Drop Rate Analysis and Treasure Hunter

[Mojo]

I'm aware that there is another Treasure Hunter thread currently on the Advanced Forums, but it's become filled with drama and lacks proper direction. I want nothing to do with it, but I am interested in looking at Treasure Hunter.

The objective of this thread is to discover the way drops function and how Treasure Hunter impacts them. There has always been debate and speculation regarding this subject, as well countless small, independent tests that try and shed some light on it, but none have been completely successful. I believe the reason for this is that they have failed to properly analyze the way that items drop regardless of Treasure Hunter. Most have simply assumed that every item that can drop from a mob has an individual drop rate and that the drop rate was simply increased, depending on the level of Treasure Hunter. However, there are already well known cases where that simply wouldn't be logical. Let's analyze Defending Ring and Pixie Earring, for example. One of them always drops, but never both. It might be logical to say that Treasure Hunter increases the drop rate of the rarer item but, regardless of whether that is the case, it defies the all encompassing model that people have assumed. To further illustrate this point, let's take a look at what we have already.

Note: All data credited to their respective sources.

We'll begin with Enedin's tests.

Spoiler: show

Group 0 - No Treasure Hunter, no THF main or sub.

• Monster killed: Gigantobugard in Misareaux Coast
• Amount killed: 400
• Bugard Skins: 127/400 = 31.75%
• HQ Bug.Skins: 43/400 = 10.75%

Group 1 - Treasure Hunter I, THF sub 15 or higher.

• Monster killed: Gigantobugard in Misareaux Coast
• Amount killed: 500
• Bugard Skins: 246/500 = 49.20%
• HQ Bug.Skins: 78/500 = 15.60%

Group 2 - Treasure Hunter I + Treasure Hunter II, THF main 45 or higher.

• Monster killed: Gigantobugard in Misareaux Coast
• Amount killed: 500
• Bugard Skins: 312/500 = 62.40%
• HQ Bug.Skins: 112/500 = 22.40%

Enedin concluded that each Treasure Hunter trait increased the drop rate of each item by 50%. Although the sample isn't tremendous, it does seem to be a fairly accurate statement in this case. However, he failed to included Treasure Hunter +1 items in his data.

Next are Shulula's tests.

Spoiler: show

Method: (I presented the method in much more detail in my previous posts but here is a quick summary.)
The method I came up with was to find a mob with multiple separate drops and track the number of drops with different TH setups. I wanted something that was Too Weak so that beastman seals wouldn't add extra drops. It also needed to be plentiful and not heavily camped (if at all). It should also have multiple spawns in a small area and hopefully drop something I could sell.

My targets were bees near Rose Garden spawn point. That way I could also camp an NM while I was working on this. I knew that those bees had four drops and you couldn't get a double drop of the same item. I gave each drop a code (0001 for Beehive Chips, 0010 for Honey etc...) so that I could track the number of items dropped. Code 1111 would mean that all 4 items dropped from one mob.

Data:


This was my baseline without any Treasure Hunter. As you can see, the most common result is for nothing to drop from the bee. A little more than a 1/3 of the time you get one drop and very rarely do you see 2, 3 or 4 items from one mob.



When you use THF as a subjob, you see the chance that nothing drops from a mob go from 63% to 49% and an increase in the chance at a double drop.



Using THF as your main job really improves your drop rate. The No Drop percentage is almost halved (63% to 33%) and the chance at a double drop goes from 1% to 10%. The total number of drops increases just by the fact that you have a 2/3 chance to get any type of drop from the mob.



Adding one of the items that increases your treasure hunter ability does increase your total drop rate. The No Drop percentage stays about the same as TH2, but the double drop percentage increases quite a bit. This was the only setup where I saw a quadruple drop.



Using both Thief Knife and Assassin's Armlets gives you the maximum Treasure Hunter ability. Again you notice that the No Drop percentage stays at 33%, but the double drop percentage increases again. Getting 3 and 4 drops remains a rarity though.

Analysis:
I have color coded the drop table to show the codes that correspond to No Drop, 1 Drop, 2 Drops, 3 Drops and 4 Drops. This table below contains all the drop values for the different TH setups. I also calculated 2 measurements. The first one is called "Total Drops/Total Kills" and measure the total number of drops per mobs killed. This may go over 100% if you get more than 100 drops over 100 mobs. This would measure total loot output. The second measurement is called "Drop Mob/Total Kills" because I couldn't come up with a good name. It measures the chance that a mob will drop anything at all.





The two important lines in this chart are the blue and the green. The blue, No Drop, line shows that as you go from TH0 to TH2 you reach the minimum No Drop rate of 33%. It seems that no matter how much you TH you add, approximately 1 in 3 bees will not drop anything. So if you reach that limit with TH2, does TH3 and TH4 increase your drop rate?

Luckily the answer is yes through an increase in your double drop rate, the green line. You can see a steady increase in the double drop rate by adding TH3 and TH4 even though you hit the No Drop limit.



This chart shows the total number of drops in blue, and basically the mirror of the No Drop Rate in Red. The chance that a mob will drop an item caps at 66% in this case so the red line flattens out after TH2. The effect of increased double drops causes the total drop line to keep going up even though you've hit that limit.

So what does it mean?

TH0: You get about 40 items per 100 kills
TH1: You get about 60 items per 100 kills. ~ 50% increase over TH0.
TH2: You get about 80 items per 100 kills. ~ 100% increase over TH0 and ~ 33% over TH1.
TH3: You get about 88 items per 100 kills. ~ 120% increase over TH0 and ~ 10% over TH2.
TH4: You get about 95 items per 100 kills. ~ 137% increase over TH0 and ~ 8% over TH3.

I would say that as far as these bees are concerned, each TH+1 item adds +9% to the total drops. Far from the +1% I hear. Of course not all mobs drop as easily or as many items as bees.

Further Testing:
I still have many questions about treasure hunter but it will require quite a bit of testing.

• How does the number of people in a party affect drop rates?
• Do two THFs in one party affect drop rates?
• Does a TH have an effect between parties in an alliance?
• Does dual wielding Thief Knife lower TH effect?
• How does moon phase affect drop rates?
• Do all mobs have a 33% No Drop rate?
• How does TH work for mobs other than these bees?

This data initially seems to follow Enedin's pattern of each Treasure Hunter trait increasing the drop rate by 50%. However, when Treasure Hunter +1 items come into play, it deviates quite a bit. If the drop rate was simply increased by 50%, the overall drop rate of any item would have been around 100% with Treasure Hunter II + 2. It's important to note that the chance of nothing dropping didn't change much between Treasure Hunter II + 0~2, although the total amount of items that dropped did increase. Shulula didn't have a solid conclusion, stating that adding +1 to Treasure Hunter seemed to increase the drop rate by 8%.

Now for divisorthoery's tests.

Spoiler: show

Here was the setup.

Mob Killed: Undisclosed, but all 3,017 mobs killed were the SAME mob in the SAME zone.
Number of times mob was killed: 3,017
Number of kills without Thief's Knife: 1,687
Number of kills with Thief's Knife: 1,330

With Thief's Knife
Drop 1:
---Number of Drops: 279
---Drop Rate: 20.98%
Drop 2:
---Number of Drops: 133
---Drop Rate: 10.00%

Without Thief's Knife
Drop 1:
---Number of Drops: 335
---Drop Rate: 19.86%
Drop 2:
---Number of Drops: 152
---Drop Rate: 9.01%


Along with this, I recorded the exact day and moon phase during every drop, but since the number of divisions of day and moon phase is so high, I don't have enough kills yet to determine a correlation between day / drop rate, and moon / drop rate. Although I can pretty certainly say that Watersday ABSOLUTELY SUCKS for drops. Unless I just had a ton of really bad streaks.

Feel free to make your own conclusions about this, but comparing with other items in the game, I am pretty confident that

Treasure Hunter +x = Drop Rate +x%

is a universal law.

Here are the possible factors that could cause my conclusion to be inaccurate:
1) Weather effects that would sporadically show up in the zone.
2) Kills being too sparsely distributed across the various days and moon phases.
3) Gear being worn, and/or elemental resistances on those gear.
4) Food being eaten (sometimes ate Meat kabob, which increases STR).
5) It's possible that the formula works more like
Treasure Hunter +N = Drop Rate x f(N, Drop Rate)%
In other words, it multiplies the drop rate by a factor which depends on the original drop rate of the monster. like 1%->2%, 10%->11%, 20%->25%, etc. Or just that it works differently for every mob. I still don't think that's the way it works though.


By the way, regarding rams in La Theine Plateau, I've killed them with the knife and i notice no real difference over killing them with Treasure Hunter 2 and no knife. Because of this, I believe that the Job Traits are considerably more powerful than Treasure Hunter +1, and probably function differently.

I agree that more testing needs to be done on a different mob to determine better the effects of Treasure Hunter +1. Hope somebody else will do it, lol

There is a good sample size for this test, although failure to include the name of the mob killed and the items that dropped cripples this greatly. Note that the difference in overall drop numbers between this test and Shulula's test differ. divisortheory concludes that Treasure Hunter +1 simply increases the chance of an item dropping by 1%, although admits more testing should be done.

This is quite a bit of data with several models presented. None are entirely correct as they have a way of refuting one another. divisorytheory states that Treasure Hunter +1 increases drop rates of individual items by 1%. Shulula's data, although limited, opposes this to a staggering degree. Enedin's theory does not hold true when Treasure Hunter +1 items are introduced. Summarily, the chance of every item a mob can drop having an individual drop rate and that Treasure Hunter modifies this is low. However, if the data is assembled together, it can be fitted to a single model that seems to be accurate.

d = drop rate - the chance of a mob dropping any amount of items for that loot pool
b = base drop rate - this is a static number based on the mob
t = this has a value of 0, 1, or 2 and correlates to the Treasure Hunter trait you have
T = this has a value of 0, 1, or 2 and correlates to the number of "Treasure Hunter +1" items you have

d = b(1 + t/2) + T

This is only one part of the model. Although there isn't an overwhelming amount of data to support, I am confident that it's fairly accurate. Every one of the data sets seem to indicate this. The layman's way to explain this is that every mob has a base drop rate for dropping any amount of loot. Treasure Hunter I increases this by 50%, Treasure Hunter II increases it by an additional 50%(for a total of 100% not 125%). Treasure Hunter +1 items add 1% on top of the modified base drop rate.

n = the number of drops that are chosen from the mob's drop table
B = this is some kind of table or matrix
T = this has a value of 0, 1, or 2 and correlates to the number of "Treasure Hunter +1" items you have

n = f(B, T)

Upon first glance, you should probably be left wondering what that even means. To be honest it's kind of a stupid way to write it, but I can't really think of anything better right now. The concept is that the number of drops you received(or even relative rarity) is determined in part by Treasure Hunter + 1 items. The function it seems to follow is very similar to Treasure Hunter job traits. In Shulula's tests, it appeared that there was a base chance of receiving multiple drops and that it was increased by 50% with Treasure Hunter +1 and another 50% with Treasure Hunter +2, although there isn't enough data to completely verify that. After n is determined, the game then checks the drop table (once, twice, however many times n came out to be) to determine which items you get. The drop table can't choose the same item twice, but there are cases where the same item might be on the drop list more than once.

Now, there are a few other things I should say about this model. First off, it's just a model. It only reflects a observation on the current available data. I do think that the concepts are accurate, but it's highly unlikely that the math used is precise(or even explained properly, as in the second part of it). The variables in the equations the game utilizes are likely base 2, although the exact unit of measure is probably the least important aspect of drops and should be the very last object to consider before nailing it all down. The other is that it's only one model. There are obviously other models that drops follow, and this model would be used in tandem with them. Bahamut II, for example, has the following drops.

One of:

• Bahamut's Staff
• Dragon Staff

One of:

• Bahamut's Mask
• Bahamut's Zaghnal
• Bahamut's Hose

Unknown Groupings of:

• Cashmere Cloth
• Cashmere Thread
• Divine Log
• Kunwu Iron
• Kunwu Ore
• Molybdenum Ore
• Siren's Hair
• Wyrm Horn

Given the information available, the first five drops are obviously handled by different models. The crafting items would be covered by the previously explained model. So, all in all, there would be at least three loot pools on Bahamut II. Two of them would be handled in the 'either or model', while the crafting items would be done with one or more of the 'synthesis materials' model. Charydbis can serve as example #2, with the following drops.

• Joyeuse
• Oxblood
• Pearl
• Shall Shell

Joyeuse drops 100% of the, so it's in a different loot pool. The Oxblood, Pearl, and Shall Shell could all be in one loot pool following the synthesis item model.

Now, if you go back and look at divisortheories data, you'll notice that TH+1 theoretically should have increased the total number more than it did if this model was true. However, he failed to include the mob he was fighting and what drops he was recording, so it's impossible to say.

Anyways... the purposing of devising that model was to clarify exactly what a drop model was and how unlikely it is that every item in a mob's loot pool follow individual drop rates. It leaves you with a few questions. How many different drop models are they(Either or, synthesis item, abjuration, etc.)? How are items that aren't included in the synthesis item model affected by Treasure Hunter(Peacock Amulet, Beastman's Seals, etc.)?

Well, I think the first step to solve this is to simply take what we know and start collecting data. The current aim is to kill the following mobs 1000 times with every level of Treasure Hunter(TH0, TH1, TH2, TH2+1, TH2+2) and observe the results.

Bumblebee[West Sarutabaruta (S)]
Carrion Crow[West Sarutabaruta (S)]
Crawler[West Sarutabaruta (S)]
Savanna Dhalmel[West Sarutabaruta (S)]

I choose these mobs for a few reasons. These Crawlers can only drop a single item, so results should be easy interpret. Crows and Bumblebees drop two items, both items on both mobs drop at different rates. Dhalmels drop five items, so if anything can be learned from the other mobs that can be applied to the Dhalmels, it will be a strong indicator of success. They're also all in the same zone, so it's quite convenient.

I will publish all of the information in a spreadsheet that can be viewed online(http://spreadsheets.google.com/pub?k...CuVYD1cgrgD-OA) as it comes in. This is quite an undertaking(20,000 mobs killed), it's not feasible to have one person to do it so any help would be welcomed. If you're interested in helping, you can post your data here or PM it to me. I only want one person to have permission to access the spreadsheet to avoid duplicate entries or vandalism, however unlikely that is.

DirectParse(https://sourceforge.net/projects/directparse) is your best bet for data collection, at least as far as I know. It will record the number of each drop you get as well as the number of times you've killed each mob. This doesn't account for multiple drops from the same mob, so every time you get one you will need to screenshot it or something and review them before you submit your data. You will need to manually update the directparse memlocks to get it to work. There is a file called DvsConf included in the download, just replace whatever is in there with MEMLOC=0x576D58.

Also, if you plan on helping out, please limit your sample sizes to at most 100 per mob. The purpose for this is to avoid any lurking variables. For instance, let's say that full moon increased drop rates by 100%. It's something that could easily be observed in the 100 mob intervals.

Either way, Qwontess and I have already started collecting data. I haven't updated the spreadsheet yet today, but I will when I obtain all of the data. Even if you can't get 100 of each mob in one sample, it's still good data. The focus right now is to finish the crawlers, which we're about 20% of the way done with. Any help is welcome.

[Zhais]

just a nitpick, *divisortheory not divisorthoery.

Just happened to notice it >.>

[kwontess]

My first sets of data from the other thread were (TH2 Crawler):

48/200
16/100
18/100

[richardd]

nice research, mojo

[Toksyuryel]

In sets of 100, these were my crawler drop rates:

15/100 (100% moon)
11/100 (98%)
8/100 (stopped caring to check)
10/100
10/100

EDIT: forgot to mention, these were without any kind of TH

[Mojo]

Good job on the data sets so far. The spreadsheet is up to date now, I'm going out to get some more TH1 data. Also, remember if you see any crows/bees/dhalmels just kill them as well. Two birds with one stone, etc.

[Izzy]

Good info. This is how tests are supposed to be done!

[Mojo]

I've added another 400 or so mobs to the spreadsheet. Once again, please anyone help out if you can spare the time(or try to convince your friends to if you are!) Even killing 100 mobs, posting the results, and then forgetting all about it can go along way.

[kwontess]

TH2, Crawlers:

25/100
17/100
18/100

[Shineko]

I know it is a slight nitpick, but the modifier on Thief's Knife and Assassin's Armlets is to "Treasure Hunter" and not "Treasure Hunter II"
That they are completely seperate job traits is also the source of my annoyance to it being called "TH4"
</derail>

[Necronus]

My Data as posted in the failed thread:


Maze of Shakrami

TH0

Carnivorous Crawler (Killed 342 times)
46 spool of silk thread [Drop Rate: 13.45 %]

Maze Scorpion (Killed 97 times)
26 scorpion claw [Drop Rate: 26.80 %]
10 scorpion shell [Drop Rate: 10.31 %]
18 scorpion stinger [Drop Rate: 18.56 %]

TH1

Carnivorous Crawler (Killed 376 times)
60 spool of silk thread [Drop Rate: 15.96 %]

Maze Scorpion (Killed 93 times)
46 scorpion claw [Drop Rate: 49.46 %]
10 scorpion shell [Drop Rate: 10.75 %]
30 scorpion stinger [Drop Rate: 32.26 %]

[Apelila]

Originally Posted by Shineko

I know it is a slight nitpick, but the modifier on Thief's Knife and Assassin's Armlets is to "Treasure Hunter" and not "Treasure Hunter II"
That they are completely seperate job traits is also the source of my annoyance to it being called "TH4"
</derail>

I thought all higher tier traits replaced their lower ones? For instance you get Clear Mind II not Clear Mind + Clear Mind II.

A better example is Kick Attacks: you get KA II @ 71, and all the equipment for Kick attacks just add's on to them but they only say "Kick Attacks". I say better subjectively since they DO increase your kick rate, but not by a % measurable against the number on the equipment.

An EVEN BETTER example would be Fast cast, and I'm dumb for not realizing it. All "Fast Cast" equipment stacks with the highest level you have. If it stacked with lower levels, the higher tiers of II and III would make spells fly out your ass almost instantly.

[Toksyuryel]

Maybe that's why those abilities are only listed for one tier... treasure hunter has the distinction of both tiers being in your list at the same time. This could be because they are meant to be separate. Or it could just be SE being weirdly lazy on one job for some reason. Experience with the way they do things would suggest the latter, but who knows with them. We can't say for sure what SE names traits internally, the ones that only show up once could all be named the same, and one just replaces the other, so gear which enhances it won't break.

[JigglyJam]

I thought it was that "Treasure Hunter" increased the base drop rates for items while "Treasure Hunter II" threw in an extra roll for another chance at the drops? Was it the other way around? Is this wild speculation I've picked up from somewhere?

[Apelila]

Wait, TH2 is a seperate Job trait? I've never leveled THF past 37 and neither wiki lists them as separate. Thats....definitely different than all the other job traits.

[Severance]

Mojo, stop winning FFXI.

[Wizerd]

Mojo, I fail to understand why you refuse to believe that normal drops are independant of one another.

I like the thread and I think the testing method is great, but when it comes down to it, I doubt SE would have put as much work into the drop system as this entails. The way I see it, there are 2 different ways loot can drop:

1) A given item is independant of any other drop. The item has a base drop rate and is affected in a certain way by Treasure Hunter. Whatever else drops has absolutely no effect on it, whatsoever.

2a) A given item is part of a larger grouping of possible items that can drop in one "slot" of the treasure pool. An item always drops in this slot and the ratio is predetermined. Treasure Hunter in no way affects these.

2b) A given item is part of a larger grouping of possible items that can drop in one "slot" of the treasure pool. The drop is not guaranteed, and Treasure Hunter has an effect on the "placeholder drop" (which would then pick a drop based on 2a).


Bahamut II and most drops in KSNM/BCNM battlefields would fall under 2a. Dynamis would be an example of something that uses 2b. Just about every normal drop off normal monsters or NMs would fall under 1.

Kindred Seals and Beastmen's Seals would drop at their normal rate provided the restriction is not in place (1 every 5 minutes per party in the alliance). Crystals would be given a roll for each person present in the party that kills the monster (a party of 4 kills a monster, there are 4 rolls for the monster's crystal, using model 1).

I think the likelihood that SE uses a model such as 2a or 2b or every drop in the game is extremely low, and that's basically what you outlined (but in a more complicated manner).

I think you'll find that the drops off each one of the 4 monsters you chose will fit my model 1; independant drop rates not affected by anything else that drops.

[Mojo]

I'm not really opposed or attached to any particular model, I just created one that matches that data that has already been presented. Although it's only a sample size of 400, if you take a hard look at Shulula's tests, it becomes very clear that it's unlikely that every item does have an individual drop rate and are not tied together in pools. For instance, the total number of drops obtained between TH2 and TH2+2 were 79 and 95, respectively, while the no drop rate between TH2, TH2+1, and TH2+2 remained almost a constant 1/3 through all 300 mobs. If you can come up with another explanation, I'd be all ears.

Also, the concept of the model I presented was that every mob could potentially have multiple loot pools, so it really goes hand in hand with all of those other models.

[Wizerd]

Originally Posted by Mojo

I'm not really opposed or attached to any particular model, I just created one that matches that data that has already been presented. Although it's only a sample size of 400, if you take a hard look at Shulula's tests, it becomes very clear that it's unlikely that every item does have an individual drop rate and are not tied together in pools. For instance, the total number of drops obtained between TH2 and TH2+2 were 79 and 95, respectively, while the no drop rate between TH2, TH2+1, and TH2+2 remained almost a constant 1/3 through all 300 mobs. If you can come up with another explanation, I'd be all ears.

Yeah, I've studied Shulula's data many times. When the testing first came out, I looked over it a lot and I replicated his tests in my own fashion on the same monster. I didn't test for the same thing, I simply tested each level of Treasure Hunter assuming independant drpos, with sample sizes varrying from 200 to 300 for each level. (I wish I still had this data floating around somewhere... I might...)

I did not record how many "No drop" outcomes I ran into; however, the major flaw in coming to any based on Shulala's data conclusion is the sample size. It's small, as you admitted, and unfortunately far too small to draw any conclusions even with a difference of 24 drops.

I broke down her data into the individual drops, and came up with this:

TH      Drop 1      Drop 2      Drop 3      Drop 4   Ttl   Kills

 0      (0%) 0    (6.6%) 7  (14.2%) 15  (18.9%) 20    42    106
 1   (0.99%) 1    (5.9%) 6  (13.9%) 14  (37.6%) 38    59    101
 2      (3%) 3      (8%) 8    (13%) 13    (55%) 55    79    100
 3      (7%) 7      (9%) 9    (31%) 31    (41%) 41    88    100
 4      (2%) 2    (15%) 15    (26%) 26    (52%) 52    95    100

Hopefully that formats properly. Looking at this, it seems quite clear that the wildly varying results between TH2, TH2+1, and TH2+2 are caused by the extremely small sample. It's no surprise that TH2 and TH+2 ran into the same amount of no drop outcomes.

Don't forget that while 88 to 95 is an 8% increase, it's also being stacked four times. In a perfect world, if you have a monster with 4 different drops and increase the drop rate on each one by exactly 1%, your total increase in drops is going to be more than 1%. If we use TH2 -> TH2+1 as an example, it would go from 79 to 83 drops (adding 1 drop to each item), which is a 5% increase. If we use TH2+1 -> TH2+2 as an example, it would go from 88 to 92 drops, which is a 4.5% increase.

With this in mind, an 8% increase is not at all out of the realm of possibility (in fact, it's very closely in it).

I feel like I've rambled on, but my main point is that Shulala's testing is far too small in terms of sample size and inconclusive to even consider trying to draw a hypothesis from.

One thing a lot of people don't realize is that if you're testing for a difference of 1%, it doesn't matter whether you use an item that drops at a 1% base rate or an item that drops at a 50% base rate. You'll need the same sample size to draw an accurate conclusion.