Diablo® III

Monster power analysis (for real this time)

First, let me lay out what we know so far from blizzard.

Here is the chart:
https://bnetcmsus-a.akamaihd.net/cms/content_folder_media/MQRC9PZ3CZ1K1349891151349.jpg?v=0

Here are the relevant blue posts:
http://us.battle.net/d3/en/forum/topic/6893750712#12
http://us.battle.net/d3/en/forum/topic/6794983614#7

Make sure you read that first post closely. It indicates that bonus items can be triggered by any item dropping, where an item is a piece of gear, pot, gem, tome, or even pile of gold. It also states that the bonus item will always be a piece of gear.

So we get situations like this:
1. Piece of gear drops, bonus item - piece of gear
2. Pile of gold drops, bonus item - piece of gear
3. Health pot drops, bonus item - piece of gear

This has fairly extreme results at high MP. From here on "item" will refer to the larger subset of gear, tome, gold, pot, etc.

How frequently each type of mob drops an item varies, but we can construct a rough framework. Drops from elites aren't affected by bonus items. The ratio of elites to whites killed varies by route, but let's start with 50% of gear coming from elites and 50% coming from whites mobs on MP0. What happens when a white mob drops an item? It can be a piece of gear, a tome, a potion, a gem, or gold. Let's say 25% of the time it's a piece of gear. The other 75% of the time it is junk, but that junk drop can trigger a bonus item which is always a piece of gear.

So our number of items looks like this:
y = 0.5*x + 0.5*x*(1 + 4*bonus%)
x is the number of gear drops gained from a run on MP0
bonus% is the value found in the chart above
y is the number of gear drops gained from the MP corresponding to the bonus

If we get 350 items on MP0, we get 1050 items on MP10. Three times more.

Converting this to a percentage:
y/x = 0.5 + 0.5*(1 + 4*bonus%)

MP %gear
0 100%
1 102%
2 116%
3 134%
4 152%
5 172%
6 194%
7 218%
8 242%
9 270%
10 300%


Now, let's bring in magic find. I will be assuming max magic find as it's accessible via either paragon or gear.

L = y*(1 + MF/100)*0.05%
L is the expectation of number of legendaries
MF is magic find
y is the number of gear drops gained at the corresponding MP

At maximum magic find, with 350 items on MP0 we can expect to find 0.83 legendaries. With 1050 items on MP10 we can expect to find 3.81 legendaries. 4.57 times more.

Converting this to a percentage:
L/L0 = [y*(1 + MF/100)]/[y0*(1 + MF0/100)]
Note the base drop rate becomes irrelevant. It simply doesn't matter what it is, so this percentage increase in gear drops can apply to anything: number of legendaries or number of 6-affix rares--whatever is most desirable in the loot hunt.

MP %gear with MF
0 100%
1 107.37%
2 128.21%
3 155.16%
4 184.00%
5 217.26%
6 255.26%
7 298.32%
8 343.89%
9 397.89%
10 457.89%


When interested in maximizing efficiency, we need some sort of measure of time spent. There comes a point where increasing dps no longer increases the speed of clearing the map: travel time. It takes me 15 minutes to run through most of the maps in Act 3 on MP0. It takes me the same 15 minutes on MP1. If there are 0.83 legendaries per run on MP0, that is 3.32 legendaries/hour. In order to surpass this rate, we have the following time limits:

MP Time limit
0 15.0
1 16.1
2 19.2
3 23.3
4 27.6
5 32.6
6 38.3
7 44.8
8 51.6
9 60.0
10 68.9


Even if it takes twice as long to run MP5, it is still more beneficial for loot than running MP0. It is not necessary to "one-shot" mobs to be efficient.

As a percentage of time, it would be identical to the "%gear with MF", so if the MP0 run takes something other than 15 minutes, the percentages two tables up can be used to calculate matching time limits.

Lower monster power will always be better for xp, but higher monster power is better for loot, due to bonus items. Exactly which MP is optimal will vary by the class's movement speed and the character's gear.
Edited by Shelendil#1520 on 1/10/2013 7:20 AM PST
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Which monster power is best is a more complex system, but it's possible to see how changes affect it. This spreadsheet includes both the math in the above post and an attempt to model legendary drops per time. All of this assumes that gear is not a factor, when in fact it will be the limiting factor for most. (This is a good thing; it means we have room to grow and room for new gear to be introduced by Blizzard.)

https://docs.google.com/spreadsheet/ccc?key=0AhlgYioNgst0dG4waUZicmZQQi1iZ2RyVFZEd0lUelE#gid=0

If you make a copy of the spreadsheet and adjust the values in the blue boxes, the graph will show you which monster power is theoretically best. More players makes higher monster power more efficient. Faster travel times make lower monster powers more efficient. A solo wizard which has no movement speed skills will want to do MP9 with perfect gear. A solo DH with tons of movement speed boosts may find MP6 best with perfect gear. Four-player groups with high synergy may want to do MP10.

When the time spent killing overwhelms the travel time, you begin to lose efficiency. Where this happens will depend highly on group composition, speed, and gear.
Edited by Shelendil#1520 on 1/9/2013 9:17 AM PST
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+1 like for O.P.

anyway

i agree, higher monster power is more efficiant and better for farming items, lower monster power is more efficiant for farming experiance but still its all about someones sweet spot and the highest monster power someone can do where it doesnt take too long to kill elites is way better for farming items then overkilling in low monster power.
Edited by NeLLy#1854 on 1/9/2013 8:32 AM PST
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Minor note: You need at least 1 NV before bonus items start working... It's an extremely minor point but it has been proven.

Try it out yourself if you want.
Edited by hampster#1586 on 1/9/2013 8:37 AM PST
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sweet spot is mp6 with decent gears i think. Alot of loot
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Now, let's bring in magic find. I will be assuming max magic find as it's accessible via either paragon or gear.

L = y*(1 + MF/100)*0.05%
L is the expectation of number of legendaries
MF is magic find
y is the number of gear drops gained at the corresponding MP

At maximum magic find, with 350 items on MP0 we can expect to find 0.83 legendaries. With 1050 items on MP10 we can expect to find 3.81 legendaries. 4.57 times more.
You are making a hidden assumption - gear drops from an elite are the same as gear drops from trash mobs. Items dropped by elites may have a higher intrinsic probability of them being a legendary compared to items from trash mobs. Your equation should be changed to:

L = z*(1 + MF/100)*0.1% + y*(1 + MF/100)*0.05%
L is the expectation of number of legendaries
MF is magic find
z is the number of gear drops from elites gained at the corresponding MP
y is the number of gear drops from trash mobs gained at the corresponding MP

Both 0.1% and 0.05% are arbitrary numbers. The end result is that you may be overestimating the benefit of bonus item drops.
Edited by Elexar#2219 on 1/9/2013 9:46 AM PST
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01/09/2013 09:43 AMPosted by Elexar
You are making a hidden assumption - gear drops from an elite are the same as gear drops from trash mobs. Items dropped by elites may have a higher intrinsic probability of them being a legendary compared to items from trash mobs. Your equation should be changed to:


No...No they don't. The only thing special about elite gear drops is they are 'floored'. Meaning that certain ones can never be worse than a certain rarity.

The most common example is the NV bonus drop can never be worse than a 4 property rare. It will still roll a chance (the exact same % chance of EVERY SINGLE GEAR DROP FOR ANYTHING ELSE) to be legendary, then set, then 6 property rare, then 5 property rare. If all those rolls fail, its 100% chance of 4 property rare.

Some gear drops have such a floor.

Note, full disclosure, by technically gear from environmental stuff like barrels are less likely due to be legendary/set/rare only because they are unaffected by MF, not because they are magic.

01/09/2013 09:43 AMPosted by Elexar
Both 0.1% and 0.05% are arbitrary numbers. The end result is that you may be overestimating the benefit of bonus item drops.


Again, we've been given enough information directly by blizzard that there are ZERO assumptions in this model. We have been told exactly, in no uncertain terms that bonus items work in the fashion he described. We have also been told that the average white mob in the game has a 30% chance to drop an item/gold. This average makes it REALLY easy to make the model he just made.

The actual drop rates literally dont matter at all. Not even one bit. He is doing basic math to make a model of the relative drop rates between all the MP. This ratio is being applied to clear times of the same 'run' since mob density is 100% identical through all MPs 1-10.
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Reserving another front page post, cause Droth just keeps getting dumber. My teeth seriously hurt.
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Nice. Droth's misinformation must be dispelled.
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01/09/2013 10:02 AMPosted by Shandlar
No...No they don't. The only thing special about elite gear drops is they are 'floored'. Meaning that certain ones can never be worse than a certain rarity.
My question is this - how do you know that they are only floored (minimum quality guaranteed)? It doesn't square with elite drop research data from diablofans (relevant section 5.4). I am unaware of published trash mob data of this type.

Again, we've been given enough information directly by blizzard that there are ZERO assumptions in this model. We have been told exactly, in no uncertain terms that bonus items work in the fashion he described. We have also been told that the average white mob in the game has a 30% chance to drop an item/gold. This average makes it REALLY easy to make the model he just made.
Look at y, it is defined as total number of gear drops. 0.5x represents 50% of items from elites and the other term 0.5x*(1+4*bonus%) are drops from trash mobs + extra item drops from trash mobs. This is sound. The problem only happens when my only objection - gear slots are not equal - happens to be correct. The number 0.05% being multiplied by y in his third equation is an arbitrary one and represents the base legendary drop rate. It is ONLY irrelevant when all gear drops have in fact the same intrinsic probability of them being legendaries.
Edited by Elexar#2219 on 1/9/2013 10:30 AM PST
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.
Edited by Shelendil#1520 on 1/9/2013 12:46 PM PST
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Very nice thread!

Another thing that was completely ignored in the green threads is the chance of getting 5 and 6 affix rares. Pretty much everybody, even those who are very selective about the rares they bother to ID, picks up rings, ammys, gloves, 1H'ers above a certain ilvl, maybe some pants and bracers. I don't know what the base chance to drop a 6 affix rare is, but once you get up into that 450%+ buffed MF territory, the number of 5 and 6 affix rares you find starts being a really significant percentage of your total rares.

Yea, legends/sets are BIS most of the time but you can find sick rares in those categories. My highest sale ever was a rare ring. Why? Because it had 6CC some CD int, vit, int/vit, and res all. Take away 2 of those and it ain't selling very high.
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No...No they don't. The only thing special about elite gear drops is they are 'floored'. Meaning that certain ones can never be worse than a certain rarity.
My question is this - how do you know that they are only floored (minimum quality guaranteed)? It doesn't square with elite drop research data from diablofans (relevant section 5.4). I am unaware of published trash mob data of this type.

Again, we've been given enough information directly by blizzard that there are ZERO assumptions in this model. We have been told exactly, in no uncertain terms that bonus items work in the fashion he described. We have also been told that the average white mob in the game has a 30% chance to drop an item/gold. This average makes it REALLY easy to make the model he just made.
Look at y, it is defined as total number of gear drops. 0.5x represents 50% of items from elites and the other term 0.5x*(1+4*bonus%) are drops from trash mobs + extra item drops from trash mobs. This is sound. The problem only happens when my only objection - gear slots are not equal - happens to be correct. The number 0.05% being multiplied by y in his third equation is an arbitrary one and represents the base legendary drop rate. It is ONLY irrelevant when all gear drops have in fact the same intrinsic probability of them being legendaries.


There is nothing in the current data to indicate that the base drop rate is unequal. However, even if elites had a base legendary drop rate twice that of white mobs, bonus items are still the most significant factor.

L/L0 = [(1+MF/100)*(2*z + y)]/[(1+MF0/100)*(2*z +y0)
L is the expectation of legendaries
MF is magic find
z is the number of items from elites
y is the number of items from whites

This gives MP10 a 356% gain in drops rather than 458%, and decreases the optimal monster power for a solo wizard from MP9 to MP8. The result is a small change even when doubling the likelihood that elites drop legendaries.
Edited by Shelendil#1520 on 1/9/2013 1:24 PM PST
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Are you using a specific route when you farm to generate these results? Maybe i missed it
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01/09/2013 03:46 PMPosted by Vibe
Are you using a specific route when you farm to generate these results? Maybe i missed it


No specific route. Most routes will be somewhere between a 40/60 and 60/40 split for gear from elites/whites on MP0. I used 50/50 for simplicity.
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I guess im not understanding how to figure out if my run times fall under the time limits on the spreadsheet for most efficient monster power without knowing which areas were completed

when you say 15min mp0 run are you talking a standard alkiezer run or what zones exactly?
Edited by Vibe#1320 on 1/9/2013 6:21 PM PST
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AHA!

Now we're actually getting somewhere.

I've adjusted the formula based on your new "insight" into the system.

The formula is now this.

1 - [ ( 1 - ( Chance to Get an Item * ( 1 + Total Magic Find ) ) ) ^ ( Number of Items Rolled * ( 1 + ( 3 * Bonus Item Chance ) ) ) ]

Note that I only have to account for 3 times as many items as the bonus item chance since I have already accounted for it from gear.

30,000 DPS
http://i.imgur.com/RmmbN.png
http://i.imgur.com/noAPY.png

100,000 DPS
http://i.imgur.com/p4VxJ.png
http://i.imgur.com/pyBt6.png

300,000 DPS
http://i.imgur.com/45PCy.png
http://i.imgur.com/eGQ6F.png

600,000 DPS
http://i.imgur.com/EeH8C.png
http://i.imgur.com/NTdCK.png

No where does MP10 ever become the most efficient way to farm.

Though, it does broaden the curve a little bit more. I'll give you that.

Congratulations on being the first person to actually suggest a change to the formula though instead of just saying "You're wrong"
________________________________________________
MVP's are not employees of Blizzard Entertainment. We are players just like you.
Nothing I say is Official word from Blizzard, everything is of my own conjecture.
My current Hero : http://us.battle.net/d3/en/profile/Drothvader-1215/hero/29603251
A Basic D3 Mechanics Compendium : http://drothvader.org/d3guide/mechanics/
Edited by Drothvader#1215 on 1/9/2013 6:27 PM PST
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OP: I really like your approach - figuring dps doesn't make much sense. Instead, you should look at timed runs at different MP levels and see which is giving you the best clear speed for that MP. If you can go up MP with less than a 13% clear time penalty, you should.

I made a similar spreadsheet.

Take a gander:
https://docs.google.com/spreadsheet/ccc?key=0AuXj3WzKy9FRdGktUnc4a3RVQnNGZ1hZU1U5a3NOQnc#gid=2
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I guess im not understanding how to figure out if my run times fall under the time limits on the spreadsheet for most efficient monster power without knowing which areas were completed

when you say 15min mp0 run are you talking a standard alkiezer run or what zones exactly?


Choose any route you like on MP0 and time it. Do the same route on MP5.

If your MP5 time divided by your MP0 time is less than the ratio of 32.59/15, then it is more efficient for loot.*

You can do this for any MP, substituting in the appropriate time limit.

*Provided the 50/50 ratio of loot from elites versus whites holds true for your chosen route.
Edited by Shelendil#1520 on 1/9/2013 9:28 PM PST
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OP: I really like your approach - figuring dps doesn't make much sense. Instead, you should look at timed runs at different MP levels and see which is giving you the best clear speed for that MP. If you can go up MP with less than a 13% clear time penalty, you should.

I made a similar spreadsheet.

Take a gander:
https://docs.google.com/spreadsheet/ccc?key=0AuXj3WzKy9FRdGktUnc4a3RVQnNGZ1hZU1U5a3NOQnc#gid=2


I agree with your time limits. The higher ratio of loot from elites favors lower MP, giving more restrictive time limits. I'm not sure I agree with your method of determining the DPS required, but I can't say I have a better idea.
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