop the same items, but supposedly at a different rate. The aim of this report is to provide a quantitative analysis of the drop rates for torment difficulties, and provide a recommendation in farming through comparing drop rates in and outside of rifts. Additionally, magic find (MF) will be factored into the consideration as an extra factor.
-----------------------
2. Equation Basis
http://us.battle.net/d3/en/forum/topic/12413271220?page=13#241 This is 1.15^N as confirmed in this blue post, where N = torment difficulty level.
This was edited. Before there was an equation here that I had manipulated and used this as another reference as comparison to the 1.15^N in case either were right, but alas, 1.15^N was confirmed 3 days ago after I had done any work so only that will be shown. If for whatever reason the previous equation that was here that linked known monster health percent versus difficulty (which also can be thought of as increasing time to kill a mob - a logical way to warrant a drop rate increase), and the blue is just agreeing to release a critical piece of information that has never been released before so whimsically, then that information is no longer public. Your standard 1.15^N formula is shown, as was all along before alongside a separate approach. Nonetheless, the two were similar.
Everything taken into consideration is just looking at the legendary drop rate factor increase for varying parameters. It is in no way explaining the most effective place to farm, as that is left up to the player skill level, gear, speed in clearing, and density/type of monsters/chests in your exclusive rift or outside location. Under the assumption that there is no clear choice/multiple options, these graphs can help lead you in a certain direction.
3. Rifting versus Non-Rifting and Magic Find
Using these values, one can make a comparison against the legendary drop rate factor inside a rift (1.25x multiplier) versus outside of a rift. As one can see below, certain points can be made.
- Torment 1 rifting is slightly worse than drop rates from Torment 3 non-rifting.
- Torment 2 rifting is slightly worse than Torment 4 non-rifting.
- Torment 3 rifting is between Torment 4/Torment 5 non-rifting.
- Torment 4 rifting is near Torment 6 non-rifting
More conclusions can be drawn based on self-inquiries.The question of magic find (MF) and its effectiveness in Reaper of Souls usually ends with 'MF NOT WORTH IT!' Below shows varying MF inside of a rift (assuming MF is multiplicative and legendaries receive 10% of their MF towards legendary drop rates [i.e. 150 MF contributes to 15%] i.e. 1.15*1.25*base_torment_droprate). The plot is shown below.
Therefore, as a recommendation for actual possible MF values (Nagelring 50%, Topaz in helm 41%, Cain's set 50%), we can say that for 150 MF farming a Torment 3 rift, we are about the same as Torment 6 outside of rifts. Since Torment 3 speed runs with 150 MF seem much more plausible with the current player/state of the game, this seems to grant the biggest bang for the buck if done consistently and at a proper pace. Comparisons for outside of rift for varying MF are omitted as most interest will likely fall upon the inside-rift scenario due to the 1.25x multiplier (which inherently acts like 250 MF as legendaries receive 10% of the MF value). Nonetheless, other conclusions can be drawn, and these graphs can be used to quantify other questions for varying player skill levels and character capabilities. Choices should be made based upon your own capabilities to optimize speed, location (possible dense area of chests outside rifts), and individual skill.
Battletag is Galice#1533 for questions/inquiries. Galice/Galiks/Galrosh @US-Kil'jaeden (retired for now) Feel free to join my diablo clan <Arch Druid> for a feisty environment and anyone looking for a full-clear heroic WoW guild check out http://www.archdruidguild.com/.