General

Drop Rate ResearchampFormula to calculate drop rate multiplier

Summary the of Drop rate Research.
•Lucky winter is 2x drop.

•Familiar cannot stack with the 2x coupon buff. My data shows Big Spider cannot stack with Lucky winter. Mutant pig cannot stack with Easter egg.

•When using both 2x coupon and familiar, doesn’t matter which buff you use first , only the highest drop rate apply the effect. Ex: When using LW and spider, doesn’t matter you use LW or spider first, only it will only have LW effect. It overwrite the lower multiplier which is Spider 1.4x-1.6x. When you use LW and Wolf, it doesn’t matter since both are 2x and they do not stack.

•2x Event and 2x CS drop do stack with Lucky winter and Easter egg.
•My data shows Greed Pendant only works for equipment, not USE or ETC drop. The description states: �"Increase your equipment drop by 20%” is true. It only work on equipments not other use/etc items like leaves, boxes, keys, etc.

•Holy Symbol hyper stats 30% drop rate DO work for other party member. HS can stack with LW and other 2x drop coupons.

•Maximum stackable drop rate are : [Total drop rate % from equips + Wealth potion + Inner ability drop + skills buff like Holy Symbol+ self buff skill such as NL showdown, DS’s demon cry, phantom’s Judgment draw] + 2x Event + 2x CS drop + 2x (Lucky winter/Easter Egg/Wolf underling/Use tab 2x coupon from event) OR Big Spider/other familiar.

•How to calculate drop rate multiplier?
Step 1: Add up all the item drop % to get the total item drop % you get.
Step 2: Translate the drop% into multiplier format and add Base (1). Ex: 125% = 1.25x + 1 = 2.25x
Step 3: Multiply all the multipliers. Ex: 125% drop, 2x event, Spider is 2.25*2x*1.4-1.6x= 6.3x-7.2x drop.
Step 4: Multiply the base with the above multiplier. Ex: Base 65 boxes *7.2x= 468 boxes calculated avg.
For boss equips base 1.5% * 7.2x = 10.8%. When you kill this boss, now you have 10.8% chance this item will drop under the above scenario drop rate.

•Formula: Base * (drop rate multiplier + 1 ) * 2x event * 2x cs drop * 2x Wolf/LW/Easter or Spider/Mutant Pig.

Objectives:
There are many uncertainties about drop rate, and people still unclear how are drop rate work. Therefore, I done this research trying to find out the mysteries of drop rate.. My original objective was mainly on lucky winter and Big Spider. As more data I gathered, I expanded the research to Easter Egg buff, Greed Pendant, Wealth Potion, Holy Symbol buff, Wolf Underling, and other item drop %. In the first part of the research, I’m trying to find out which buff/items able or unable to stack with each other. On later part, I will use the data & analysis to figure out the correct way of calculating the true drop rate multiplier.

Location:
I collect all the data from Dimension Invasion Party Quest(DIPQ) and Normal Hilla. DIPQ is for Use & Etc items. The main reason I collect data in DIPQ because the spawn rate is constant unlike other places like Evolution lab or MP3 where the amount of monsters killed depends on your killing speed(sometime you kill faster, sometime slower). On other map, if it has previous kinshin effect, that might affects the monster spawn rate, which will affects the drop rate too. Normal Hilla is for equipments data collection.

Sampling:
On DIPQ, the sample size is 10-30. Only base drop got 30 sample size. On Hilla normal, the sample size is 20. If 10 rounds of DIPQ cannot draw reasonable conclusion on the result, I will expand the sample size to 20. I got sampling on Base drop, Greed Pendant, Big Spider/Mutant Pig, Lucky Winter, LW+Spider, Easter Egg, Easter+Mutant Pig, 2x event, Holy Symbol, Wolf Underling(only on Hilla), 50% item drop, 100% item drop, 170% item drop. I also did sampling on LW+ wealth potion, LW+HS, 2x event+Spider, 2x event+LW, 2x CS drop+LW, Easter+100% drop, Spider+170% drop, LW+HS+170% drop and 2x event+Easter egg+HS+170% drop because I want to find out how do each item drop correlate with each other. On Hilla sampling, I got Base drop, big spider, Lucky winter, Easter Egg, 2x event, Wolf Underling, 2x Event + Spider, 2x Event + Lucky winter.

Setting and Procedures:
I did DIPQ on multiple characters. All the characters have no other drop buff except the buff I used for this test. I did the test on different time and day. This is the best approach to get random result. I solo all DIPQ, HS buff before enter. For Hilla with Wolf Underling, my friends do the full kill, I do not attack(I don’t want to affects with the result of the drop rate). For DIPQ, I used Anderson Keys as the testing sample.

Complete data

http://i.imgur.com/FDv2Hmk.jpg

http://i.imgur.com/nJdq0sZ.jpg

http://i.imgur.com/niKzmTp.jpg

http://i.imgur.com/qsU2aFJ.jpg

Average keys under different buff. (I grouped all the same drop % into same category)
Base average 779 734 768 = 76
Greed Pend average 711 743 = 72.7
Base+HS average 884 888 947 = 90.63
50% item drop average= 111
Spider/MP average=1061 1118= 109
LW/LW+spider/Easter+MP/2x Event/2x CS/100% drop 1391 1320 1388 1347 1374 1377 = 136.6
LW + Wealth potion = 149.4
LW + HS 1548 1469 = 150.85
2x Event + Spider 2157 2128 = 214.25
170% item drop = 196.5
2x Event + LW/2x Event + 2x cs drop/Easter+100% drop 2801 2655 2639 = 269.83
Spider + 170% drop = 305.6
LW + HS + 170% drop = 440.7
2x Event + Easter + HS + 170% drop = 850.3

Based on the data result, we can answer some of the drop rate questions.
Is Lucky Winter 1.5x or 2x Drop rate?
Some people believe Lucky winter is 1.5x drop because they say Enjoyable Winter is 1.5x EXP, so they assume LW is 1.5x drop too. However, my data indicates Lucky Winter is 2x drop rate!
Lucky winter got 1391 key (range from 119 - 155).
Easter Egg buff got 1347 keys (122-140).
Nexon 2x event got 1374 keys (126-155).
100% item drop got 1377 keys (125-151)
Big Spider is either 1.4x-1.6x, if lucky winter is 1.5x drop, these 2 should shows similar outcome. But this is not the case.
Big Spider only 1061 keys (97-117).
Mutant Pig only got 1118 keys (92-128).
Both spider and mutant pig clearly shows significant lower boxes and keys, while lucky winter, Easter egg buff and 2x event and 100% item drop have similar result.
Hilla equips and weapons drop also prove lucky winter is 2x drop.
Lucky winter got 135 (avg 6.75), (3-12) equip.
Easter Egg got 131 (avg 6.55), (4-13) equips.
2x Event got 135 (avg 6.75), (3-10) equips.
Wolf Underling got 130 (avg 6.5), (3-9) equips.
Big spider got 101 (avg 5.05), (1-10) equips.
All the 2x buff show higher drop rate than Big spider.

Can Lucky Winter/Easter Egg stacks with Big Spider/Mutant Pig?
Some people mistakenly believe Lucky winter stack with Big spider because both icon showing on the buff.
But my data shows Lucky winter CANNOT stack with Big spider.
Lucky winter got 1391 keys (119-155), 6 equips
LW + spider got 1320 keys (122-140), 7 equips
Easter+Mutant pig got 1388 keys (125-152), 16 equips. ï�'Ÿ*(one run got 6 equips while normally 0-3)
Assume LW + spider stack, the data should be way higher, but this test shows similar keys and equips. I also did Easter egg+Mutant pig. Total number and range number of keys are similar to LW and LW+spider. This sample got total 16 equips because 1 run got 6 equips alone while all other runs normally get 0-3 equips.
Now that we know LW is 2x, so let us use the 2x event + spider. If they stack, compare the result:
2x Event + Spider 2157 keys (198-240), 17 equips.
As we can see, 2x event + spider CAN stack, the number are much higher than LW+Spider or Easter+MPig. This strongly prove LW+Spider cannot stack, while 2x event + spider can stack to each other.

This also comes to another question: when use both, which one took on the effect?
I think the higher non stackable drop buff took the effect, in this case LW took on the effect because LW drop rate is higher than Spider. On LW + spider test, first 5 rounds I buffed LW, then summoned Spider, last 5 rounds I summoned spider, then used LW. But all 10 rounds got similar data range as LW data (11x-15x) keys. As data comparison purpose, big Spider only got 1061 keys (97-117).

Can 2x Event, 2x CS drop stack with Lucky winter?
My data shows 2x event, 2x CS drop card CAN stack with Lucky winter.
2x event + LW got 2801 keys (250-295) and 24 equips.
2x cs drop + LW got 2655 keys (239-300) and 28 equips.
Lucky winter only got 1391 keys (119-155), 6 equips.

Can Wealth potion(WP) stacks with Lucky winter(LW)?
Since wealth potion only increase item drop by 10%, it is much harder to get conclusion.
WP+LW keys 1494 vs. LW 1391 keys
WP+LW keys 1494 vs. LW 1320 keys
WP + LW keys are more than just LW by small amount. So I can conclude WP CAN stack with lucky winter.

Is Greed Pendant work on USE, ETC drop too or only for Equips?
The description on Greed Pendant states �"Increase your Equipment drop rate by 20%”. Based on my research, this statement is true. It only works for equipment, not USE or ETC drop.
Base drop keys 779 (55-93), 734 (55-86), 768 (65-94)
Greed pendant keys 711 (59-83), 742 (68-93)
Base equips 5, 6, 7 vs. 11, 8 equips from Greed pendant.
Greed pendant get similar amount of keys as base drop. While Greed pendant get slightly more equips than the base. Therefore, Greed pendant only affect equips, not Use or Etc drop.
Another player IGN: Rexaar did an extensive research on Greed Pendant too. He concluded Greed Pendant only apply to equipments, but has no effect on Use & Etc items such as leaves and event boxes.
http://maplestory.nexon.net/community/#%2Fshowthread.php%3F1433624-Greed-Pendant-description-increased-drop-rate-effect-is-not-specific

Is Bishop’s HS self buff or it works to party members?
Some people claim HS only work by themselves, but most people believe HS works on party members.
Base+HS(tested on bishop) got 884 (77-111) and 888 (79-105) keys.
Base+HS(buff on other) 947 (83-109) keys.
Base keys are 779 (55-93), 734 (55-86), 768 (65-94)
This shows HS work for other player, because keys and equips are significantly more than base with no buff.

Can HS stack with other drop coupon like LW/Easter Egg?
HS + LW keys are 1548 (134-175), 1469 (125-161)
Lucky Winter keys 1391 (119-155) and 1320 (122-140).
This data comparison shows HS CAN stack with drop buff/coupons.

What are the equipments drop rate?
There are 9 accessories able to get drop rate on main potential. They are 4 rings, 2x pendant, face, eye, earring.
Level 0-30 equips = 10% item drop, Level 31-70 = 15% item drop. Level 71 above = 20% item drop.
Shoulder, Belt and other armors CANNOT get drop rate on main potential, but they can get 2-5% drop rate from Legendary Bonus pot(depends on level of the equips).
Level 0-20 = 2%, Level 21-50 = 3%, Level 51-90 = 4%, Level 91+ = 5% drop rate
Reference: http://strategywiki.org/wiki/MapleStory/Potential_System#Item_drop_rate_.25_increase

What are the best item drop%? Depends on if you want more drop% untradable or less drop% that can be tradable. 3 gollux rings and black bean ring are the best because they can be tradable. Eye use spec goggle, Face use lvl 40 branch nose or SW tattoo, then use half earning, any lvl 71+ pendant and greed pendant is fine.

What is the maximum drop rate a person can get?
[Total drop rate % from equips + Wealth potion + Inner ability drop + skills buff like Holy Symbol+ self buff skill such as NL showdown, DS’s demon cry, phantom’s Judgment draw] + 2x Event + 2x CS drop + 2x (Lucky winter/Easter Egg/Wolf underling/Use tab 2x coupon from event) OR Big Spider/other familiar
*The plus symbol means items are stackable.

How are all the item drop% work with the familiar or 2x event/coupons/wolf underling?
50% item drop keys 1113 (100-121), 8 equips
Big spider/MP keys 1061 (97-117) 6 equips and 1118 (92-128) 8 equips.
50% drop shows similar result to the 1.6x spider/mutant pig result.
100% item drop keys 1377 (125-151)
Lucky winter keys 1391 (119-155)
Easter Egg keys 1347 (120-153)
2x Event keys 1377 (125-151)
100% item shows similar result to all the 2x buff.
The above shows 40%-60% drop = 1.4x-1.6x and 100% drop = 2x. They are just in different format.
Big Spider = 40%-60%( item drop in percentage format) = 0.4x-0.6x increase from the base (multiplier format exclude the base) = 1.4x-1.6x (final multiplier format include the base)
Ex: On base drop, you get 50 boxes, with spider assume 60%(0.6x) increase, you get 30 more. (50x0.6x=30). Add into the base of 50+30=80 boxes. If you use 50 * 1.6x also is 80 boxes.
Many people don’t know how the all the item drop % plug into the 2x event/coupon or familiar because these 2 are in different format. To calculate the drop %, you need to change the drop% into multiplier format + base of 1 to get into the same format as these 2x and 1.4-1.6x buff.
Ex: Assume you have 120% item drop=1.2x increase of the base. The final multiplier in this case is base 1+1.2x increase from the base=2.2x multiplier.

My data prove the above theory.
Ex 1: Spider+170% drop keys 3056 (285-321). Since spider is 1.6x * 2.7x(170%=1.7x+1=2.7x)=4.32x.
Base average key 76 * 4.32x = 328 calculated average vs. my data 305 average keys. Under any multiplier, tested data average will always fall into the reasonably range of the calculated average. I guess the reasonable average range could be 280-330.
Ex 2: 170% item drops got 1965 (178-207) keys. We know 170% = 1.7x + 1 = 2.7x multiplier. Base average keys 76 * 2.7x = 205 calculated average vs. tested average 196. Reasonable average range would be 170-210.
Ex 3: LW+HS+170% drop got 4407 (405-455) keys. Calculation is 2x * 3x multiplier (200%=2x+1=3x)=6x.
Base average 76 * 6x = 456 calculated average vs. my data 440. Reasonable average range would be 400-460.
Ex 4: 2x Event+Easter+HS+170% equips got 8503 (833-870) keys. Therefore, 2x * 2x * 3x (200%=2x+1=3x) =12x multiplier. Base average 76 * 12x = 912 calculated average vs. 850 data average. This data is larger difference, but if we lower the 2x to 1.95x multiplier into the calculation, the number is not much off.
1.95x * 1.95x * 3x = 11.4075x * 76 = 867 calculated average. This number is close to my 850 average.
From the above example, we see the tested average is always lower than the calculated average, and that is totally reasonable. If base you get 100 boxes. Then with 2x event, you could only get 180 boxes. That doesn’t mean 2x is rigged you get less boxes, this is how the drop rate work. Sometime you get more, sometime you get less base on your luck, but the average will fall into the average 2x range.

Hilla equipments drop data.
Base average equips is 3.5 (from 1 to 7 equips).
Big Spider average equips is 5.05 (from 1 to 10 equips).
Lucky Winter average equips is 6.75 (from 3 to 12 equips).
Easter Egg average equips is 6.55 (from 4 to 13 equips).
2x Drop average equips is 6.75 (from 3 to 10 equips).
Wolf Under average equips is 6.5 (from 3 to 9 equips).
2x + Spider average equips is 9.75 (from 5 to 14 equips).
2x + LW average equips is 12 (from 8 to 16 equips).
As you can see the above data, with higher drop rate, the minimum, maximum and average number slowly shift into higher number. Any multiplier below 2x is not much noticeable difference from the base. On 4x drop, you will get a slightly noticeable drop difference, any higher multiplier is where you see bigger difference. This means higher the drop rate, you get more effective drop than with lower multiplier. But at the same time, it will way more. Think about how expensive to cube drop% equip.

How to calculate the correct drop rate multiplier?
Drop rate multiplier is calculated in mix of multiplicative and additive.
Step 1: Add up all the item drop % to get the total drop %. Ex: 20% ring+15% ring+20% Earring+10% inner + 10% wealth potion = 75%.
Step 2: Change the drop % into multiplier format. Ex: 75% item drop = 0.75x + base (1) = 1.75x multiplier.
Ex: 10% = 0.1x= 1.1x multiplier, 30%=0.3x increase = 1.3x multiplier, 85% =0.85x increase=1.85x multiplier, 100%=1x increase=2x multiplier, 125% = 1.25x increase=2.25x multiplier, 180%=1.8x increase=2.8x multiplier, 220%= 2.2x=3.2x multiplier, etc.
Step 3: Multiply the item drop multiplier with 2x event, 2x cs drop, 2x wolf/LW/Easter or 1.6x Spider.
Ex: Assume you are on 2x event and spider with 75 % drop. It is 1.75x * 2x * 1.4x-1.6x = 4.9-5.6x multiplier.
Step 4: Base * multiplier from step 3 will get the estimated outcome. Ex: Assume base get 85 boxes * 5.6x = 476 boxes on average. For equipments, each equips got different base drop %. Assume an item/equip have 1.5% chance to drop under base, with 5.6x multiplier, now you will have 1.5% * 5.6x = 8.4% change this item will drop when you kill the boss or each monster mob you kill.
But since we don’t know the exact base % on each items in maple, so the result might be hard to calculate.
Formula: Base * (drop rate multiplier + 1 ) * 2x event * 2x cs drop * 2x Wolf/LW/Easter or Spider.
Ex: Assume you got total 200% drop(equip, wealth pot, HS), 2x Event, 2x cs drop, 2x Wolf underling.
200%=2x+1= 3x * 2x event * 2x cs drop * 2x Wolf = 24x multiplier drop.

Special thanks to Nyan helps me on Hilla data with his Wolf Underling Thanks Slick, Pearlheaven, HeaterTh13F for providing HS.