I just have to interject that it is completely asinine that "Adds 10% to fire damage" does not take the fire damage you and amplify it by 10%. Clearly it should be reading 10% as fire damage.
For players in Inferno participating in the Infernal Machine event (we’ll provide more info on this event soon), Monster Power will also increase the drop chance for Keywarden Keys and Demonic Organ Pieces by 10% for each MP level, all the way up to 100% at MP 10.
Once you stop putting a limit on the number of rings to craft, the calculation simplifies a lot. It's already clear that you need 30/MP key runs on average to craft one machine. On average you need 30/MP machines to gather three ring mats. Now they might not be the correct three mats, but over time they should average out. So it's just
30/MP * 30/MP = 900/MP^2 runs for one ring
Yes, key runs. Will edit to fix.
That formula is nearly right but I feel like it's a bit too disconnected from reality because no one is going to want infinite keys, and the difference between infinite and 10 and 1 is pretty large.
Do you basically start with gathering 9 keys, 3 of each, then opening 3 portals?
Eh, not exactly. Basically, I had it determine how many machines you would need, and then it simulates finding a set of keys for each machine. The result is the same except for the case where you showed up with 3 machines on your last run and only ended up needing 1 or 2 of them (so small effect, but I could probably refine code to correct that).
I changed to code to do this properly. OP updated.
I think it could be useful to add the expected numbers of keys per ring, for many rings. That is simply 3*10/MP machines per ring, and 3*10/MP runs per machine.
Divide the first number by 4 for a full party.
After some runs at MP 1, the 10%/MP-level assumption looks more reasonable again. However, the size of the dataset is poor, just 33 key runs, 7 plan runs plus 19 organ runs.
For multiple rings, the key runs per ring is diminished. The reason is that... well, say you try to get a ring and you get the organs from portal 1 and 2 but not from 3. Next time, let's say your first portal is 1 again. It's not wasted if you wanted 2 rings instead of 1, because you wanted that portal again anyway. The difference not huge. If you wanted, say, 10 rings, here are the results:
Monster Power: 1
Rings Wanted: 10
Average Machines: 343.3471
Average Machines per Ring: 34.33471
Median Machines: 339
Median Machines per Ring: 33.9
Average Keys: 10307.5062
Average Keys per Ring: 1030.75062
Median Keys: 10163
Median Keys per Ring: 1016.3
Monster Power: 2
Rings Wanted: 10
Average Machines: 170.022
Average Machines per Ring: 17.0022
Median Machines: 167
Median Machines per Ring: 16.7
Average Keys: 2550.5963
Average Keys per Ring: 255.05963000000003
Median Keys: 2513
Median Keys per Ring: 251.3
Monster Power: 3
Rings Wanted: 10
Average Machines: 112.7076
Average Machines per Ring: 11.27076
Median Machines: 112
Median Machines per Ring: 11.2
Average Keys: 1127.5897
Average Keys per Ring: 112.75897
Median Keys: 1114
Median Keys per Ring: 111.4
Monster Power: 4
Rings Wanted: 10
Average Machines: 83.9712
Average Machines per Ring: 8.39712
Median Machines: 83
Median Machines per Ring: 8.3
Average Keys: 629.7703
Average Keys per Ring: 62.97703
Median Keys: 620
Median Keys per Ring: 62.0
Monster Power: 5
Rings Wanted: 10
Average Machines: 66.3255
Average Machines per Ring: 6.63255
Median Machines: 65
Median Machines per Ring: 6.5
Average Keys: 398.0607
Average Keys per Ring: 39.80607
Median Keys: 393
Median Keys per Ring: 39.3
Monster Power: 6
Rings Wanted: 10
Average Machines: 54.7384
Average Machines per Ring: 5.47384
Median Machines: 54
Median Machines per Ring: 5.4
Average Keys: 273.6837
Average Keys per Ring: 27.36837
Median Keys: 271
Median Keys per Ring: 27.1
Monster Power: 7
Rings Wanted: 10
Average Machines: 46.3121
Average Machines per Ring: 4.63121
Median Machines: 46
Median Machines per Ring: 4.6
Average Keys: 198.4168
Average Keys per Ring: 19.84168
Median Keys: 196
Median Keys per Ring: 19.6
Monster Power: 8
Rings Wanted: 10
Average Machines: 39.9846
Average Machines per Ring: 3.99846
Median Machines: 39
Median Machines per Ring: 3.9
Average Keys: 149.9349
Average Keys per Ring: 14.99349
Median Keys: 148
Median Keys per Ring: 14.8
Monster Power: 9
Rings Wanted: 10
Average Machines: 34.8634
Average Machines per Ring: 3.4863399999999998
Median Machines: 35
Median Machines per Ring: 3.5
Average Keys: 116.1321
Average Keys per Ring: 11.613209999999999
Median Keys: 115
Median Keys per Ring: 11.5
Monster Power: 10
Rings Wanted: 10
Average Machines: 30.0
Average Machines per Ring: 3.0
Median Machines: 30
Median Machines per Ring: 3.0
Average Keys: 90.0
Average Keys per Ring: 9.0
Median Keys: 90
Median Keys per Ring: 9.0
Yeah, that's a monte carlo simulation, which is what I expected. I'm far too rusty with my probability theory to try outright calculating any final probabilities, so this method should work fine.
Do you basically start with gathering 9 keys, 3 of each, then opening 3 portals?
Eh, not exactly. Basically, I had it determine how many machines you would need, and then it simulates finding a set of keys for each machine. The result is the same except for the case where you showed up with 3 machines on your last run and only ended up needing 1 or 2 of them (so small effect, but I could probably refine code to correct that).
After that if you're still missing 3 organs, repeat until missing 2 or less, then open portals 1, 2, or 3 at a time? Also, do you track excess organs obtained while hunting for the last one?
Yeah, it will open 3 portals in one game but only open portals after the first if the organ from that portal is needed for the targeted number of rings. I do not track excess organs, but you can get a sense of their benefit by telling the program you want to find 10 rings instead of just 1.
I originally intended to use a formula to compute this. That can be easily done if you only open one portal per game. It makes more sense to make decisions along the way based on how many of the unopened portals in your game are still valuable to you, though, and that made the math more complicated than I could tackle.
Basically, what the program does is say two things.
In a subfunction, it says goes and finds three keys for a machine. For each key, it creates a random decimal number (0-1). If that number less than the chance to find a key, then the key is successfully gathered. If it's not less, then you add one to the attempt count and try again. For example, if your MP is 3, you'd have to roll 0.3 or less to be a success.
The main function basically does the same thing with organs. The difference is that it also assigns an order for each game for the portals to open. (Portal 1, then 2, then 3; or portal 3, then 1, then 2, etc). The player will only bother opening the second and third portals if he needs organs from them. That reduces the total number of machines needed... and also make the math more involved. Simulation was pretty simple.
It basically runs this "ring hunt" for 10,000 players at each MP, logging how many keys and organs it took to get the ring. Then it just summarizes.
I am NOT a programmer, but I took a stab at writing a bit of code to simulate the key and organ hunt based on MP level. The current theory is that the chance of finding a key or organ is MP*0.1. That is, 10% at MP1, 20% at MP2... up to 100% at MP10. We don't know that this is exactly true yet. All that has been stated by blues is that MP1 is >0% and MP10=100%. Seems logical but may possible be incorrect.
The other thing to note is that you can open three portals in a single game and they are guaranteed to be different. So, if you need portal 2 and 3 and you open portal 1, you have a 100% chance of getting a portal you need by opening a second portal in that same game. The optimal strategy, then, is to always have 3 machines with you in case the portal you need is not the first one to open (since subsequent portals have a better chance of matching your need than the first).
Code is at the bottom (python 3.3)
1 Ring Wanted:
Rings Wanted: 1
Monster Power: 1
Average Machines: 42.6
Average Machines per Ring: 42.6
Median Machines: 38
Median Machines per Ring: 38.0
Average Key Runs: 1307.1
Average Key Runs per Machine: 30.7
Average Key Runs per Ring: 1307.1
Median Key Runs: 1158
Median Key Runs per Machine: 30.5
Median Key Runs per Ring: 1158.0
Monster Power: 2
Average Machines: 20.9
Average Machines per Ring: 20.9
Median Machines: 19
Median Machines per Ring: 19.0
Average Key Runs: 327.7
Average Key Runs per Machine: 15.7
Average Key Runs per Ring: 327.7
Median Key Runs: 293
Median Key Runs per Machine: 15.4
Median Key Runs per Ring: 293.0
Monster Power: 3
Average Machines: 13.7
Average Machines per Ring: 13.7
Median Machines: 12
Median Machines per Ring: 12.0
Average Key Runs: 145.7
Average Key Runs per Machine: 10.6
Average Key Runs per Ring: 145.7
Median Key Runs: 131
Median Key Runs per Machine: 10.9
Median Key Runs per Ring: 131.0
Monster Power: 4
Average Machines: 10.0
Average Machines per Ring: 10.0
Median Machines: 9
Median Machines per Ring: 9.0
Average Key Runs: 81.5
Average Key Runs per Machine: 8.1
Average Key Runs per Ring: 81.5
Median Key Runs: 74
Median Key Runs per Machine: 8.2
Median Key Runs per Ring: 74.0
Monster Power: 5
Average Machines: 7.8
Average Machines per Ring: 7.8
Median Machines: 7
Median Machines per Ring: 7.0
Average Key Runs: 51.4
Average Key Runs per Machine: 6.6
Average Key Runs per Ring: 51.4
Median Key Runs: 47
Median Key Runs per Machine: 6.7
Median Key Runs per Ring: 47.0
Monster Power: 6
Average Machines: 6.3
Average Machines per Ring: 6.3
Median Machines: 6
Median Machines per Ring: 6.0
Average Key Runs: 34.9
Average Key Runs per Machine: 5.5
Average Key Runs per Ring: 34.9
Median Key Runs: 32
Median Key Runs per Machine: 5.3
Median Key Runs per Ring: 32.0
Monster Power: 7
Average Machines: 5.2
Average Machines per Ring: 5.2
Median Machines: 5
Median Machines per Ring: 5.0
Average Key Runs: 24.8
Average Key Runs per Machine: 4.8
Average Key Runs per Ring: 24.8
Median Key Runs: 24
Median Key Runs per Machine: 4.8
Median Key Runs per Ring: 24.0
Monster Power: 8
Average Machines: 4.3
Average Machines per Ring: 4.3
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 17.9
Average Key Runs per Machine: 4.1
Average Key Runs per Ring: 17.9
Median Key Runs: 15
Median Key Runs per Machine: 5.0
Median Key Runs per Ring: 15.0
Monster Power: 9
Average Machines: 3.6
Average Machines per Ring: 3.6
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 13.0
Average Key Runs per Machine: 3.6
Average Key Runs per Ring: 13.0
Median Key Runs: 10
Median Key Runs per Machine: 3.3
Median Key Runs per Ring: 10.0
Monster Power: 10
Average Machines: 3.0
Average Machines per Ring: 3.0
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 9.0
Average Key Runs per Machine: 3.0
Average Key Runs per Ring: 9.0
Median Key Runs: 9
Median Key Runs per Machine: 3.0
Median Key Runs per Ring: 9.0
10 Rings Wanted:
Rings Wanted: 10
Monster Power: 1
Average Machines: 342.8
Average Machines per Ring: 34.3
Median Machines: 338
Median Machines per Ring: 33.8
Average Key Runs: 10312.9
Average Key Runs per Machine: 30.1
Average Key Runs per Ring: 1031.3
Median Key Runs: 10164
Median Key Runs per Machine: 30.1
Median Key Runs per Ring: 1016.4
Monster Power: 2
Average Machines: 170.2
Average Machines per Ring: 17.0
Median Machines: 168
Median Machines per Ring: 16.8
Average Key Runs: 2567.1
Average Key Runs per Machine: 15.1
Average Key Runs per Ring: 256.7
Median Key Runs: 2532
Median Key Runs per Machine: 15.1
Median Key Runs per Ring: 253.2
Monster Power: 3
Average Machines: 112.6
Average Machines per Ring: 11.3
Median Machines: 111
Median Machines per Ring: 11.1
Average Key Runs: 1135.8
Average Key Runs per Machine: 10.1
Average Key Runs per Ring: 113.6
Median Key Runs: 1120
Median Key Runs per Machine: 10.1
Median Key Runs per Ring: 112.0
Monster Power: 4
Average Machines: 83.8
Average Machines per Ring: 8.4
Median Machines: 83
Median Machines per Ring: 8.3
Average Key Runs: 635.5
Average Key Runs per Machine: 7.6
Average Key Runs per Ring: 63.6
Median Key Runs: 627
Median Key Runs per Machine: 7.6
Median Key Runs per Ring: 62.7
Monster Power: 5
Average Machines: 66.4
Average Machines per Ring: 6.6
Median Machines: 66
Median Machines per Ring: 6.6
Average Key Runs: 403.8
Average Key Runs per Machine: 6.1
Average Key Runs per Ring: 40.4
Median Key Runs: 399
Median Key Runs per Machine: 6.0
Median Key Runs per Ring: 39.9
Monster Power: 6
Average Machines: 54.7
Average Machines per Ring: 5.5
Median Machines: 54
Median Machines per Ring: 5.4
Average Key Runs: 278.3
Average Key Runs per Machine: 5.1
Average Key Runs per Ring: 27.8
Median Key Runs: 275
Median Key Runs per Machine: 5.1
Median Key Runs per Ring: 27.5
Monster Power: 7
Average Machines: 46.4
Average Machines per Ring: 4.6
Median Machines: 46
Median Machines per Ring: 4.6
Average Key Runs: 202.6
Average Key Runs per Machine: 4.4
Average Key Runs per Ring: 20.3
Median Key Runs: 201
Median Key Runs per Machine: 4.4
Median Key Runs per Ring: 20.1
Monster Power: 8
Average Machines: 40.0
Average Machines per Ring: 4.0
Median Machines: 39
Median Machines per Ring: 3.9
Average Key Runs: 153.1
Average Key Runs per Machine: 3.8
Average Key Runs per Ring: 15.3
Median Key Runs: 152
Median Key Runs per Machine: 3.9
Median Key Runs per Ring: 15.2
Monster Power: 9
Average Machines: 34.9
Average Machines per Ring: 3.5
Median Machines: 35
Median Machines per Ring: 3.5
Average Key Runs: 118.7
Average Key Runs per Machine: 3.4
Average Key Runs per Ring: 11.9
Median Key Runs: 118
Median Key Runs per Machine: 3.4
Median Key Runs per Ring: 11.8
Monster Power: 10
Average Machines: 30.0
Average Machines per Ring: 3.0
Median Machines: 30
Median Machines per Ring: 3.0
Average Key Runs: 90.0
Average Key Runs per Machine: 3.0
Average Key Runs per Ring: 9.0
Median Key Runs: 90
Median Key Runs per Machine: 3.0
Median Key Runs per Ring: 9.0
Note that this is solo. If there are 3 of you, each can build up the mats for one machine and you can each open a portal and use each others', so the actual number of runs needed is the result above divided by cooperating players.
Code:
import random[/size]
portals = [0,1,2]
Iterations = 100000
rings_wanted = 1
def Keys_for_machine(MonsterPower):
keys = [0,0,0]
keytrials = 0
while keys[0] == 0:
keytrials = keytrials + 1
trial = random.random()
if trial <= MonsterPower*0.1:
keys[0] = 1
while keys[1] == 0:
keytrials = keytrials + 1
trial = random.random()
if trial <= MonsterPower*0.1:
keys[1] = 1
while keys[2] == 0:
keytrials = keytrials + 1
trial = random.random()
if trial <= MonsterPower*0.1:
keys[2] = 1
return keytrials
print("Rings Wanted:",rings_wanted)
for MonsterPower in [1,2,3,4,5,6,7,8,9,10]:
Results_keys=[]
Results_machines=[]
while len(Results_keys)<Iterations:
machines_used = 0
keys_used = 0
organ = [0,0,0]
while organ[0]<rings_wanted or organ[1]<rings_wanted or organ[2]<rings_wanted:
skipped = 2
keys_used = keys_used + Keys_for_machine(MonsterPower)
random.shuffle(portals)
machines_used = machines_used + 1
trial = random.random()
if trial <= MonsterPower*0.1:
organ[portals[0]] = organ[portals[0]]+1
if organ[portals[1]]<rings_wanted or organ[portals[2]]<rings_wanted:
skipped = 1
keys_used = keys_used + Keys_for_machine(MonsterPower)
machines_used = machines_used + 1
trial = random.random()
if trial <= MonsterPower*0.1:
organ[portals[1]] = organ[portals[1]]+1
if organ[portals[2]] < rings_wanted:
skipped = 0
keys_used = keys_used + Keys_for_machine(MonsterPower)
machines_used = machines_used + 1
trial = random.random()
if trial <= MonsterPower*0.1:
organ[portals[2]] = organ[portals[2]]+1
Results_keys.append(keys_used+skipped*Keys_for_machine(MonsterPower))
Results_machines.append(machines_used)
print("\n")
print("Monster Power:",MonsterPower)
average_machines = 0
for i in Results_machines:
average_machines = average_machines + i
average_machines = average_machines / Iterations
print("Average Machines:", round(average_machines,1))
print("Average Machines per Ring:",round(average_machines/rings_wanted,1))
Results_machines.sort()
print("Median Machines:",Results_machines[int(Iterations/2)])
print("Median Machines per Ring:",round(Results_machines[int(Iterations/2)]/rings_wanted,1))
average_keys = 0
for i in Results_keys:
average_keys = average_keys + i
average_keys = average_keys / Iterations
print("Average Key Runs:", round(average_keys,1))
print("Average Key Runs per Machine:",round(average_keys/average_machines,1))
print("Average Key Runs per Ring:",round(average_keys/rings_wanted,1))
Results_keys.sort()
print("Median Keys:",Results_keys[int(Iterations/2)])
print("Median Keys per Machine:",round(Results_keys[int(Iterations/2)]/Results_machines[int(Iterations/2)],1))
print("Median Keys per Ring:",round(Results_keys[int(Iterations/2)]/rings_wanted,1))
Thanks! I still need to aggregate what info we have. I got side tracked and haven't had a chance to do this yet. I was hoping for several thousand data points and it looks like we'll end up with just a few hundred, so the results won't be as robust as I was hoping.
hm ok, just did some crafting (~350 4-prop bracers) and now i'm filling out this spreadsheet..is there any other (quicker) way to translate the stats of the items into the sheet?
Not that I know of, unfortunately There's been some work on OCR, but I don't think it's working yet.
PTR is our zero-cost chance to learn about affixes.
Anything you do there is free since you can't transfer anything back. What I'm wanting is pretty simple. If you're willing, please do the following:
Craft as many of something as possible (rare-quality only please)
-- preferably the same thing that someone else is crafting. Post your intention here and let's collaborate
-- less affixes is better because it will be more clear (4-prop is best)
Take a screenshot of every item you craft and put all of its stats into a big excel sheet.
Link the sheet here.
I'll be starting this tonight. I am going to start with 4-prop bracers. Bracers are unique because other armor types get the chance to roll the primary rank of at least 1 primary stat (belts can roll primary strength, pants can roll primary vit, etc). I'm going to stick with Bracers for now so that the whole primary vs secondary thing doesn't muddy the water, but we will probably want some datapoints on things that DO get a primary primary (sorry, they share the same name) so we can see how that affects it.
I will aggregate all the data and see what conclusions can be drawn.
I recommend keeping all the screenshots and typing the stats in later because it makes it easier to log them and if there is a a suspicious entry later we can go back and confirm (which means it will be very useful to write down which screenshot it is as you log that item).
Any questions?
I think I have enough mats for ~600 bracers, so I'll be doing that first. And then disenchanting them and doing what I can with the remainder. Will anyone else do the same with me?
Yep. I've set up the spreadsheet now to differentiate between 1 affix, 2 affix, and rare. We can later compare the "rare" to 6 affix and see if there's a difference, and we can compare 1 and 2 affix to themselves and to the rares. Unfortunately, the more we break up the data, the more datapoints we need, but I have a couple other people contributing and hopefully that number will continue to grow. I get about 20-30 on short runs, so it doesn't take long for a handful of people to come up with a couple thousand drops.
Unfortunately, as I discovered from the run I just did, you really don't get very many 1-affix magic drops once you've got some NV stacks up. I just got eight blues with single resist - all of them 2-affix. Hardly saw any 1-affix items amongst all the other blues, either.
Yeah, that's gonna take a while. I'm finding same thing.
Yep. I've set up the spreadsheet now to differentiate between 1 affix, 2 affix, and rare. We can later compare the "rare" to 6 affix and see if there's a difference, and we can compare 1 and 2 affix to themselves and to the rares. Unfortunately, the more we break up the data, the more datapoints we need, but I have a couple other people contributing and hopefully that number will continue to grow. I get about 20-30 on short runs, so it doesn't take long for a handful of people to come up with a couple thousand drops.
Damn.. interesting stuff. Have you seen anything about magic vs. rare affix quality discussed before?
The only thing I recall is that guy who said that magic items always have one max-rank affix - which is what prompted me to mark magic & rare separately on your spreadsheet, but which was swiftly disproved by a screenshot.
A worrying possibility is, of course, that 4-affix, 5-affix and 6-affix rares have different calculations. e.g. it could be something like the first affix generated has full chances, then each one after that is rolled from a worse table or penalized roll?
I believe there was something like that for legendaries, but I never heard anything about that for rare or magic items. I think the way it may be working is that the top rank has x% to be rolled. Failing that, all other ranks have equal chance. I think x% may be 60% for magic gear and 40% for rare. Will have to get more data, though.
that's a nice result. In the crafted gear, can you see whether items can have 5 or 6 max rank affixes? It might be difficult because of base stats adding up in a weird way, but maybe you can find something with single res + all res + life regen + ...
The crafted gear was all 6 affix.... perhaps I should also differentiate between 1-affix and 2-affix magic items.
Bah, forgot to change thread title. I started this thinking that crafted gear was inferior to looted. Now I'm just thinking that magic gear has a higher chance of good rolls than rare.
Ok, guys. I need some brainpower here.
Background
I've been wondering about how the game decides to roll affixes. It's a pretty complicated pursuit do the vast qty of affixes out there, so I wanted to start small and build up. I decided the easiest place to start would be single resists because they are very common. There were three questions I originally asked:
1 - Is the determination of which rank of affix to give completely random or is it skewed? For example, if the item is capable of rolling rank 52, 58, 60, 61, and 62, do each appear the same % or no?.
2 - Once a rank is determined, is the actual roll inside that min and max of that rank rolled randomly or is it skewed.
3 - Is the determination of the rank related to Act at all.
We started a project to log every piece of gear that has single resist on it. Basically, if you found any piece of gear that had a single resist, you'd just put the ilvl and resist amount into a spreadhsheet and we'd keep track of which ranks had been selected.
Looted: https://docs.google....FXWmN5YkE#gid=1
Pulling ilvl62-only pieces from the gear we looted and screen-capped:
Samples: 216
Samples that rolled Max Rank: 130 (60.2%)
Range with 95% confidence: 54% - 67%
Crafted:
Samples: 780
Samples that rolled Max Rank: 306 (39.2%)
Ranged with 95% confidence: 36% - 43%
So... I thought at first that this was indicating that crafted gear was not as good as looted gear. However, I then remembered that one of our contributors had been flagging rare drops vs magic. I went back and looked at just his rare drops, and THEY were ~40%, too. We're going to restart the research, tracking rare vs magic, but I feel strongly that Blizz gives magic items a better chance to get high rolls than rare items.
If anyone would like to help, I'd appreciate the additional datapoints.
I've setup a new sheet to track it, but ignore the charts for now because I haven't finished fixing them yet.
http://us.battle.net/d3/en/blog/7540457/Monster_Power_More_Guts_More_Glory-10_11_2012
Yes, key runs. Will edit to fix.
That formula is nearly right but I feel like it's a bit too disconnected from reality because no one is going to want infinite keys, and the difference between infinite and 10 and 1 is pretty large.
For multiple rings, the key runs per ring is diminished. The reason is that... well, say you try to get a ring and you get the organs from portal 1 and 2 but not from 3. Next time, let's say your first portal is 1 again. It's not wasted if you wanted 2 rings instead of 1, because you wanted that portal again anyway. The difference not huge. If you wanted, say, 10 rings, here are the results:
Ok, cool. Have not heard that term before.
Eh, not exactly. Basically, I had it determine how many machines you would need, and then it simulates finding a set of keys for each machine. The result is the same except for the case where you showed up with 3 machines on your last run and only ended up needing 1 or 2 of them (so small effect, but I could probably refine code to correct that).
Yeah, it will open 3 portals in one game but only open portals after the first if the organ from that portal is needed for the targeted number of rings. I do not track excess organs, but you can get a sense of their benefit by telling the program you want to find 10 rings instead of just 1.
Basically, what the program does is say two things.
In a subfunction, it says goes and finds three keys for a machine. For each key, it creates a random decimal number (0-1). If that number less than the chance to find a key, then the key is successfully gathered. If it's not less, then you add one to the attempt count and try again. For example, if your MP is 3, you'd have to roll 0.3 or less to be a success.
The main function basically does the same thing with organs. The difference is that it also assigns an order for each game for the portals to open. (Portal 1, then 2, then 3; or portal 3, then 1, then 2, etc). The player will only bother opening the second and third portals if he needs organs from them. That reduces the total number of machines needed... and also make the math more involved. Simulation was pretty simple.
It basically runs this "ring hunt" for 10,000 players at each MP, logging how many keys and organs it took to get the ring. Then it just summarizes.
The other thing to note is that you can open three portals in a single game and they are guaranteed to be different. So, if you need portal 2 and 3 and you open portal 1, you have a 100% chance of getting a portal you need by opening a second portal in that same game. The optimal strategy, then, is to always have 3 machines with you in case the portal you need is not the first one to open (since subsequent portals have a better chance of matching your need than the first).
Code is at the bottom (python 3.3)
1 Ring Wanted:
Rings Wanted: 1
Monster Power: 1
Average Machines: 42.6
Average Machines per Ring: 42.6
Median Machines: 38
Median Machines per Ring: 38.0
Average Key Runs: 1307.1
Average Key Runs per Machine: 30.7
Average Key Runs per Ring: 1307.1
Median Key Runs: 1158
Median Key Runs per Machine: 30.5
Median Key Runs per Ring: 1158.0
Monster Power: 2
Average Machines: 20.9
Average Machines per Ring: 20.9
Median Machines: 19
Median Machines per Ring: 19.0
Average Key Runs: 327.7
Average Key Runs per Machine: 15.7
Average Key Runs per Ring: 327.7
Median Key Runs: 293
Median Key Runs per Machine: 15.4
Median Key Runs per Ring: 293.0
Monster Power: 3
Average Machines: 13.7
Average Machines per Ring: 13.7
Median Machines: 12
Median Machines per Ring: 12.0
Average Key Runs: 145.7
Average Key Runs per Machine: 10.6
Average Key Runs per Ring: 145.7
Median Key Runs: 131
Median Key Runs per Machine: 10.9
Median Key Runs per Ring: 131.0
Monster Power: 4
Average Machines: 10.0
Average Machines per Ring: 10.0
Median Machines: 9
Median Machines per Ring: 9.0
Average Key Runs: 81.5
Average Key Runs per Machine: 8.1
Average Key Runs per Ring: 81.5
Median Key Runs: 74
Median Key Runs per Machine: 8.2
Median Key Runs per Ring: 74.0
Monster Power: 5
Average Machines: 7.8
Average Machines per Ring: 7.8
Median Machines: 7
Median Machines per Ring: 7.0
Average Key Runs: 51.4
Average Key Runs per Machine: 6.6
Average Key Runs per Ring: 51.4
Median Key Runs: 47
Median Key Runs per Machine: 6.7
Median Key Runs per Ring: 47.0
Monster Power: 6
Average Machines: 6.3
Average Machines per Ring: 6.3
Median Machines: 6
Median Machines per Ring: 6.0
Average Key Runs: 34.9
Average Key Runs per Machine: 5.5
Average Key Runs per Ring: 34.9
Median Key Runs: 32
Median Key Runs per Machine: 5.3
Median Key Runs per Ring: 32.0
Monster Power: 7
Average Machines: 5.2
Average Machines per Ring: 5.2
Median Machines: 5
Median Machines per Ring: 5.0
Average Key Runs: 24.8
Average Key Runs per Machine: 4.8
Average Key Runs per Ring: 24.8
Median Key Runs: 24
Median Key Runs per Machine: 4.8
Median Key Runs per Ring: 24.0
Monster Power: 8
Average Machines: 4.3
Average Machines per Ring: 4.3
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 17.9
Average Key Runs per Machine: 4.1
Average Key Runs per Ring: 17.9
Median Key Runs: 15
Median Key Runs per Machine: 5.0
Median Key Runs per Ring: 15.0
Monster Power: 9
Average Machines: 3.6
Average Machines per Ring: 3.6
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 13.0
Average Key Runs per Machine: 3.6
Average Key Runs per Ring: 13.0
Median Key Runs: 10
Median Key Runs per Machine: 3.3
Median Key Runs per Ring: 10.0
Monster Power: 10
Average Machines: 3.0
Average Machines per Ring: 3.0
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 9.0
Average Key Runs per Machine: 3.0
Average Key Runs per Ring: 9.0
Median Key Runs: 9
Median Key Runs per Machine: 3.0
Median Key Runs per Ring: 9.0
10 Rings Wanted:
Monster Power: 1
Average Machines: 342.8
Average Machines per Ring: 34.3
Median Machines: 338
Median Machines per Ring: 33.8
Average Key Runs: 10312.9
Average Key Runs per Machine: 30.1
Average Key Runs per Ring: 1031.3
Median Key Runs: 10164
Median Key Runs per Machine: 30.1
Median Key Runs per Ring: 1016.4
Monster Power: 2
Average Machines: 170.2
Average Machines per Ring: 17.0
Median Machines: 168
Median Machines per Ring: 16.8
Average Key Runs: 2567.1
Average Key Runs per Machine: 15.1
Average Key Runs per Ring: 256.7
Median Key Runs: 2532
Median Key Runs per Machine: 15.1
Median Key Runs per Ring: 253.2
Monster Power: 3
Average Machines: 112.6
Average Machines per Ring: 11.3
Median Machines: 111
Median Machines per Ring: 11.1
Average Key Runs: 1135.8
Average Key Runs per Machine: 10.1
Average Key Runs per Ring: 113.6
Median Key Runs: 1120
Median Key Runs per Machine: 10.1
Median Key Runs per Ring: 112.0
Monster Power: 4
Average Machines: 83.8
Average Machines per Ring: 8.4
Median Machines: 83
Median Machines per Ring: 8.3
Average Key Runs: 635.5
Average Key Runs per Machine: 7.6
Average Key Runs per Ring: 63.6
Median Key Runs: 627
Median Key Runs per Machine: 7.6
Median Key Runs per Ring: 62.7
Monster Power: 5
Average Machines: 66.4
Average Machines per Ring: 6.6
Median Machines: 66
Median Machines per Ring: 6.6
Average Key Runs: 403.8
Average Key Runs per Machine: 6.1
Average Key Runs per Ring: 40.4
Median Key Runs: 399
Median Key Runs per Machine: 6.0
Median Key Runs per Ring: 39.9
Monster Power: 6
Average Machines: 54.7
Average Machines per Ring: 5.5
Median Machines: 54
Median Machines per Ring: 5.4
Average Key Runs: 278.3
Average Key Runs per Machine: 5.1
Average Key Runs per Ring: 27.8
Median Key Runs: 275
Median Key Runs per Machine: 5.1
Median Key Runs per Ring: 27.5
Monster Power: 7
Average Machines: 46.4
Average Machines per Ring: 4.6
Median Machines: 46
Median Machines per Ring: 4.6
Average Key Runs: 202.6
Average Key Runs per Machine: 4.4
Average Key Runs per Ring: 20.3
Median Key Runs: 201
Median Key Runs per Machine: 4.4
Median Key Runs per Ring: 20.1
Monster Power: 8
Average Machines: 40.0
Average Machines per Ring: 4.0
Median Machines: 39
Median Machines per Ring: 3.9
Average Key Runs: 153.1
Average Key Runs per Machine: 3.8
Average Key Runs per Ring: 15.3
Median Key Runs: 152
Median Key Runs per Machine: 3.9
Median Key Runs per Ring: 15.2
Monster Power: 9
Average Machines: 34.9
Average Machines per Ring: 3.5
Median Machines: 35
Median Machines per Ring: 3.5
Average Key Runs: 118.7
Average Key Runs per Machine: 3.4
Average Key Runs per Ring: 11.9
Median Key Runs: 118
Median Key Runs per Machine: 3.4
Median Key Runs per Ring: 11.8
Monster Power: 10
Average Machines: 30.0
Average Machines per Ring: 3.0
Median Machines: 30
Median Machines per Ring: 3.0
Average Key Runs: 90.0
Average Key Runs per Machine: 3.0
Average Key Runs per Ring: 9.0
Median Key Runs: 90
Median Key Runs per Machine: 3.0
Median Key Runs per Ring: 9.0
Note that this is solo. If there are 3 of you, each can build up the mats for one machine and you can each open a portal and use each others', so the actual number of runs needed is the result above divided by cooperating players.
Code:
import random[/size] portals = [0,1,2] Iterations = 100000 rings_wanted = 1 def Keys_for_machine(MonsterPower): keys = [0,0,0] keytrials = 0 while keys[0] == 0: keytrials = keytrials + 1 trial = random.random() if trial <= MonsterPower*0.1: keys[0] = 1 while keys[1] == 0: keytrials = keytrials + 1 trial = random.random() if trial <= MonsterPower*0.1: keys[1] = 1 while keys[2] == 0: keytrials = keytrials + 1 trial = random.random() if trial <= MonsterPower*0.1: keys[2] = 1 return keytrials print("Rings Wanted:",rings_wanted) for MonsterPower in [1,2,3,4,5,6,7,8,9,10]: Results_keys=[] Results_machines=[] while len(Results_keys)<Iterations: machines_used = 0 keys_used = 0 organ = [0,0,0] while organ[0]<rings_wanted or organ[1]<rings_wanted or organ[2]<rings_wanted: skipped = 2 keys_used = keys_used + Keys_for_machine(MonsterPower) random.shuffle(portals) machines_used = machines_used + 1 trial = random.random() if trial <= MonsterPower*0.1: organ[portals[0]] = organ[portals[0]]+1 if organ[portals[1]]<rings_wanted or organ[portals[2]]<rings_wanted: skipped = 1 keys_used = keys_used + Keys_for_machine(MonsterPower) machines_used = machines_used + 1 trial = random.random() if trial <= MonsterPower*0.1: organ[portals[1]] = organ[portals[1]]+1 if organ[portals[2]] < rings_wanted: skipped = 0 keys_used = keys_used + Keys_for_machine(MonsterPower) machines_used = machines_used + 1 trial = random.random() if trial <= MonsterPower*0.1: organ[portals[2]] = organ[portals[2]]+1 Results_keys.append(keys_used+skipped*Keys_for_machine(MonsterPower)) Results_machines.append(machines_used) print("\n") print("Monster Power:",MonsterPower) average_machines = 0 for i in Results_machines: average_machines = average_machines + i average_machines = average_machines / Iterations print("Average Machines:", round(average_machines,1)) print("Average Machines per Ring:",round(average_machines/rings_wanted,1)) Results_machines.sort() print("Median Machines:",Results_machines[int(Iterations/2)]) print("Median Machines per Ring:",round(Results_machines[int(Iterations/2)]/rings_wanted,1)) average_keys = 0 for i in Results_keys: average_keys = average_keys + i average_keys = average_keys / Iterations print("Average Key Runs:", round(average_keys,1)) print("Average Key Runs per Machine:",round(average_keys/average_machines,1)) print("Average Key Runs per Ring:",round(average_keys/rings_wanted,1)) Results_keys.sort() print("Median Keys:",Results_keys[int(Iterations/2)]) print("Median Keys per Machine:",round(Results_keys[int(Iterations/2)]/Results_machines[int(Iterations/2)],1)) print("Median Keys per Ring:",round(Results_keys[int(Iterations/2)]/rings_wanted,1))Not that I know of, unfortunately
PTR is our zero-cost chance to learn about affixes.
Anything you do there is free since you can't transfer anything back. What I'm wanting is pretty simple. If you're willing, please do the following:
Craft as many of something as possible (rare-quality only please)
-- preferably the same thing that someone else is crafting. Post your intention here and let's collaborate
-- less affixes is better because it will be more clear (4-prop is best)
Take a screenshot of every item you craft and put all of its stats into a big excel sheet.
Link the sheet here.
I'll be starting this tonight. I am going to start with 4-prop bracers. Bracers are unique because other armor types get the chance to roll the primary rank of at least 1 primary stat (belts can roll primary strength, pants can roll primary vit, etc). I'm going to stick with Bracers for now so that the whole primary vs secondary thing doesn't muddy the water, but we will probably want some datapoints on things that DO get a primary primary (sorry, they share the same name) so we can see how that affects it.
I will aggregate all the data and see what conclusions can be drawn.
Here's an example of someone who has done this previously with 6-prop belts:
https://docs.google.com/spreadsheet/ccc?key=0AiK4Z3ahtYl8dDd3bDBsendZNUxVQ0x6U18yVDZJdnc#gid=0
I recommend keeping all the screenshots and typing the stats in later because it makes it easier to log them and if there is a a suspicious entry later we can go back and confirm (which means it will be very useful to write down which screenshot it is as you log that item).
Any questions?
I think I have enough mats for ~600 bracers, so I'll be doing that first. And then disenchanting them and doing what I can with the remainder. Will anyone else do the same with me?
Yeah, that's gonna take a while. I'm finding same thing.
What you probably saw was 4 mods only, so one of them must have overlapped (like you got str, vit, and str+vit)
I believe there was something like that for legendaries, but I never heard anything about that for rare or magic items. I think the way it may be working is that the top rank has x% to be rolled. Failing that, all other ranks have equal chance. I think x% may be 60% for magic gear and 40% for rare. Will have to get more data, though.
The crafted gear was all 6 affix.... perhaps I should also differentiate between 1-affix and 2-affix magic items.
Ok, guys. I need some brainpower here.
Background
I've been wondering about how the game decides to roll affixes. It's a pretty complicated pursuit do the vast qty of affixes out there, so I wanted to start small and build up. I decided the easiest place to start would be single resists because they are very common. There were three questions I originally asked:
1 - Is the determination of which rank of affix to give completely random or is it skewed? For example, if the item is capable of rolling rank 52, 58, 60, 61, and 62, do each appear the same % or no?.
2 - Once a rank is determined, is the actual roll inside that min and max of that rank rolled randomly or is it skewed.
3 - Is the determination of the rank related to Act at all.
We started a project to log every piece of gear that has single resist on it. Basically, if you found any piece of gear that had a single resist, you'd just put the ilvl and resist amount into a spreadhsheet and we'd keep track of which ranks had been selected.
I also pulled data out of these threads:
http://www.diablofan...ula-to-compare/
http://www.diablofan...-craft-results/
http://www.diablofan...o-compare-them/
I happened to compare the results today.
Results:
Looted:
https://docs.google....FXWmN5YkE#gid=1
Pulling ilvl62-only pieces from the gear we looted and screen-capped:
Samples: 216
Samples that rolled Max Rank: 130 (60.2%)
Range with 95% confidence: 54% - 67%
Crafted:
Samples: 780
Samples that rolled Max Rank: 306 (39.2%)
Ranged with 95% confidence: 36% - 43%
So... I thought at first that this was indicating that crafted gear was not as good as looted gear. However, I then remembered that one of our contributors had been flagging rare drops vs magic. I went back and looked at just his rare drops, and THEY were ~40%, too. We're going to restart the research, tracking rare vs magic, but I feel strongly that Blizz gives magic items a better chance to get high rolls than rare items.
If anyone would like to help, I'd appreciate the additional datapoints.
I've setup a new sheet to track it, but ignore the charts for now because I haven't finished fixing them yet.
https://docs.google....RYUkF4amc#gid=9