Question on Drop Rate

Guesstimating, you need to do this 100 times just to beat the variance, before factoring the difference between the two drop rates. We can consider based on sum of quills, or we can consider based on individual data points. But lets come to that after more people help us out.

Unfortunately I think the quills will stop dropping today or tomorrow.
At 10 runs a day it will be hard to get 100 runs (per drop-buff configuration, at that) of any event drop, unless we can get a lot of people helping. Which nobody but tecul1 seems inclined to do.

Must find some other consistent scenario that can be repeated more often.

I'll gladly help if you guys could instruct me on how I should tackle it.
I have 9 pieces of 20% drop gear ready to use (40% greed pendant) along with a wolf underling.

I'll gladly help if you guys could instruct me on how I should tackle it.
I have 9 pieces of 20% drop gear ready to use (40% greed pendant) along with a wolf underling.

I think it's best to do all 10 runs of the day with the same configuration. From what I've seen, changing your drop gear seems to have strange lingering effects that may or may not get lost in the noise (variance).

Two things I would like you to test:

- All your gear, no wolf. This will hopefully be able to tell us whether the drop buff is additive or multiplicative, because with 9 pieces it would be 280% drop if additive, and 516% if multiplicative. That's a big enough difference that even with the noise we should be able to see the pattern.

- Just the wolf. We "know" it's 2x drop but unless someone can show official notice from Nexon to that effect, it needs verification.

After we get that, and if the quills are still dropping, I'll want to see:
- All the gear and the wolf. This should tell us whether drop buffs from different sources add or multiply.


So, for today, please do 10 DIPQ runs with all your drop gear but no wolf, and of course make sure to loot all philosoquill pens that drop. (Most tricky part is sweeping the bottom at the end of stage 3, before going up top. If you wait until after the gargoyles, the drops will expire). Count how many dropped in each run.
And, Thank you

Today I did 10 runs with only the Greed pendant.
Results: 55, 46, 52, 50, 57, 51, 58, 40, 52, 42 for an average of 50.3

That's only ~15% more than my average for runs with no drop buffs, though.
My average for a run with no drop buffs is 43.8, which is close enough to a drop rate of 1 in 25 to make me believe that's the base rate (have to remember these are numbers entered by people, so they are likely nice and round).
It is also corroborated by Commerci-Rien runs (though they only have 340 mobs and I can only do 3 runs a day, so the variance is even more problematic).

But if that's the case then there is something amiss with the Greed pendant.

Will get right into it, thanks!

My runs with 200% drop gear 8x 20% + 20% greed + 20% greed potential gave me :
- 202 (?)
- 103
- 134
- 105
- 136
- 122
- 116
- 96
- 120
- 139

That makes it an 127,3 average. If you ignore the highest and lowest it would average at 121,5

(?) Differ very much in comparison to the rest, I have no idea why whatsoever.

My runs with 200% drop gear 8x 20% + 20% greed + 20% greed potential gave me :
- 202 (?)
- 103
- 134
- 105
- 136
- 122
- 116
- 96
- 120
- 139

That makes it an 127,3 average. If you ignore the highest and lowest it would average at 121,5

(?) Differ very much in comparison to the rest, I have no idea why whatsoever.

Thank you, that helps a lot.

That's 2.8 (or 2.9 if we do count outliers) times my average no-buff run, which means gear drop rate enhancements are definitely additive rather than multiplicative.
(Although it's a tad low even for that. I'd have expected 3x because you have 10 20% lines).
We still need to test whether familiars, cash shop 2x drop, event 2x drop, or coupon buffs stack additively with that or not, but this is still a very significant result.

As for the first run that was so much higher than the rest: did you by some chance use the wolf before going to DI?

Thank you, that helps a lot.

That's 2.8 (or 2.9 if we do count outliers) times my average no-buff run, which means gear drop rate enhancements are definitely additive rather than multiplicative.
(Although it's a tad low even for that. I'd have expected 3x because you have 10 20% lines).
We still need to test whether familiars, cash shop 2x drop, event 2x drop, or coupon buffs stack additively with that or not, but this is still a very significant result.

As for the first run that was so much higher than the rest: did you by some chance use the wolf before going to DI?

Before my first run I was doing the Kritias daily quests, so indeed I had my wolf out.
But upon entering the Dimensional PQ map, familiars automatically 'go away' since you change channels. So I'm not sure what happened here .. o-o

I've always thought that drop rate potential were additive since it says + and the drop rate events/card/wolf/easter is multiplicative since it says x.
The only drop rate factors that raises questions for me are Holy Symbol, Wealth Acquisition (I assume additive), Showdown, Monkey spirit Kanna and Inner Ability.

Before my first run I was doing the Kritias daily quests, so indeed I had my wolf out.
But upon entering the Dimensional PQ map, familiars automatically 'go away' since you change channels. So I'm not sure what happened here .. o-o

I know they disappear. But I observed, upthread, that even after the familiar goes away, it still has some effect that slowly fades.
Might last as long as it has less than full vitality, or something along those lines. It bears investigating, but I think that can wait until the more common situations are cleared up.

I've always thought that drop rate potential were additive since it says + and the drop rate events/card/wolf/easter is multiplicative since it says x.
The only drop rate factors that raises questions for me are Holy Symbol, Wealth Acquisition (I assume additive), Showdown, Monkey spirit Kanna and Inner Ability.

I'm not sure about those x's being multiplicative. I know that when exp bonus lines got split up, multiplicative stacking of some buffs broke. So I'd rather check, if possible.
I can't ask anyone to waste events/cards/coupons/potions on these tests, but the familiars and skills just require time and the right class, so hopefully we can get to them.

I know they disappear. But I observed, upthread, that even after the familiar goes away, it still has some effect that slowly fades.
Might last as long as it has less than full vitality, or something along those lines. It bears investigating, but I think that can wait until the more common situations are cleared up.



I'm not sure about those x's being multiplicative. I know that when exp bonus lines got split up, multiplicative stacking of some buffs broke. So I'd rather check, if possible.
I can't ask anyone to waste events/cards/coupons/potions on these tests, but the familiars and skills just require time and the right class, so hopefully we can get to them.

When you put away a mutant snail familiar, like some seconds after it's gone it will heal your hp/mp again (once). This might be the case of drop rate familiars as well.
Like after they're put away, they recast their buff one more time. But like you said, this can be discussed later.

Yeah, tomorrow before the server check (if one is finding place) I'll run 10 times again on 200% drop gear along with my wolf underling.
If base drop is 100% and drop gears are additive whilst wolf is multiplactive, I should be getting 6 times the amount that you normally receive without any factors. So give or take 250 pens

Today's runs were with pig only.
Results: 61, 58, 72, 70, 74, 54, 74, 60, 64, 72.
For an average of 65.9, which is only 1.5x my average with no drop buffs.

This can mean one of three things:

1) Mutant Ribbon Pig familiar is only 1.5x drop, not 1.6x as we have always thought.

2) I have a 20% drop buff somewhere. That would also explain why the Greed pendant is only giving me ~15% instead of 20, and why Straatlamp's 3x drop was only 2.8x my "base". But I have checked all my gear, skills, link skill, character cards, monster life, inner ability, and can't find anything that would do this. If I do have this mysterious buff, it is additive with both the pendant and the familiar.

3) RNG is messing with me. Need more data.

gear being additive is consistent with the rules for EXP. the gear bonus is a small little thing added on after you get all the familiar cards and buffs and event boosts.
I remember it was this way for a long time. first noticed it grinding at the lion king place when it was party play. the pendant bonus was very lame, tiny and it doesn't even multiply with party bonus...

I had always assumed they would run by the same rules.

I might review my stats courses if I had time...

also check your honour stats, i got bonus drop for one of mine







EDIT 3
wow I have remembered more stats.

standard deviation of the number of drops based on 0.04 chance of drop (1/25)
is 6.5

	prob drop	drop rate	standard dev	expected average drops
	0.04	1	6.499230724	44
	0.048	1.2	7.089823693	52.8
	0.056	1.4	7.625640957	61.6
	0.064	1.6	8.117536572	70.4
	0.072	1.8	8.573074128	79.2
	0.08	2	8.997777503	88
	0.088	2.2	9.395828862	96.8
	0.096	2.4	9.77048617	105.6
	0.104	2.6	10.12434689	114.4
	0.112	2.8	10.45952198	123.2
	0.12	3	10.77775487	132
	0.128	3.2	11.0805054	140.8
	0.136	3.4	11.36901051	149.6
	0.144	3.6	11.64432909	158.4
	0.152	3.8	11.90737587	167.2
	0.16	4	12.15894732	176

Standard dev table for each multiple of drop rate, based on a basic drop rate of 1/25, 1100 monsters

(OK i know this is prob not right method, but i forgot how to to do properly and this will do for now until a stats expert comes in)

take diff between the mean you get from test and the expected value based on your hypothesis, divide by standard deviation. get Z score.



Z = (average of tests - expected average) / (standard dev / sqrt of number of tests you do)

http://en.wikipedia.org/wiki/Standard_normal_table

get probability there from your Z score ( use cumulative table) higher your value, higher chance your hypothesis is wrong.
in stats usually go for 0.95. if it is greater than 0.95 hypothesis is wrong

0.95 corresponds fo Z score of 1.96

basically if your Z score more than 1.96, your hypothesis is wrong. if not you cannot reject it

so suppose you thought drop rate is 3.0 and you did tests and Z score turns out to be 1. the result seems off like 10 from what you exoect or so but you cannot conclusively say that the drop rate is not 3.0.
it might still be 3.0 and you need more tests


EDIT 4 - more explanation - for example
so you might think like is greed pendant additive or mult with 2x drop

so here, you test two hypotheses with 2.2 and 2.4.
if you can reject 2.2 and not 2.4, then you can prob say it is 2.4
if you cannot reject either then it may still be either of them and more tests needed.

ANOTHER EDIT
I will redo it for this data pack
(ok when i first did it i forgot formula)

Today's runs were with pig only.
Results: 61, 58, 72, 70, 74, 54, 74, 60, 64, 72.
For an average of 65.9, which is only 1.5x my average with no drop buffs.

This can mean one of three things:

1) Mutant Ribbon Pig familiar is only 1.5x drop, not 1.6x as we have always thought.

2) I have a 20% drop buff somewhere. That would also explain why the Greed pendant is only giving me ~15% instead of 20, and why Straatlamp's 3x drop was only 2.8x my "base". But I have checked all my gear, skills, link skill, character cards, monster life, inner ability, and can't find anything that would do this. If I do have this mysterious buff, it is additive with both the pendant and the familiar.

3) RNG is messing with me. Need more data.

Z score is 4.5/(8.11/sqrt10) = 1.75
P value is 0.92
8% chance of more further from what you expect.
so there is an 8% chance of a more extreme result.

so it is just within the 95% threshold. so it depends on what threshold you think is right. in psychology, climate studies and otherr fluffy subjects they lower threshold to 90% or lower so their papers contain "results"

but since it is within 95%, I would say you cannot reject the hypothesis that drop rate is 1.6. So the drop rate is 1.6, until you do more tests

back some time ago, me and guild collected data on the trait boost potion. it was also on the edge of the threshold, but just inside - haha nexon RNG is a bit iffy at times.

Managed to do 8 and a half run before SC happened.
Results with 200% drop gear and a wolf are :
- 227
- 244
- 250
- 241
- 228
- 233
- 245
- 230
- 188 with 3 waves of birds and last stage left I'd estimate about 240. x

That's an average of 237,25 whereas my estimate was 250. (not counting the half run)

Managed to do 8 and a half run before SC happened.
Results with 200% drop gear and a wolf are :
- 227
- 244
- 250
- 241
- 228
- 233
- 245
- 230
- 188 with 3 waves of birds and last stage left I'd estimate about 240. x

That's an average of 237,25 whereas my estimate was 250. (not counting the half run)

Your average without the wolf was 121 (not counting the outliers), so if wolf is double we should expect 242. 237 is close enough to that to decide that the wolf is indeed multiplicative with the gear. (If it were additive we'd only see an average of about 160).

Very good. Thank you.

And thanks [MENTION=9421]RayGun[/MENTION]; for the statistical analysis. We'll have to see whether the quills still drop after the maintenance, so more data can be gathered. The philosopher's book sale was supposed to end last week, per the cash shop notices, so I have no idea how long it's going to keep going.

Pens are still dropping even after the server check, on what drop rate should I do my dimension pq's next?

Pens are still dropping even after the server check, on what drop rate should I do my dimension pq's next?

If you mean the one left for today, do it the same as the previous 8, just to complete that data set.

If you mean tomorrow... hmmm... There were all the skill buffs and coupon buffs we wanted to check for stacking... Do you happen to have any available?

Otherwise, I'd like to see your base drop rate with no gear or wolf. The numbers we're getting look a lot more consistent if I assume that I have a 20% buff somewhere that I'm not aware of. I'm curious whether your base rate is lower than mine.

If you mean the one left for today, do it the same as the previous 8, just to complete that data set.

If you mean tomorrow... hmmm... There were all the skill buffs and coupon buffs we wanted to check for stacking... Do you happen to have any available?

Otherwise, I'd like to see your base drop rate with no gear or wolf. The numbers we're getting look a lot more consistent if I assume that I have a 20% buff somewhere that I'm not aware of. I'm curious whether your base rate is lower than mine.

I'll do 10 runs on 0x drop on one of my mules and 200% + wolf + HS on my main then.
I'm not sure if the difference of additive/multiplicative will be noticable at only 4x drop though, but we'll see.

Otherwise, I'd like to see your base drop rate with no gear or wolf. The numbers we're getting look a lot more consistent if I assume that I have a 20% buff somewhere that I'm not aware of. I'm curious whether your base rate is lower than mine.

I have remembered more stats. so is your base drop rate different? short answer no.

t-Test: Two-Sample Assuming Unequal Variances	Variable 1	Variable 2
Mean	39.60784314	41.1875
Variance	14.23937908	21.21961806
Observations	17	10
Hypothesized Mean Difference	0
df	16
t Stat	-0.918223236
P(T<=t) one-tail	0.186068602
t Critical one-tail	1.745883669
P(T<=t) two-tail	0.372137205
t Critical two-tail	2.119905285

I took the info from straatlamp's posts 26 and 33, and divided by the rlevent multiple 3 and 6.

yours from 31 divided by 1.6

compared means test.

there is no statistically significant difference between your base rate and straat's
you were group 2 in the table, your base drops was 1.6 drops for the pq higher than his

EDIT: based on these, base drop rate appears to be 1 in 27.3
which is in between 1 in 25 and 30. so if we take it that they entered a round number could be either

of course, conduct more tests, though now we have to think of new scenario since pens gone?

hmm now that I think about maybe drop rate has range too just like dmg o.0 something like this base drop rate is 50% to 100%? LOL that would be funny... but who know it just a guess

I have remembered more stats. so is your base drop rate different? short answer no.

t-Test: Two-Sample Assuming Unequal Variances	Variable 1	Variable 2
Mean	39.60784314	41.1875
Variance	14.23937908	21.21961806
Observations	17	10
Hypothesized Mean Difference	0
df	16
t Stat	-0.918223236
P(T<=t) one-tail	0.186068602
t Critical one-tail	1.745883669
P(T<=t) two-tail	0.372137205
t Critical two-tail	2.119905285

I took the info from straatlamp's posts 26 and 33, and divided by the rlevent multiple 3 and 6.

yours from 31 divided by 1.6

compared means test.

there is no statistically significant difference between your base rate and straat's
you were group 2 in the table, your base drops was 1.6 drops for the pq higher than his

EDIT: based on these, base drop rate appears to be 1 in 27.3
which is in between 1 in 25 and 30. so if we take it that they entered a round number could be either

of course, conduct more tests, though now we have to think of new scenario since pens gone?

I checked right after the SC, pens are still dropping. Unless there was an usc when I was asleep..