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/.
I am not into crunching numbers.. hence the reason i'm in law school, but I do have a 49% nagelring and I have the 3 set cains (with the ring) and do have that 41% mf gem, so by using good ol logic, it seems as if i was on the right track baby -- GG and great post man keep it up.
All my noob friends will be salty when i'm raking in the legendaries speeding those T3 rifts 5 min at a time... Would love to read more about this i find it rather interesting! Usually i just bend a knee and do a voodoo dance to the RNG gods...
Would be cool if you would take split bounty farming into the comparison. Since with a lot of horadic caches within a small amount of time combined with doing the actual bounties end killing mobs that seems to yield quite a lot of legendaries as well.
The derivation will be omitted, but the end result is the following expression (where N again is a torment difficulty value):
Can you please post the derivation because I don't see where that equation comes from. It seems unreasonable. Increasing the health of the mods increases the drop rate of legendaries, what? And (health_n+1/health_n)^1/3 will always be 1.6^1/3 ~= 1.17 since health increase is 60% per T.
Also y-axis from 0 would make for a more honest comparison.
He probably assumed that blizzard wanted some kind of roughly equivalent droprate based on the time it takes to kill enemies so he used health to calculate it. The math doesnt necessarily check out though, as you say. His formula has no more ground to stand on than the assumption of 1.15^N.
Really, you cant calculate the droprate bonuses when given only 2 points of data. There are an infinite number of equations that would satisfy those requirements. For now at least, the best guess might be the simplest (1.15^n)
EDIT: In light of the post above me, it really is 1.15^n
This post is built on a completely incorrect assumption. It was confirmed by Lylirra in that very same thread that it is, in fact, a 15% multiplicative per torment level buff (eg 1.15^N):http://us.battle.net/d3/en/forum/topic/12413271220?page=13#241
Taking this into account, the drop chance for 150 MF is effectively the same thing as farming a rift one torment level higher. That is to say, farming a rift on T3 with 150 MF is effectively the same thing as farming a rift on T4 with 0 MF. It is nowhere near the drop chance of T6 rifts.
Very disappointed to see such clearly incorrect and misleading information be prominently displayed on the front page of the site.
This post is built on a completely incorrect assumption. It was confirmed by Lylirra in that very same thread that it is, in fact, a 15% multiplicative per torment level buff (eg 1.15^N):http://us.battle.net/d3/en/forum/topic/12413271220?page=13#241
Taking this into account, the drop chance for 150 MF is effectively the same thing as farming a rift one torment level higher. That is to say, farming a rift on T3 with 150 MF is effectively the same thing as farming a rift on T4 with 0 MF. It is nowhere near the drop chance of T6 rifts, as shown in your standard extrapolation graph on the right.
Very disappointed to see such clearly incorrect and misleading information be prominently displayed on the front page of the site.
Does this take into account that MF towards legendaries is only 10% effective?
It should, I think, assuming your MF chance is multiplied against the separate torment/rift modifier. 10% of 150% MF is 15% legendary MF, which is the same thing as the legendary chance increase going up one torment level.
Guys. Why do you have to flame the guy the made an effort? Indicating a mistake is fare. The others that ahve other ideas, how about making a new thread and so some actual research instead of bullshitting with napkin maths?
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.
Here's my ranking of whats happening in this thread, its very similar to the rest of the internet:
(1) Name-calling
(2) Inability to clearly state issues with someone's post without attacking them or their effort in any way - i.e. just pointing out where someone went wrong doesn't do anything. Improve the model. I saw that at least once in the comments, that guy gets a gold internet star. That internet star, however, does not show on his character sheet's dps, toughness, or healing.
...
(10000000) Guy trying to do you a favor by starting work on a statistical model that has questionable significance in its current state
Good job! But from statistical point of view, all the drops are random and leg drops less than 1%. It might need tens of thousands or maybe even million drops to notice the difference.
Honestly, I feel a bit bad for the OP... He put this much effort into something this wrong...
Try the following:
Use the correct formula instead of one you apparently pulled out of your ass. Your formula gives the same result for every torment level between 2 and 6, a 17 % increase of the base.
Confirm if you used the correct way of calculating MF for legendaries.
Also, to the guy who put this on the frontpage: Be better than that. Take a look at what you are posting before you slap it on the front page.
This might be a dumb question, but doesn't the MF cap out at 300% anyways even with the bonus given? So I show as 405% MF but the game will still only count 300%?
MF only accounts for 10% towards legendaries so if you were wearing 150 as OP suggest in Torment 3 that would only be 15% - I have a hard time believing this would have an impact if any at all.
Would this mean since the new legendary multiplier for rifts is 25% would this be an additional 15%?
---------------------------------------
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.
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/.
All my noob friends will be salty when i'm raking in the legendaries speeding those T3 rifts 5 min at a time... Would love to read more about this i find it rather interesting! Usually i just bend a knee and do a voodoo dance to the RNG gods...
~always be farming
Psimos
Would be cool if you would take split bounty farming into the comparison. Since with a lot of horadic caches within a small amount of time combined with doing the actual bounties end killing mobs that seems to yield quite a lot of legendaries as well.
http://eu.battle.net/d3/en/profile/Storm-21498/hero/47687845
Really, you cant calculate the droprate bonuses when given only 2 points of data. There are an infinite number of equations that would satisfy those requirements. For now at least, the best guess might be the simplest (1.15^n)
EDIT: In light of the post above me, it really is 1.15^n
Taking this into account, the drop chance for 150 MF is effectively the same thing as farming a rift one torment level higher. That is to say, farming a rift on T3 with 150 MF is effectively the same thing as farming a rift on T4 with 0 MF. It is nowhere near the drop chance of T6 rifts.
Very disappointed to see such clearly incorrect and misleading information be prominently displayed on the front page of the site.
Nothing beyond repairing anyway... And it's not like the main page is the 100% definite truth of everything diablo related. Msitakes happen.
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.
http://www.diabloprogress.com/hero/sodomir-2220/
(1) Name-calling
(2) Inability to clearly state issues with someone's post without attacking them or their effort in any way - i.e. just pointing out where someone went wrong doesn't do anything. Improve the model. I saw that at least once in the comments, that guy gets a gold internet star. That internet star, however, does not show on his character sheet's dps, toughness, or healing.
...
(10000000) Guy trying to do you a favor by starting work on a statistical model that has questionable significance in its current state
Good luck farming!
Try the following:
I hate Galiks. One of the biggest douchebags I've ever had the misfortune of sharing a WoW server with.
Would this mean since the new legendary multiplier for rifts is 25% would this be an additional 15%?