Please Read This Before Posting About Drop Rates

[Notso]

So I've been around for a while, I spend more time on the forums than I do in game, and one thread I see over and over is people complaining about one drop or another not dropping for them. In this post I'll try to explain why the fact that you haven't got your drop yet probably does not mean that DE needs to change the loot tables, and that you've probably just been cursed by the RNG gods.

As and when I get hold of more data I will update the maths; if, when farming for a boss, people record how many BPs they got and how many runs they got them in that would help me enormously [just plop it in a response below]. Similarly if any dedicated soul wants to record their mod drops... I'd do it myself but I've got exams coming up and I've banned myself from video games :P

If you're interested in the maths behind all the percentage chances I'm going to throw at you, its all in the spoiler tags. If anybody spots an error in how I've calculated probabilities, please give me a shout below and I'll fix it.

N refers to "the expected number of runs to get drop X"
P(X = Y) means the probability that the result of the test X is specific result Y
∴ = therefore

#1 - Blueprints dropped from bosses

How many runs should should it take me to get all three BPs?
28

The probability of a BP dropping is roughly 1/5, Most people will expect to have all three BPs after 15 runs. However the probability of getting a BP you need actually diminishes as you get more BPs:

0 Bluprints:
P(X = Helmet, Chassis, Systems) = 1/5
∴N = 5

1 Blueprint:
P(X = H or C, H or S, C or S) = 2/15
∴ N = 15/2 = 7.5

2 Blueprints:
P(X = H or C or S) = 1/15
∴ N = 15

5 + 7.5 + 15 = 27.5

∴ expected number of runs to get all three blueprints: 27.5

 

This is just a simplified method of calulating the probability, if anybody is interested in the full proof of why it works just PM me.

 

I've done 28 runs, why haven't I got it yet?

This is commonly known as the gambler's fallacy; the false belief that if deviations from expected behaviour are observed in repeated independent trials of some random process, future deviations in the opposite direction are then more likely.

 

In simple English, it's the false belief that if I didn't get what I want after loads of tries, I'm more likely to get it the next time. While some games increase the probability of getting something as the number of times you haven't got it increases, I am 95% sure that Warframe does no employ this system.


#2 - Anecdote ≠ Data

I've done over 100 runs! Why haven't got the final BP part yet?
Because you're unlucky. The RNG gods have cursed you. Maybe you walked under a ladder, or broke a mirror a few years back. About 750 people will experience needing more than 100 runs to get all the BPs for at least one 'frame given current player numbers.

First and foremost, you probably have not done over 100 runs. People tend to overestimate the number of runs they've done, by quite a substantial amount. A while back I did some speed runs of M Prime to test the loot table for the end mission mod reward. And I really do mean speed run. I didn't kill a single enemy, and I used a fully speed modded Volt. Initially I planned to do 100 runs. Do you know how long it took me? Three and a half hours. That's at an average speed of 2 minutes per run [including load times and mission select]. Doing 100 runs of a boss is going to take a lot longer.

Secondly, let's look at the let's look at how likely you are to be one of the unlucky people who actually have done 100 runs of a boss, and not got that last BP. Of the ~50000 active Warframe players, there should be about 50 people who'll end up doing the same run more than 100 times for a single boss.

 

Obviously, the reverse is also true. Just because you got the Latron Prime Receiver in five Tower II runs does not immediately invalidate all other claims about it being rare.

This calculation only considers people who have two of the three BPs they need.

P(X ≠ C, H, S) = 1 - P(X = C, H, S) = 1 - 1/15 = 14/15

After two runs P(X ≠ C, H, S) = 196/225

After n runs P(X ≠ C, H, S) = (14/15)^n

After 100 runs P(X ≠ C, H, S) = (14/15)^100 = 0.001

This is the shakiest part. A while back DE announced Warframe was peaking at 20000 simultaineous players each day on Steam. Add 5000 for natural growth of the game's playerbase. Add 15000 for off-peak players. Add 10000 for non-Steam users: ~50000 people. While this is a very rough estimation, it is sufficient to illustrate the mathematics.

50000 x 0.001 = 50

There are 11 Warframes obtainable through boss drops

50 x 11 = 550

Estimate ~200 players will be even more unlucky and need < 100 runs on two or more bosses

550 + 200 = 750 players

 

I got all the BPs I need in 3 runs of Jackal by running the mission before it on solo mode just before I did the boss mission! Guys this is a super legit way to get the drops!

While it would certainly be nice if there was some action we could perform to boost our chances of getting a drop, unfortunately the fact that it worked for you once or twice does not mean it actually increases the chances of getting the drop. Let's have a look at some numbers again. The probability of getting all three BPs in three runs is 0.0018. That means we'd expect about 90 people to be as lucky as possible, on just one boss. When it works for you 100 times in a row, come back to me, and I'll believe you :P

 

It's a lot easier to show how this works using a tree diagram, however I'm not at home so I can't make one easily.

 

if we have no BPs, the probability that we get a BP we want is:

1/5

 

If we already have one BP, the probability of getting a BP we need is:

1/5 * 2/3 = 2/15

 

If we already have 2 unique BPs, the probability of getting the last one we need is:

1/5 * 1/3 = 1/15

 

To find the probability of these three events happening in succession we we just multiply them together:

1/5 * 2/15 * 1/15 = 2/1125 ≈ 0.0018

_____________________________

 

oh and if a mod could sticky this so people can see, that would be just fabulous <3

Edited May 28, 2013 by Notso

[Law_Abiding_Engineer]

So I've been around for a while, I spend more time on the forums than I do in game, and one thread I see over and over is people complaining about one drop or another not dropping for them. In this post I'll try to explain why the fact that you haven't got your drop yet probably does not mean that DE needs to change the loot tables, and that you've probably just been cursed by the RNG gods.

 

If you're interested in the maths behind all the percentage chances I'm going to throw at you, its all in the spoiler tags. If anybody spots an error in how I've calculated probabilities, please give me a shout below and I'll fix it.

 

N refers to "the expected number of runs to get drop X"

P(X = Y) means the probability that the result of the test X is specific result Y

∴ = therefore

 

 

 

#1 - Blueprints dropped from bosses

 

How many runs should should it take me to get all three BPs?

28

 

The probability of a BP dropping is roughly 1/5, Most people will expect to have all three BPs after 15 runs. However the probability of getting a BP you need actually diminishes as you get more BPs:

 

0 Bluprints:

P(X = Helmet, Chassis, Systems) = 1/5

∴ N = 5

 

1 Blueprint:

P(X = H or C, H or S, C or S) = 2/15

∴ N = 15/2 = 7.5

 

2 Blueprints:

P(X = H or C or S) = 1/15

∴ N = 15

 

5 + 7.5 + 15 = 27.5

 

∴ expected number of runs to get all three blueprints: 27.5

 

 

 

#2 - Anecdote ≠ Data

 

I've done over 100 runs! Why haven't got the final BP part yet?

Because you're unlucky. The RNG gods have cursed you. Maybe you walked under a ladder, or broke a mirror a few years back. About 750 people will experience needing more than 100 runs to get all the BPs for at least one 'frame given current player numbers.

 

First and foremost, you probably have not done over 100 runs. People tend to overestimate the number of runs they've done, by quite a substantial amount. A while back I did some speed runs of M Prime to test the loot table for the end mission mod reward. And I really do mean speed run. I didn't kill a single enemy, and I used a fully speed modded Volt. Initially I planned to do 100 runs. Do you know how long it took me? Three and a half hours. That's at an average speed of 2 minutes per run [including load times and mission select]. Doing 100 runs of a boss is going to take a lot longer.

 

Secondly, let's look at the let's look at how likely you are to be one of the unlucky people who actually have done 100 runs of a boss, and not got that last BP. Of the ~50000 active Warframe players, there should be about 50 people who'll end up doing the same run more than 100 times for a single boss. 

 

This calculation only considers people who have two of the three BPs they need.

 

P(X ≠ C, H, S) = 1 - P(X  = C, H, S) = 1 - 1/15 = 14/15

 

After two runs P(X ≠ C, H, S) = 196/225

 

After n runs P(X ≠ C, H, S) = (14/15)^n

 

After 100 runs P(X ≠ C, H, S) = (14/15)^100 = 0.001

 

This is the shakiest part. A while back DE announced Warframe was peaking at 20000 simultaineous players each day on Steam. Add 5000 for natural growth of the game's playerbase. Add 15000 for off-peak players. Add 10000 for non-Steam users: ~50000 people. While this is a very rough estimation, it is sufficient to illustrate the mathematics.

 

50000 x 0.001 = 50

 

There are 11 Warframes obtainable through boss drops

 

50 x 11 = 550

 

Estimate ~200 players will be even more unlucky and need < 100 runs on two or more bosses

 

550 + 200 = 750 players

 

 

Very well done, but this is why I hated stats, and just did differentials instead.

[bitlard]

+1

 

It's time people understand how mathematical probabilities work. There's a lot of the gambler's fallacy going around lately. Just because you have NOT been getting a mod or a blueprint for the past 10 runs doesn't mean the 11th run gives you a higher chance of getting the mod or blueprint. The probability remains the same.

[SciKnight]

Now tell me why I can't get all the rare mods that I want! I want a thunderbolt! DE is stupid! RNG is lame! 

 

But seriously, any idea on the chances to get rare mods? I can't really complain because I have everything I need (got 2 multishot mods in under 10 minutes).

[Notso]

Very well done, but this is why I hated stats, and just did differentials instead.

 

Haha, I prefer calculus too :P But I have to take 2 modules in statistics for my course unfortunately. Although none of the stats I learned has really been of any use here. Hmm maybe I could use a binomial distribution then approximate it to a standard normal distribution...

[Law_Abiding_Engineer]

+1

 

It's time people understand how mathematical probabilities work. There's a lot of the gambler's fallacy going around lately. Just because you have NOT been getting a mod or a blueprint for the past 10 runs doesn't mean the 11th run gives you a higher chance of getting the mod or blueprint. The probability remains the same.

 

 

Yup, probably the most famous and well noticed fallacy of them all.  thats why when people say "I have a 1 of 5 chance of winning this.  If I do it 5 times, i should get it at least once."    Heck, its like flipping a coin.  You can flip the damn thing over and over and voer, but if it keeps landing on heads, its chances of being tails, is the same as its chances for being heads.

[SymphNo9]

Haha, I prefer calculus too :P But I have to take 2 modules in statistics for my course unfortunately. Although none of the stats I learned has really been of any use here. Hmm maybe I could use a binomial distribution then approximate it to a standard normal distribution...

 

A few Gaussian graphs would be neat to look at. Nevertheless good job on the math! 

[Law_Abiding_Engineer]

Haha, I prefer calculus too :P But I have to take 2 modules in statistics for my course unfortunately. Although none of the stats I learned has really been of any use here. Hmm maybe I could use a binomial distribution then approximate it to a standard normal distribution...

 

Those were the same thoughts I had when I took stats.  "How am I actually going to use them?"  And please, stop. Hearing binomial distribution and standard normal distribution, makes me remember those long and dry lectures from college >_<

[Notso]

Now tell me why I can't get all the rare mods that I want! I want a thunderbolt! DE is stupid! RNG is lame! 

 

But seriously, any idea on the chances to get rare mods? I can't really complain because I have everything I need (got 2 multishot mods in under 10 minutes).

 

Well for one thing there are too many rare mods. The rare mod pool is significantly larger [due to Warframe powers] than the other pools, which means that the chances of you getting the rare mods you want are even lower. Obviously, the same depreciation rule applies to mods as it does to BPs; as you get the mods you want, the chances of you getting mods you want decreases [as the number of mods you want decreases as you get the ones you want]. Unfortunately I don't have any probabilities for mod drops, so I can't really help you much more than that.

Edited May 16, 2013 by Notso

[Notso]

Yup, probably the most famous and well noticed fallacy of them all.  thats why when people say "I have a 1 of 5 chance of winning this.  If I do it 5 times, i should get it at least once."    Heck, its like flipping a coin.  You can flip the damn thing over and over and voer, but if it keeps landing on heads, its chances of being tails, is the same as its chances for being heads.

 

Actually, one would expect to win after 5 times. I believe the fallacy is instead that people think "Well I've lost four times, I'm sure to win on the fifth!"

[Notso]

Those were the same thoughts I had when I took stats.  "How am I actually going to use them?"  And please, stop. Hearing binomial distribution and standard normal distribution, makes me remember those long and dry lectures from college >_<

 

Je peux vous intéresser à un poisson?

 

Sorry, I'll stop making maths jokes now. :-P

[Law_Abiding_Engineer]

Actually, one would expect to win after 5 times. I believe the fallacy is instead that people think "Well I've lost four times, I'm sure to win on the fifth!"

 

 

Your second part, is true, but your first part, is maybe not?   After all, if you have, say a die and you roll it 6 times, saying that you expect to roll a 3, then for each roll, your odds are 1 of 6.  Even after 5 rolls, your chances on that 6th roll, is the same as it was the first.

[Elyan]

Well, you've explained how things work, it does not follow that they *should* stay that way... In some games, even when you don't get the expected loot, you gain more frequently some lesser version that *can* later be upgraded when found in large quantities. Some other mechanism could be used to alleviate the need, for example allowing the players to exchange BP for the same warframe.

[Notso]

Your second part, is true, but your first part, is maybe not?   After all, if you have, say a die and you roll it 6 times, saying that you expect to roll a 3, then for each roll, your odds are 1 of 6.  Even after 5 rolls, your chances on that 6th roll, is the same as it was the first.

 

Of course, but if every person on earth were to roll a dice until they got a 3, the average number of rolls to get a 3 is 6 [the reciprocal of the probability, 1/6].

[Notso]

Well, you've explained how things work, it does not follow that they *should* stay that way... In some games, even when you don't get the expected loot, you gain more frequently some lesser version that *can* later be upgraded when found in large quantities. Some other mechanism could be used to alleviate the need, for example allowing the players to exchange BP for the same warframe.

 

Whether the system is appropriate is not what this thread is about. I am purely explaining firstly how many runs you should expect to do when farming for the BPs of a Warframe and secondly why the fact that an individual has done 100 runs or more of a boss does not mean that something is screwy with the RNG.

 

As a matter of fact, I agree with you though; I don't like loot tables in any game, for the exact reason that there will be a significant number of unlucky players. I have a number of ideas on how this can be avoided, but that is not for this thread. Let's stay on topic :D

[Argoms]

Some games actually increase the chance of a drop the more you play to reduce the variation between the luckiest and unluckiest guy. Might be nice if we had this- you're very unlikely to get a blueprint on your first 2-3 runs, but after 35, the chance increases exponentially or something.

[Notso]

Some games actually increase the chance of a drop the more you play to reduce the variation between the luckiest and unluckiest guy. Might be nice if we had this- you're very unlikely to get a blueprint on your first 2-3 runs, but after 35, the chance increases exponentially or something.

 

Indeed, however I am 95% sure this doesn't happen in Warframe. Again though, let's keep that idea for another thread [ :

[Kyrkitao]

I cannot give you enough upvotes.  Thank you for the data.

[Argoms]

Indeed, however I am 95% sure this doesn't happen in Warframe. Again though, let's keep that idea for another thread [ :

Oh right, I forgot to write the first line of what I was thinking. What I meant to start with is:

People may not be expecting the chance for a drop to be the same every kill though.

[Notso]

Oh right, I forgot to write the first line of what I was thinking. What I meant to start with is:

People may not be expecting the chance for a drop to be the same every kill though.

 

Ahh yes I get you now :P

[Mercathin]

I first off think the post is great and quite well done.

 

I would include the gambler's fallacy in the initial post, or at least allude to it.

 

Secondly, I feel the title could be better phrased. The information presented can benefit more than just those whom are intent on complaining.

 

Perhaps, "Please Read This To Better Understand Drop Rates" would be more agreeable.

[Elyan]

Well I think it would be more usefull to consider the probability *not* to obtain what you seek after N tries. Let's say it is 9/10 for 1 try, so it becomes (9/10)^N for N tries. Assuming you want a specific drop, if you expect less than 5% probability to fail you need to reach N=E(ln(0,05)/ln(9/10))=29.

[Bubsters]

If you can do the drop rates for this multishot mod myth,

 

that'd be great.

[Notso]

If you can do the drop rates for this multishot mod myth,

 

that'd be great.

 

Haha, I wish I could. Unfortunately I don't have any numbers as a starting point, never having recorded how many multishot mods I've got :[

 

 

I first off think the post is great and quite well done.

 

I would include the gambler's fallacy in the initial post, or at least allude to it.

 

Secondly, I feel the title could be better phrased. The information presented can benefit more than just those whom are intent on complaining.

 

Perhaps, "Please Read This To Better Understand Drop Rates" would be more agreeable.

 

1/ I will add that

2/ While the information can benefit more people than those who are upset with their bad luck, I don't think your title will be especially helpful in catching those people before they post

 

 

 

Well I think it would be more usefull to consider the probability *not* to obtain what you seek after N tries. Let's say it is 9/10 for 1 try, so it becomes (9/10)^N for N tries. Assuming you want a specific drop, if you expect less than 5% probability to fail you need to reach N=E(ln(0,05)/ln(9/10))=29.

 

I did that for the second part actually - probability to fail after 100 tries :P

[Muflon]

Hello! Since we have probability mathematicians here and I am deeply interested in probability, could you please check if this formula to compute the number of all rare mods dropping is valid (the number of enemies killed to get all the rare mods considering all rare mods drop only from foes)? P(mod_drop)*P(rare)*(number_of_rare_mods!/number_of_rare_mods^number_of_rare_mods) I know it computes the % probability, but just wanted to check if its a valid formula.

 

Thanks in advance

Edited May 16, 2013 by Muflon