The Math Of Farming

[elele]

Second, I hope DE thinks seriously about setting minimum drop rates and that the structure presented in this thread helps them think about the implications. For the Armored Agility example in the original post, for every person who manages to farm Armored Agility within 102 runs there will be someone who requires more than 102 runs to get the item. Think about that - half the community farming this item will not get it after 102 runs.

 

Pretty sure DE sets the drop rate as such with their own reasons. They must have looked how many runs an average player can tolerate to farm a specific item and then CALCULATED a specific probability number so that the vast majority of the players WILL NOT get that specific item. Because DE wants to encourage platinum trading for special items. 

 

Between the release of each Prime Access, releasing unobtainable mods is DE's way of making platinum. For example, High Noon -- Nov. 27, 2014; Four Riders -- Mar. 19, 2015; Armored Agility -- Jul. 2, 2015. Every three months or so, DE release an unobtainable mod that's worth a lot of platinum.

[Thief_Slayer]

Most of you guys are forgetting to include other variables. Yea armored agil is the "goal" but in that 51 runs of 99+% chance your also garunteed the other mods

[GoneBlank]

@elele: I don't think people have an issue with some things being "ultra rare", some being "rare" and some being "common". What I think annoys people is when they don't know what the true status of an item is and the ramifications that flow from that. For example, the current batch of mods (Armored Agility/Seeking Fury/Animal Instinct) are all advertised simply as "rare"; see link https://warframe.com/buyplatinum. The reality is that Armored Agility is ultra rare and Seeking Fury/Animal Instinct are common (at least from a statistical perspective). I suspect there would be quite a few people that would not have bothered looking for Armored Agility if they had a clearer understanding of the likelihood of success. I have no desire to farm for Armored Agility now that I know how many runs are involved just on getting to a 50-50 chance. I'll wait until it is on alert (or if - one day - I'm flush with plat then I'll buy it). I also suspect trade pricing would be much more straightforward if drop-rates were known with a higher degree of accuracy.

 

@Thief_Slayer: unfortunately the longer you play this game the smaller the pool of items becomes that you classify as a 'success'. I think Armored Agility is the only nightmare mod that I don't have.

 

PS I don't want to give the impression that I'm angry about anything - this is/was more of learning exercise for me than anything else.

Edited July 23, 2015 by GoneBlank

[(PSN)Draconis1981]

i knew this day would come! a use for math!

[BBOTAA]

Ehh just 1 more reply, to see if this post gets some more atention.

[Ham606]

I'm not sure why this post would need more attention. Most of us (including me obviously) lost the guy when he said something along the lines of:

 

"math math math, armored agility, math, math, more math, mod, math, math, even more math, math, math, farming, math, math, non-linear equations and advanced thermo-nuclear theory, RNG, drop, loot-table."

 

PS: I only understood the bold parts.

 

Long story short, we all get it. Farming is painful.

 

On-topic: I have really no clue what the thread is about, but kudos to OP for taking the time to go through this with simple English that I can understand.

[Odadda]

Long story short, we all get it. Farming is painful.

 

Yes, but how much is painful? That's what math (here) is about.

 

For istance, now that you know how many runs you are likely to do for Armored Agility, would you go farm one?

[Ishki88]

I'm shocked at myself, I actually understand the OP entirely.

 

Either way.

 

WTB Armored Agility 30p :^)

[Sitchrea]

@Sitchrea: Hello. The above math assumes the result of each mission is independent of any previous mission and that the drop rate for the item being farmed is constant. I don't think there is any type of "reset upon each mission" (but I'm not 100% sure - it's been years since I thought about this stuff seriously). All I'm looking at is the range of losing-streaks you need to consider for a given probability of success.

 

I know that RNG is all about luck and that low drop rates = unlikely outcome. Saying that drop rate for X = 0.67% is one thing - but saying that you may have to run up to 342 missions to have a 90% chance of successfully getting the item casts the issue in whole different light (well at least it did for me).

 

That's my whole thing - RNG in games does not stack each time you run the mission

 

If you run a mission to get an item with a .5% chance of dropping, running the mission twice does not make that item have a 1% chance of dropping. Every time you do that mission you role on a .5% chance.

[Ham606]

Yes, but how much is painful? That's what math (here) is about.

 

For istance, now that you know how many runs you are likely to do for Armored Agility, would you go farm one?

 

That is a good question really.

 

Generally I'm not a huge fan of numbers in that regard. Yes, it's a grind/farm game and yes loot is important, but I would rather have no clue how many runs it might need. I'd rather just get a couple of mates and go run nightmare modes for the sheer fun of shooting things while looking cool and laughing over VoIP software.

 

Maybe it's just me, but knowing the numbers takes a bit of the magic away. At the end of the day it sounds a lot better to say "hey fellas, let's go farm Armored Agility!" than saying "alright lads, we need 246 runs for Armored Agility, so stock up on energy drinks and smokes and get ready to forget how sleep feels like!"

 

I've gone both ways in the past. The first way is a lot more fun, for me at least. When Armored Agility feels like dropping for poor ol' me, it will :D

 

Again though, I do not wish to belittle the amount of work the OP put into this and the people who have the brain power to understand it. It is interesting surely, but I'd rather stay away ^^

[Odadda]

That's my whole thing - RNG in games does not stack each time you run the mission

 

If you run a mission to get an item with a .5% chance of dropping, running the mission twice does not make that item have a 1% chance of dropping. Every time you do that mission you role on a .5% chance.

 

Let's suppose you are flipping a coin.

 

it's evident that for a regular coin you have 50% chance of a tails and 50% chance of an heads.

 

Let's flip it twice.

 

The first flip has a 50% chance for each party while the second flip... still has 50% chance. As you stated each flip is indipendent, so is the chance to obtain a tails or an heads.

 

However let's now consider the chance I have to get 2 tails in a row. On the first flip I have 50% to have it, for the second flip we have to consider something else this time.

 

You see, if my request is to obtain 2 tails in those 2 flips, then it would be pointless to consider the chance to have a tails on the second flip if I got an heads on the first try. Thus I have to consider only the 50% to get a tails on the second flip over the 50% to get a tails of the first flip.

 

50% of a 50% (a.k.a. 0.5*0.5) is 25%, which is the chance to have 2 tails on 2 flips.

 

What is then the other 75%? Well is the chance to NOT have 2 tails, which means that AT LEAST one of the flips is an heads.

 

Now that we got the mechanism, let's go for 10 flips, and let's suppose we want 10 tails.

 

If we do a 50% of a 50% 10 times (0.5^10) we get around 0.097% , which also mean the other 99.9% is the chance to obtain at least an heads over 10 flips.

 

Let's translate it to something else. We'll now consider the flips as Nightmare missions and the tails as any raward that's not Armored Agility.

 

Chance for Arm. Agility is 0.67%, so the chance to not obtain it is 99.33%. Let's run 103 missions and consider the chance to never get it.

 

99.33% = 0.9933

 

0.9933 ^ 103 =  0.5005 = 50%

 

Which also means I have 50% chance to get the mod on one of those runs.

 

Consider it under this light: the more one tries, the more likely is to succeed because, even with very little odds, he cannot always lose. 

[Odadda]

That is a good question really.

 

Generally I'm not a huge fan of numbers in that regard. Yes, it's a grind/farm game and yes loot is important, but I would rather have no clue how many runs it might need. I'd rather just get a couple of mates and go run nightmare modes for the sheer fun of shooting things while looking cool and laughing over VoIP software.

 

Maybe it's just me, but knowing the numbers takes a bit of the magic away. At the end of the day it sounds a lot better to say "hey fellas, let's go farm Armored Agility!" than saying "alright lads, we need 246 runs for Armored Agility, so stock up on energy drinks and smokes and get ready to forget how sleep feels like!"

 

I've gone both ways in the past. The first way is a lot more fun, for me at least. When Armored Agility feels like dropping for poor ol' me, it will :D

 

Again though, I do not wish to belittle the amount of work the OP put into this and the people who have the brain power to understand it. It is interesting surely, but I'd rather stay away ^^

 

Fun should always be the top priority of every player, yet one should be prepared for certain things.

 

Now for istance we are talking about Armored Agility, but what if I name you Life strike? I cannot give out details, so I'll just say that Life strike... has the same issue as Armored agility.

 

Now, again, it is just a mod, but as you said this is a loot game, and drops define the ways a player can play and the content it can access. Simply saying that such mods are "rare" is not telling the harsh truth behind them. I don't want to criticise (criticize?) DE's way of making money, but I still belive a developer deserves is paycheck as much the player deserve to not be lied to. 

[Lightsmith]

Drop rates are fixed so your odds of getting it increase with every mission you don't get the item.

I'm just not sure I understand the goal of this. If the odds of an item being received is 10% per kill then you should receive one every 10 kills on average, of course that won't happen exactly like that so the more you kill the closer you get to the actual rate.

I.e. if you kill 10,000 you should have 1000 of the item.

Also if loot is determined at the time of death (opposed to the enemy having an inventory) which is how it is, failure would not need to be factored in as you don't miss a potential item and reset.

Any char would show that odd increase for each mission you don't receive the reward you are looking for.

But to create the curve you would just poll people how many times that ran the mission to receive the reward. Chart those results, from that you can use tool to graph your curve based on various reports.

X axis would be number of times run.

Y axis would be number of people who received the item on the nth run.

This will create a statistical bell curve. Overall this will match the drop rate with a large enough data pool.

If you create a straw poll you can have people put how many runs and the result (given enough data) will show the Bell curve (pivoted)

Of course the number of entries on the poll would be quite large so such a method may not be possible.

Honestly if a mission reward is 10% the Bell curve will be at its peak at 10 missions.

https://www.mathsisfun.com/data/standard-normal-distribution.html

Edited July 23, 2015 by Lightsmith

[GoneBlank]

Hello Lightsmith: "drop rates are fixed" - agree (or, at least that's my understanding. Coding anything other than that would be painful).

 

"so your odds of getting it increase with every mission you don't get the item" - disagree.

 

As Sitchrea says above "If you run a mission to get an item with a .5% chance of dropping, running the mission twice does not make that item have a 1% chance of dropping. Every time you do that mission you role on a .5% chance." Restated, your past failures do not improve your probability of a success.

 

Your bell-curve example: I see more along the following lines. Imagine you are able to analyze the results of people trying to farm for Armored Agility (which according to the wiki has a 0.67% drop rate). If you look at multiple samples of 1000 outcomes there may be 6 drops, do it again...again....again....you will see results like 5/7/6/..... the top of the bell (most frequent result after looking at enough samples) would be 7. There would be dispersion - the sides of the bell (you might see some 3/4's or 9/10's). I have a vague recollect that the central limit theorem is behind this.

 

Anyway...what was the goal of all this? Well - for me - I found it difficult to contextualize drop rates. Sure, I know that 0.67% drop rate (for a mission reward is low), but what does that really mean? It means that I have to run the mission 102 times just to have a 50% chance of receiving the reward. I find that statement more tangible. Even though it is exactly the same information - in some instances presenting information in a different form is more intuitive to people.

[Lightsmith]

Hello Lightsmith: "drop rates are fixed" - agree (or, at least that's my understanding. Coding anything other than that would be painful).

"so your odds of getting it increase with every mission you don't get the item" - disagree.

I don't mean coding wise I mean statistically.

Example.

If you flip a coin the more heads you get in a row the higher the probability the next flip will be tails. Perhaps I said odds in error, I meant probability.

Edited July 24, 2015 by Lightsmith

[321agemo]

I don't mean coding wise I mean statistically.

Example.

If you flip a coin the more heads you get in a row the higher the probability the next flip will be tails. Perhaps I said odds in error, I meant probability.

Kind of.... Sorta.... Not really?

I think i get what your saying, but i think you're thinking it the wrong way?

Lets say you flipped the coin 50 times and every time its head. Now you're about to flip the coin for the 51st time. What is the probability it landing on heads?

Its still 50%, as the first 50th times you done it is ignored in the equation in probability.

[GoneBlank]

The more heads you get in a row has absolutely no influence on the probability that the next flip will be tails. If it is a fair coin it will be 50% heads, 50% tails, regardless of what you have previously flipped. The outcome of a toss is independent of anything that has happened previously.

 

I suspect you wouldn't be alone in your thinking - I suspect psychologists/behavioural economists would be all over this as a field of research. The notion that I haven't won the lottery for the last 20 years so I am more likely to win tonight is probably what drives the bulk of lottery ticket sales.

[Hypernaut1]

The more heads you get in a row has absolutely no influence on the probability that the next flip will be tails. If it is a fair coin it will be 50% heads, 50% tails, regardless of what you have previously flipped. The outcome of a toss is independent of anything that has happened previously.

 

I suspect you wouldn't be alone in your thinking - I suspect psychologists/behavioural economists would be all over this as a field of research. The notion that I haven't won the lottery for the last 20 years so I am more likely to win tonight is probably what drives the bulk of lottery ticket sales.

yes you are right, but the chances of flipping 10 tails in a row is NOT 50%.  Thats what the post is getting at.- its like a meta of probability. If something has a 10% chance at dropping, overall, there is a good chance it will drop within 100 tries. it may be at the beginning, or it may be at the end. so basically- after a certain number of tries you're more likely to have succeeded at one point, than to have not succeeded. If i flipped a coin 20x, there's a 90% chance that i got at least 1 heads and 1 tails at a certain point. Same goes for playing a mission, where after a certain number of tries the chances of having had success is greater that the chances at never having success.

 

Its not gamblers fallacy, but sounds similar. 

Edited July 24, 2015 by Hypernaut1

[GoneBlank]

I hadn't heard the term 'gamblers fallacy' before.

 

https://en.wikipedia.org/wiki/Gambler%27s_fallacy

 

Interesting read.

 

I agree with you that after a certain number of tries you're as likely to have succeeded than to have not succeeded. I put that number at ln(0.5)/ln(1 – drop_rate) - 1.

[Lightsmith]

The statistical probability of getting 10 coin flips resulting in heads is less likely than getting 9 coin flips as heads. It's the law of averages the longer you go the closer to the odds you get.

You have to look at the scope, yes the next individual coin flip is 50/50 but when viewing the full number of flips the further you are from the odds of 50/50 the higher the statistical probability is you will shift back towards the odds.

Example odds of getting a Royal Flush in poker is about 31,000:1. You see a person get that you'd be impressed. If he does it again would you be equally impressed or more, and a third time, etc.

Everyone would be more impressed each time because statistically its even greater odds. The odds are not simply repeated when looking at stastics they become exponential. I.e. 31,000^2. That represents a much less likely chance of it happening, from a macro view.

In fact your statement about not winning the lottery so you are more likely to win is correct understanding 2 things, 1. You play the same numbers every time, 2. You played every time for 20 years. Of course the change in odds is so minute it isn't something to bet on as a basis.

Statistics bra.

Edited July 24, 2015 by Lightsmith

[Ham606]

Fun should always be the top priority of every player, yet one should be prepared for certain things.

 

Now for istance we are talking about Armored Agility, but what if I name you Life strike? I cannot give out details, so I'll just say that Life strike... has the same issue as Armored agility.

 

Now, again, it is just a mod, but as you said this is a loot game, and drops define the ways a player can play and the content it can access. Simply saying that such mods are "rare" is not telling the harsh truth behind them. I don't want to criticise (criticize?) DE's way of making money, but I still belive a developer deserves is paycheck as much the player deserve to not be lied to. 

 

Fair point, but in reality how prepared can one be?

 

When someone is about to start playing Warframe (or any game that involves loot lists and grinding for that matter) for the first time he's not going to ask how rare or how mathematically impossible are certain mods that he will either way have no clue of what they're doing. And no developer is his right mind will advertise the truth.

 

"Join now and you can get a Life Strike mod in just under 500 runs!"

 

At the end of day, nobody wants the harsh truth (and that is a really long discussion for another thread) and developers know it. They will play to their strengths, and just not give out everything because as you said they need to make money. It is not as much as being lied to, rather than not getting the whole truth at the start. Then again, almost everything in the world works this way, can we really blame a developer with a technically free-to-play game?

 

PS: Both criticise and criticize are correct :P

[GoneBlank]

@Ham606: Fair points. I still think we could have broad classifications of items (e.g., ultra-rare/rare/uncommon/common) that actually corresponded to their drop chances. It would give people much more realistic expectations when farming (and I suspect result in less 'why hasn't this dropped yet?' threads).

 

@Lightsmith: Assuming cards are dealt from fresh decks (putting aside issues of replacement etc), the probability of the second Royal Flush is the same as the first Royal flush. So I would say they are both equally probable (improbable?) events. The probability of getting two in a row is a different event - agree, that's extraordinarily improbable. So I think one needs to be specific about the event being referenced. The probability of getting two Royal Flushes in a row is a joint probability event. {PS For me a Royal Flush would be an Ash BP.}

[Coryphaus]

Making mods or parts guaranteed to attain after a "reasonable" amount of runs guarantees they will be traded as "junk parts/mods" on trade chat.

 

Perhaps the solution is to include a complex and involving gear/weapons customisation/upgrading process via day/week-limited crafting components that you can farm for with reasonable success.

 

That way people won't try to grind for "rare" mods and parts. They'd play missions to get components and if a prime part or mod drops that is a bonus. The value of these parts and mods will also be preserved as far as is possible.

[Coryphaus]

RE: Statistics

 

Perhaps the question that these mathematics answer is not so much "how many times do I have to run the mission to succeed once" but what range of attempts gives me what probability of success.

 

Next, the necessity of a dedicated human operator, and putting certain rewards behind time-dependent mission types guarantees that brute force attempts will be hampered by the time requirements and simple human fatigue.

When you see that 100 attempts equals a minimum of 2000 minutes = 33.33 hours for the LOW range of probability the player should realize that it is not a feasible goal to "grind" for rare parts.

 

There is a slight difference between this and that of calculating the odds of a shark attack or plane crash in a given population. The similarity is that based on the odds, a certain number of outcomes is guaranteed per population. However no guarantees can be made regarding who or when the outcome happens to.

 

I would greatly appreciate it if my logic with regards to this could be assessed.

 

~~~~~~~~~~~~~~~

 

We might have noticed that Cephalon Simaris and Conclave, Syndicate rewards have moved towards a more predictable form of getting rewards. I think the response has been good, perhaps we could have more of that.

Edited July 24, 2015 by Coryphaus

[Odadda]

 Ham606, at this point I think it's down to personal preferences the way one wants to play. Don't get me wrong, I still have fun playing the game, Nightmares included, even thought I have very little odds to get a rewards I don't own already. Point is

 

 

It is not as much as being lied to, rather than not getting the whole truth at the start. 

 

counts as a lie to me, as long you have been driven to think something different to reality. To say, both Streamline and Armored Agility are gold mods.

 

I don't pretend DE gives out their schemes, yet

 

I still think we could have broad classifications of items (e.g., ultra-rare/rare/uncommon/common) that actually corresponded to their drop chances. It would give people much more realistic expectations when farming (and I suspect result in less 'why hasn't this dropped yet?' threads).

 

would be a far more honest way to "inform" us of such rarity.