Warframe - Math and statistics - Quantifying the Grind

[master_of_destiny]

Hello all,

 

At this point I find that many people complain about the grind from things, but can never seem to quantify the problem.  I'd very much like to take a look at some of the most horrible grinds in this game, separate the RNG, and make people aware the garbage.

 

Eidolons

Let's start with something that everyone has seen before, Eidolons.  Is it reasonable to go out and expect to get a fully ranked arcane from an Eidolon in a week, a month, or will it take multiple months?  Let's do the math.

 

If we check the drop tables, the Hydrolyst when captured has a 5% chance of dropping any of the three highest level arcanes.  This means the chance of getting a drop can be expressed mathematically as:

p=1-(1-0.05)ⁿ where p is the probability and n is the number of runs.

This yields different numbers than we would inductively consider.  Instead of two runs having a 10% probability you actually have 9.75% probability.  This is because the four potential states are drop and drop, no drop and drop, drop and no drop, or no drop and no drop.  Basically, as you add more drop chances the probability decreases so that it never exceeds 100%.

 

What does this mean?  Well, it means for a 50% chance to get something you need 14 runs.  For a 99% chance you need 99 runs.  That means somebody out there actually ran the Eidolon capture 100 times and didn't ever see an Arcane Grace.

 

It also means that to get 21 of the arcanes for a fully ranked one you need to multiply the individual chances to see the probability of getting a drop to get the probability of getting the required number of drops.  That's a long way to say the the probability of getting all 21 drops gets tiny quickly.  As an example, what does it take to have a 50% chance of getting all 21 drops?  Well, p^21=0.50.  p = 0.9678, so 67 runs 21 times.

In short, to have a 50% chance of getting at least 21 arcane drops at 5% each the Hydrolyst needs to be captured 1407 times with only a 3% drop of players each round.

-Edit-

I have clarified the underlined from the original.  Basically, I'm saying each round you lose 3% of players due to burn out for each arcane drop.  This is not the average chance of getting the reward, assuming of course that the RNG reward function is 100% accurate.  It is saying that 50% of players will at least have the 21 required arcanes, many will have less, and the hard grinders will have inventories to sell so that platinum trades can benefit them.

-Edit end-

 

Let's work backwards, and say you can do 4 captures in a night with a mix of coordinated groups and random players.  You have a life outside the game, so you get one night cycle per day to work.  That's 1407/4 = 351.75 days.  So, if you grind every single day for an entire year you have a 50% chance of getting the rarest arcanes.

 

Now, let's say you go out and buy said arcanes from somebody else.  150 platinum a piece, means 3150 per fully ranked arcane.  You get 2625 platinum for buying the prime access pack at 80 USD, so let's call this 4 prime access packs to buy the three arcanes.  It'll be slightly less, but 80*4 = 320 USD.  This amount to less than a dollar per day of grind, which is an hourly compensation rate of 1.22 USD per hour of grind.  You can literally work a minimum wage job and buy prime access and it values your time orders of magnitude greater than the game does.

The counter argument here is that you enjoy playing the game, but 4 eidolon runs per night for an entire year is going to sap all of that joy.  This is especially true when this only represents an assured maximum rank arcane for 50% of players.

 

 

 

Necramechs

With new content comes new grinds.  Introducing the Necramechs.  Each one now requires you grind out new mods, and the mod drop rate is set like most mods....specifically sub 1%.  How bad is this?  Well the tier 3 isolation vaults have 3 mechs spawn.  Each has a 0.201% chance of dropping.  What does our equation look like?

p₃= 1-(1-0.00201)^^(n*3)

The worst part of this is that tier 1 and tier 2 also pull from separate mod pools.  Their drop rates are:

p₂= 1-(1-0.00201)^^(n*2)

p₁= 1-(1-0.00201)^⁽ⁿ⁾

 

The net effect here is that you need 345 total drop chances for a 50% chance at one of these mods to drop.  If we're looking at tier 3 mods with a full run of 40 minutes it's 115*40 = 76 hours and 40 minutes.

 

 

The Conclusion:

The conclusion here is that even with the pay to progress reasonably mod drop chance booster this system is utter mindless grind.  Let me frame things correctly, the reason that the community lost their collective cool when the arcane change was announced was related to this insane level of grind.

 

What did DE do?  Well, they promised Scarlet Spear.  It was a poorly received operation, as it focused on insane levels of grind on a buggy system.  Nobody can rationally argue otherwise.  As of today though, new players do not have this option.  The arcane grind is garbage for the most desired ones.  Likewise, the introduced grind for necramech mods is utterly horrid.  115 runs for a reward is bad, 345 is insane, and the drop chances actually being stacked such that most runs of the isolation vault will not drop a mod is utterly insulting to our intelligence.  Doing the math, it's almost 2 weeks of a full time job for just one mod to have a 50% chance of dropping.  That's silly.

 

So, when people complain about the grind in this game it's time to listen and measure.  Are they complaining about poor RNG rolls, or are they talking about a system heavily stacked against getting rewards?  Please, do the math for yourself, as it isn't hard.  For me, arcanes and necramech mods are DE doing a terrible job of balancing rewards and grind.  It's insulting to the players, and we need to make it clear.  Barring that, DE will continue with these garbage drops to increase engagement.  I for one believe that this crosses that line in the sand between free to play done well, and pay or endure miserable grind.  That's a disappointment from a company whose social media still touts interviews where the discussion is about removing gambling systems.

 

I also want to make it clear this is but two examples.  Steel Essence, Vitus Essence, Braton Prime, Kuva Weapons, and a litany of other items bear the same inherent flaws of grind over content.  I don't choose to elaborate on them here because I'll inevitably have people defending these grinds here and need to explain.  To be clear, if you want 20+ hour boss grinds and the like the above is probably just par for the Korean grind-MMO course.  The issue is that warframe is selling prime access, vault access, tennogen, cosmetics, basic gear slots, and so many other things that tacking on these huge grinds for basic power is not acceptable.

[DrivaMain]

The thing you are forgetting is they are currently optional. Arcanes and necramech (currently) are not necessary for the main progression, so DE can get away with unreasonable drop rates. If they addresses these drop rates they would have already addressed that monstrosity of multi layer RNG that is the riven mod system.
 

In Arcane’s defense. At least once you do 1407 Hydrolyst you can gather enough other hydrolyst arcanes to sell and buy a max rank platinum arcane. The most common trickery is 25 plat per 21 piece and you get 67 rank 5s from those runs.

Oh and you are forgetting in those 1407 Hydrolyst runs you also got 1407 Gantulyst Arcanes and 1407 Teralyst Arcanes to sell.

and counter argument, there are players who enjoy Eidolon Hunts even after they collected everything (myself included). You may not like the gamemode, but others do.

To end it all, Why is DE doing this? Encouraging players to spend money by nudging with these methods to do so. At the end of the day, they are a business and needs money to survive.

Warframe’s grind is still nothing compared to those korean MMOs or other asian MMOs in general.
 

[(PSN)Madurai-Prime]

Welcome to online games, it's gonna be like this mostly anywhere you go. PC gets Plat discounts. Console gets 370p for 20 bucks or a Prime unvaulting for 150 with 4k plat. There's your Energize, guardian and whatever else you want. 

This is a business and not a charity. Online games are about patience and building over time. If you need something immediately, they offer that option. A one time purchase and you never have to touch the content ever again. 

[o0Despair0o]

38 minutes ago, master_of_destiny said:

p=1-(1-0.05)ⁿ where p is the probability and n is the number of runs.

And that's where you lost me.

 

I knew I was bad at math but hory sheet I don't understand anything about this. Might as well be hieroglyphs right there.

[Krankbert]

vor 5 Minuten schrieb o0Despair0o:

And that's where you lost me.

 

I knew I was bad at math but hory sheet I don't understand anything about this. Might as well be hieroglyphs right there.

0.05 (or 5%) is the probability of getting Arcane Grace. (Percent is just shorthand for 'divided by 100'.)

1 - 0.05 (or 100% - 5%, or 95%) is the probability of not getting Arcane Graces.

95% times 95% (or (95%)² is the probability of not getting Arcane Graces in two attempts. 95% * 95% * 95% (or 95%)³ is the probability of not getting Arcane Graces in three attempts. (95%)ⁿ is the probability of not getting Arcane Grace in n attempts. (That's just shorthand for 'multiplication by itself'.)

1-(1-0.05)ⁿ or 100% - "the probability of not getting any Arcane Graces in n attempts" is then the probability of getting at least one Arcane Grace.

[bejuizb]

I've mostly relied on discounts for when I get burned out over the years and return for new content drops. That nets me enough plat to buy a good chunk of stuff. It's the case with a lot of games that working a real job will be more efficient and time friendly than grinding the game out. 

[nslay]

The < 1% chance mods are definitely questionable for Necramechs. I think 2-3% is definitely more reasonable.

Remember the Sentient mods before Scarlet Spear? Vengeful Revenant, for example, didn't exist for most people. It's a 0.42% drop chance from Conculysts (before all the new Sentient enemies were added).

Now compare this situation to Necramech mods:

Sentients

• ~5 minute Lua missions for 2 Sentients (and it's possible that neither Sentient is a Conculyst... or even that both are Conculysts).
• Ropalolyst run 4 Sentients spawn. This is a pretty short mission and you can get up to 4 Conculysts!
• Now we have Railjack anomalies with more Sentients! Although these missions can be lengthy depending on the anomaly node.
• Rare Conculyst mod drop chance? 0.42%?

Necramechs

• Each Necramech has a different drop table per tier.
• Six Necramechs in ~40 minutes.
• Intensify/Streamline drop chance? 0.2%
• Reach, Stretch, Hydraulics, et al.? ~1%
• T1 == 1 draws from T1 Necramech drop table.
• T2 == 2 draws from T2 Necramech drop table (but not T1).
• T3 == 3 draws from T3 Necramech drop table (but not T1 or T2).

I mean this is obviously a lot more grindy than Sentient mods used to be. The time difference? 40 vs 5 minutes per attempt? Tiered drop tables for < 1% drop chances?

I'm not complaining... but that's how it is. This will be a long drawn out farm (longer than Sentients) and better get a mod booster from Baro next time he brings it (or maybe you'll get one from Sorties).

References:

https://warframe.fandom.com/wiki/Vengeful_Revenant

https://warframe.fandom.com/wiki/Necramech_(Enemy)

[C-Core]

This post is literally the reason I haven't got any good arcanes, even at MR 26 with 3k hours on steam as a mostly F2P player. DE thinks making the good rewards harder to get will make people play more, but for me, it did the opposite. I tried farming arcanes once, and I kept getting the same crappy ones over and over and over and over. What did I do? Stop doing eidolon runs. I wasn't going to go do these semi annoying boss fights just for a CHANCE to get ONE of the many many arcanes I'd need to max out whatever one I wanted. It's an utter joke. The fact that DE think people will want to do this is just absurd, and like you said, an insult to us.

As far as necramechs go, I haven't even gotten a necramech yet. I've had literally 2 of the same broken part drop out of all of my vault runs, and the update has been out for 2 weeks. Sure, I haven't been doing the vault runs constantly, but I've been doing quite a damn lot of them, and I literally cannot get my hands on the parts. It just makes me want to get the thing less and less the more I do it. I'm very close to just giving up on the necramechs now.

The problem here is that it's mindless grind - you don't see any progress as you're going through. You see the same crap drop over and over, and feel like you're just standing still, getting nowhere. If I actually felt like I was progressing something, I might want to do it, but I'm not. It's the main thing that's making players leave this game imo. They see past the shiny new update where the art team did a great job, and see the same stuff they have to slog through for hours on end just to get a chance at getting something they want, and they leave. And honestly, I don't blame them.

I understand that the game is grindy. The game has always been grindy. Even back when I first played in 2015, I thought "Wow, this takes a while to get x thing". But it was never as bad as this. 

Sure, people say "You don't *need* to get a necramech to progress, or you don't *need* arcanes to be strong", but, the point is, warframe is a game about collecting things. Doing everything you can to get everything you can to make yourself stronger to do it more efficiently. If someone can't collect something that they want, and are getting cheated by low drop rates, they're not going to want to play...

[Buff00n]

When you're talking about a probability P of something, where 0<P<1, it's far easier to talk about the expected average, which is simply 1/P.  Anyway, I think I was with you until here:  

1 hour ago, master_of_destiny said:

As an example, what does it take to have a 50% chance of getting all 21 drops?  Well, p^21=0.50.  p = 0.9678, so 67 runs 21 times.

In short, to have a 50% chance of getting at least 21 arcane drops at 5% each you need to capture a Hydrolyst 1407 times.

Your expected average for a single P probability drop is 1/P tries, and if you need N of them then it turns out to be (1/P)*N.  In this case, your expected average to get a complete set of one single arcane is (1/0.5)*21 = 420 runs. 

I'm not sure exactly how you came up with 1407, but if you're trying to figure out the expected average for all three rare arcanes then you can't just multiply by three.  They're not independent variables, because you don't just farm one arcane at a time.  When you have multiple drops in the same drop table the math becomes so complicated that it's easier to just run a simulation.  Here is that simulation for getting 21 of all three rare Arcanes dropped by the Hydrolyst:

The expected average turns out to be around 500, with the 90th and 99th percentiles around 600 and 700.  That's still a crap ton of Hydrolyst runs, but it's not 1400.

Interestingly, if you add in getting 21 all the rest of the arcanes the Hydrolyst drops then it barely makes a dent in the expected average, those three rare ones are that hard to get.  Here is that simulation for getting 21 of all the arcanes dropped by the Hydrolyst:

Anyway, I think regardless of whether you use my numbers of yours, the conclusion is you're better off just waiting for the Scarlet Spear event to return.

 

1 hour ago, master_of_destiny said:

Necramechs

Oh man, the Necramech mod grind is possibly the most brutal in the game, if the published drop rates are correct.  Here's the simuation and here's the distribution:

Necramech Streamline is a killer; the fact that its drop rate is an order of magnitude less than the other four gives this distribution an incredibly long tail.  The expected average of frickin' 700 is bad enough, but this distribution shows that a small number of unlucky players will take thousands. 

I think the conclusion from this is don't even bother to farm these mods right now.  The drop rates will be adjusted, or they will get added to Loid's syndicate offerings, or Necramechs will become another system gathering dust.

[C-Core]

4 minutes ago, Buff00n said:

Necramech Streamline is a killer; the fact that its drop rate is an order of magnitude less than the other four gives this distribution an incredibly long tail.  The expected average of frickin' 700 is bad enough, but this distribution shows that a small number of unlucky players will take thousands. 

I literally don't even understand what is going through DE's head when they think of drop chances. Though I'm pretty sure they're like "Pick a number between 0 and 1!" and then another guy goes "0.015 LOL", and then they use that as the drop chance for a mod.

[Skaleek]

12 minutes ago, Buff00n said:

I think the conclusion from this is don't even bother to farm these mods right now.  The drop rates will be adjusted, or they will get added to Loid's syndicate offerings, or Necramechs will become another system gathering dust.

This is the best advice for anyone. When i factor'd in the time it takes to get necramech kills/hour, I knew that this would get changed. This is insanity levels of grind and to top it off the other rewards you are getting meanwhile are incredibly lackluster and have other far more efficient methods of acqusition (the relics, the resources from the vaults, etc).

[DrivaMain]

6 minutes ago, C-Core said:

I literally don't even understand what is going through DE's head when they think of drop chances. Though I'm pretty sure they're like "Pick a number between 0 and 1!" and then another guy goes "0.015 LOL", and then they use that as the drop chance for a mod.

The correct term is multi layer RNG. a Necramech Mod for example Have a 10% chance to drop, but when that number hits that 10% the drop table that contains all of necramech the mods is then rolled for one of the necramech mods that is going to drop. Necramech streamline for example has 2.01% drop chance in the necramech mod drop table.

[Kraethius]

Yeah, the Necramech mod grind is the reason I got burnt out now. I did quite a few runs each day until I found out the drop chance and just felt cheated. Whether or not that feeling was justified I'll leave to the reader but I just lost all motivation to do anything in the game, unsurprisingly including Hydrolyst farming.

[ryu-hayabusa1]

2 hours ago, master_of_destiny said:

The conclusion here is that even with the pay to progress reasonably mod drop chance booster this system is utter mindless grind

I would like to confirm that,  by saying ,  I've run ISO vaults 15+ , with an active mod drop chance booster and still no rare nechramech mods, sometimes with a Nekros,too.

[AnimatedJester]

Literally the only reason to go hunting for Necramech Mods at the moment is if you really want to feed on the suckers that will pay exorbitant prices just to not have to farm for it when it is an extremely rare drop. I have 3.8k hours logged in this game on Steam (2.3k in missions)  and I have no qualms waiting for the drop tables to be increased or the acquisition be enhanced in some way. I already am at max rank for both of the new syndicates and aside from maybe needing to hop on every 24 hours to feed a new frame to the Helminth / give tokens to a syndicate I have Zero Reason to play the game now and throw my face at a brick wall of RNG.

I am not screaming content drought or complaining that I got through the content too quickly. I enjoyed the pace i took getting to that max rank. I am voicing my complaint only about drop rates on items that, for all intents and purposes, should not be balanced based on normal drop tables of enemies we loot by the dozens when at best we are able to fight 6 in ~20 minutes (assuming you ignore the bonus objective of opening the vault and leave as soon as you loot the mechs).... But in doing it in that manner, you cripple yourself in farming the drop table rewards of the weapon parts since you will only get 1 per mission as opposed to 2 for completing the bonus.

[BahamutKaiser]

I'm pretty sure some of this math is wrong, I haven't killed 20 Necramechs total, and I have 6 Necramods. 

The grind is sorta unreal, but these figures paint a false image of gains, the game supports trading with premium currency, and many of the Arcanes from Eidolon have effective liquidity. This means that the total auxiliary gains and platinum accessed acquires these arcanes and even Necramods much faster in a complete experience.

A player who wants to grind in isolation of the economy will suffer unreasonable average by choice, not design. 

In order to get a complete look at the actual effort value toward gain, the drops should be compiled as a liquid aggregate of all exchangables earned and the time it takes to acquire enough platinum to get everything a player wants, not just a single item in isolation of the economy. 

That's kind of like saying bread is to hard to acquire because you need to fell a forest, to clear the land, to lay a crop, to grow the crop... you just have to buy it from the store for a pittance in reality.

There are several META squads out there that do 6x3 several times an actual day to earn platinum from other players, and fill the market with arcane access. 

I agree that they should dramatically increase the loot offered, and add several layers of guarenteed access to prevent unreasonable misfortune, but that's mostly so more casuals can access the complete content of the game rather than having a dramatic minority of the game with tremendous advantages over most customers. 

They could make Necramechs drop a guarenteed mod every time one goes down, so most players will at least have the common mods, and they could double the number of arcanes acquire with each Eidolon, maybe triple on Steel Path, so the general supply would increase and make them more affordable. 

But there's an important lesson in being accurate rather than using mathematical hyperbole. You don't properly support your opinion by making unrealistic claims. 

[schilds]

9 minutes ago, BahamutKaiser said:

I'm pretty sure some of this math is wrong, I haven't killed 20 Necramechs total, and I have 6 Necramods. 

I haven't looked at his maths to check whether it's correct, but one anecdote/sample proves nothing. The flip side of there being some percentage of players expected to have bad rng, is that there is some percentage of players expected to have good rng. Your personal experience doesn't confirm or deny his claims.

[Buff00n]

3 minutes ago, BahamutKaiser said:

I'm pretty sure some of this math is wrong, I haven't killed 20 Necramechs total, and I have 6 Necramods. 

I have a handful of common Necramech mods as well, but I don't remember exactly where they dropped.

OP is referring to the five Necramech mods mentioned in the official drop tables as dropping from the Necramechs themselves.  Now that I look closer, I don't actually see any of these mods in the in-game Codex, and they don't work as chat links, either.  It's possible the drop table page has some bad and/or unreleased info.  I also don't see the Isolation Vault bounty drops on there either.

As to your other point, in general I agree that trading is supposed to be the game's relief valve on bad luck.  However, with OP's example of the rare Hydrolyst arcanes, you're looking at a minimum of around 1200P to complete some of those sets.  At that level, trading becomes just a different kind of grinding if you're not into that kind of thing.

[master_of_destiny]

3 hours ago, Buff00n said:

When you're talking about a probability P of something, where 0<P<1, it's far easier to talk about the expected average, which is simply 1/P.  Anyway, I think I was with you until here:  

Your expected average for a single P probability drop is 1/P tries, and if you need N of them then it turns out to be (1/P)*N.  In this case, your expected average to get a complete set of one single arcane is (1/0.5)*21 = 420 runs. 

I'm not sure exactly how you came up with 1407, but if you're trying to figure out the expected average for all three rare arcanes then you can't just multiply by three.  They're not independent variables, because you don't just farm one arcane at a time.  When you have multiple drops in the same drop table the math becomes so complicated that it's easier to just run a simulation.  Here is that simulation for getting 21 of all three rare Arcanes dropped by the Hydrolyst:

The expected average turns out to be around 500, with the 90th and 99th percentiles around 600 and 700.  That's still a crap ton of Hydrolyst runs, but it's not 1400.

Interestingly, if you add in getting 21 all the rest of the arcanes the Hydrolyst drops then it barely makes a dent in the expected average, those three rare ones are that hard to get.  Here is that simulation for getting 21 of all the arcanes dropped by the Hydrolyst:

Anyway, I think regardless of whether you use my numbers of yours, the conclusion is you're better off just waiting for the Scarlet Spear event to return.

 

Oh man, the Necramech mod grind is possibly the most brutal in the game, if the published drop rates are correct.  Here's the simuation and here's the distribution:

Necramech Streamline is a killer; the fact that its drop rate is an order of magnitude less than the other four gives this distribution an incredibly long tail.  The expected average of frickin' 700 is bad enough, but this distribution shows that a small number of unlucky players will take thousands. 

I think the conclusion from this is don't even bother to farm these mods right now.  The drop rates will be adjusted, or they will get added to Loid's syndicate offerings, or Necramechs will become another system gathering dust.

 

So, here's the base assumption that you're working with and I'm not.  I don't just want a rare arcane, I want a specific rare arcane.  It's thus not a (5%+5%+5% =15%) chance, but a 5% flat chance.

1407 is the result of:

67 runs for a 0.9678 chance at getting a single drop

21 drops required.

0.9678^21 = 50% drop chance (so individual drop chance needs to be 97%, for 21 total rounds, to get the 50% attainment figure)

 

I can appreciate that you've done the work to show a normal distribution curve.  I'm a bit too lazy to put in all of that work, given that my goal is simply to demonstrate the insanity of grinding this stuff out.  It's also a question of valuing player time....and I don't need to see the 1% figures to know that this is horrendous grind.  The point was never to try and give everyone a deep understanding of the statistical probabilities, but a general understanding of how a 5% chance can feel so utterly horrible despite the inductive logic in our heads.

Case in point, inductively 5% means a 1 in 20 chance.  This would mean 420 runs to get 1 full arcane.  Mathematically half of all people get it in under 1407, while half require longer.  That's off by a factor of more than 3 because inductive logic and statistics are not friends.  It's what I was attempting to demonstrate.

[master_of_destiny]

57 minutes ago, BahamutKaiser said:

I'm pretty sure some of this math is wrong, I haven't killed 20 Necramechs total, and I have 6 Necramods. 

The grind is sorta unreal, but these figures paint a false image of gains, the game supports trading with premium currency, and many of the Arcanes from Eidolon have effective liquidity. This means that the total auxiliary gains and platinum accessed acquires these arcanes and even Necramods much faster in a complete experience.

A player who wants to grind in isolation of the economy will suffer unreasonable average by choice, not design. 

In order to get a complete look at the actual effort value toward gain, the drops should be compiled as a liquid aggregate of all exchangables earned and the time it takes to acquire enough platinum to get everything a player wants, not just a single item in isolation of the economy. 

That's kind of like saying bread is to hard to acquire because you need to fell a forest, to clear the land, to lay a crop, to grow the crop... you just have to buy it from the store for a pittance in reality.

There are several META squads out there that do 6x3 several times an actual day to earn platinum from other players, and fill the market with arcane access. 

I agree that they should dramatically increase the loot offered, and add several layers of guarenteed access to prevent unreasonable misfortune, but that's mostly so more casuals can access the complete content of the game rather than having a dramatic minority of the game with tremendous advantages over most customers. 

They could make Necramechs drop a guarenteed mod every time one goes down, so most players will at least have the common mods, and they could double the number of arcanes acquire with each Eidolon, maybe triple on Steel Path, so the general supply would increase and make them more affordable. 

But there's an important lesson in being accurate rather than using mathematical hyperbole. You don't properly support your opinion by making unrealistic claims. 

 

Let me help you.  The Necramech mod on the high end is a 0.201% chance of dropping.  The total likelihood of a mod dropping is about 10%.   

 

This means the chance per mech to not drop a mod is 90%.  You can then do the math on your own, and figure out what the likelihood is of getting your result.  Let's see:

((6*.1)+(14*.9)/20 = 13.2/20 = 0.66 = 66%  What does this mean?  66% of the total population in 20 runs will have the same outcome as you did (6 drops, 14 no-drops).

 

 

Now, stopping for a minute, were any of those mods common or uncommon?  Were any rare?  The rare drops at 0.201%, while the commons have greater than 1% chances.  That's the mathematical discrepancy here, not your experience.  You'll also note that this is an overall probability.  There is somebody out there statistically that got 3 rare mods in a vault run.  It's just a 0.00201³*0.99799³ chance, or 0.00000000807 = 0.000000807% chance.  It'll only tale about 100,000,000 chances to see it come up. 

 

-Edit-

How about you do some reading before you suggest that somebody else doesn't understand?

I ask because you seem to want to call me out, and haven't bothered to even see that I'm stating a single mod drop chance is 0.201%.  That's backed up by the drop tables and information on the wiki.  Your inability to understand the difference between getting a drop and getting a specific drop doesn't mean that somebody is wrong.  It also points to your fundamental inability to read and understand, but entitlement to dismiss is high.

 

Let's also not be stupid.  At 0.201% drop chances it only took 500 random runs for some group to get the rare mod on their first try.  Yep, 0.201% = 0.00201, so 500*0.00201 > 1, so in a normal distribution somebody will have gotten the rare mod.  Please refer to Buff00n's work above to see a normal distribution curve.

 

Finally, assumptions were made.  You obviously read them, given that your retort was the generic "but meta does it faster."  It's a stupid response though.  It's stupid because even a meta group could be in that above 50% group.  That means even 50% faster than the stated assumption would require more than a year of grind.  Of course, that's always the excuse, isn't it.  You can do eidollons faster as a coordinated group, and you can do two in a night.  It's not really acknowledging the assumptions given, but it must negate the argument.  Right?  Oh....no it doesn't.  It's also why I stated the assumptions.  Please come back with a real argument.  A real argument based on numbers and not magic wishes.

-Edit end-

[0_The_F00l]

I don't really like to get involved in things that have to do with monetization of game assets,

DE does need to give players incentive to buy plat - it is absolutely not a charity - you either pay in money or you pay in time.

 

Arcanes improve the effectiveness of already capable builds or compensate for min maxed builds,

i did quite a few runs but i got tired cause of the migraine inducing atmosphere and sounds as well as the meta ,

I never got all the Arcanes (i still don't have the barrier) but i traded for them a little over time , then scarlet spear dropped and i got most of what i wanted.

 

I also dont see a use for the mechs at the moment other than FOR THE GLORY OF THE EMPEROR!

i expect that when the next expansion hits there will actually be a reason to use the mechs and we will have enemies / bounties where that is a reward.

 

I do completely despise multiple levels of RNG on a personal level though.

[master_of_destiny]

4 minutes ago, 0_The_F00l said:

I don't really like to get involved in things that have to do with monetization of game assets,

DE does need to give players incentive to buy plat - it is absolutely not a charity - you either pay in money or you pay in time.

 

Arcanes improve the effectiveness of already capable builds or compensate for min maxed builds,

i did quite a few runs but i got tired cause of the migraine inducing atmosphere and sounds as well as the meta ,

I never got all the Arcanes (i still don't have the barrier) but i traded for them a little over time , then scarlet spear dropped and i got most of what i wanted.

 

I also dont see a use for the mechs at the moment other than FOR THE GLORY OF THE EMPEROR!

i expect that when the next expansion hits there will actually be a reason to use the mechs and we will have enemies / bounties where that is a reward.

 

I do completely despise multiple levels of RNG on a personal level though.

So....how did DE function in their first few years of operation?

 

I'm asking as someone who experienced that time, and was happy to fork over money for prime access when the game had way less content.  I remember using super jump, being happy with Zephyr because it meant less fiddly wall jumping in the void to get resources, and the utter mess that was the introduction of the first and only decaying resource in the entire game.

I can tell you I forked over money because DE released stuff constantly and it was small.  An operation might be a new game mode, and you might get 3 whole new weapons to experiment with.  I can also tell you that the lives for money system was basically playing the game as an arcade machine, and not bad at the time (despite it being unthinkable now).  I can also state the last time I paid DE was with Hydroid Prime, because since then their releases have not warranted my money.  It's Fallout 76 level bugs, that if they are ever smoothed out take months.  I understand the beta tag, but as you put it multi-layered grinds for content stretching are killing my ability to look past bugs.

 

 

Regarding mechs and the future....it took more than a year (nearly two) to be able to use a secondary gun on a k-drive.  I cannot really suggest that the future is a solution when it comes to DE.  Remember, Railjack was two years of hype....and we're still short on the Command intrinsic tree and only have grineer content despite their recent interviews stating that things have been moved out of priority.  If I loved railjack that would be heart breaking.

[Buff00n]

11 minutes ago, master_of_destiny said:

So, here's the base assumption that you're working with and I'm not.  I don't just want a rare arcane, I want a specific rare arcane.  It's thus not a (5%+5%+5% =15%) chance, but a 5% flat chance.

The first distribution I showed was not for getting 63 of any rare arcane, it was for getting at least 21 of each of the three rare arcanes.  That comes out to be ~500 runs, experimentally.

If you pare that back to just 21 of one rare arcane, then it's this:

The expected average is pretty close to the analytical solution of exactly 420, but the 90th and 99th percentiles are 537 and 565, respectively.  I encourage you to click that link and play with the simulation, it's pretty fun if you nerd out over that kind of thing.

22 minutes ago, master_of_destiny said:

1407 is the result of:

67 runs for a 0.9678 chance at getting a single drop

21 drops required.

0.9678^21 = 50% drop chance (so individual drop chance needs to be 97%, for 21 total rounds, to get the 50% attainment figure)

Okay, you are correct that 67 trials puts you in the 97th percentile for at least one success.  But you can't take that and construct a new "meta-trial", treat that as a single trial for getting 21 successes, and expect to get a meaningful number out of that.  That 97% chance of at least one success also includes many scenarios where you have more than one success.  In those 67 trials you can have up to 67 success, but your average is going to be a bit over three.

All this means your chances of hitting 21 total success by 1407 trials are much, much greater than 50%.  They are, in fact, as close to 100% as my simulation can calculate even if I run it millions of times.

14 minutes ago, master_of_destiny said:

I can appreciate that you've done the work to show a normal distribution curve. 

It not actually a normal distribution.  It's a Negative Binomial Distribution, which can approach a normal distribution when it has many degrees of freedom.  In the case of the above graph, it has 21 degrees of freedom and is pretty close to normal, but you can tell that it's still somewhat skewed and the mean of 420 is not equal to the median of around 413.

It's easier to see this if you reduce the number of degrees of freedom.  Consider how many runs it takes to just get six Arcane Energizes:

With just six degrees of freedom it's clearly not normally distributed.  In fact, my app is cutting the picture off at the 99.9th percentile.  The tail on the right extends for a very long way, which explains how the occasional very unlucky 1 in 10000 player can go hundreds of runs without getting anything.  It sucks being an outlier, and the Negative Binomial Distribution shows us exactly how much it sucks.

[Galuf]

Git gud before spraying statistics where you shoundn't.

Nonsense about arcanes

Arcane is one of the most "unfair" things in the game as it is P2W to some extent because these represent a big part of the powerlevel of an account and can be bought entierly with platinum. It may create issues in groups of friends, for instance the one who bought arcane is no more on par, etc... However all the reasoning on this topic is flawed as hell. It is not because you display graphics and make unilateral review of those that you are in the rights, numbers always tell the truth you want. The reality is that high end stuffs like arcanes, riven, etc are market driven and it is on you to play the market if you don't want to invest hard money.

Arcane energize r0 DOESN'T WORTH 150p, it's actually less than half that.

https://warframe.market/fr/items/arcane_grace

https://warframe.market/fr/items/arcane_energize

Those are the 2 BIG BIG ones, the other arcanes are significantly less expensive. At its historical highest having a r3 energize was costing you 350*10(raid era) while things painfull grinding for was like 120p or something(loki prime system for example). It was unlikely getting there without buying plat or tremendously investing in the game.

When you are doing Eidolons, you are working on 1 to 2 daily caps wich can generate plat, maxing your focus schools(and the way bounds are really really nice to have) and getting a bunch of arcanes that you may not want but have some small extra value. I think it is fair to say that on a 45mn cycle once per day you get overall enough plat, worst case scenario to finish a r5 grace or energize in 2 to 3 weeks(depending on your rng), assuming you are not stuck at doing 3x3.

Alternatively Scarlet Spear event is meant to be a recursive event and it generates a r5 legendary arcanes in less than 3 hours if you play correctly

 

Necramech mods

Atm the community aknowledges that the drop rates are BS and it is normal, it is the content sink for DE atm. The availability will dramatically increase in the future, the correct behavior is to either farm them for plat or waiting. It is not worth slotting 1500p or something of mods on a necramech, and it probably never will ^^.

[master_of_destiny]

5 hours ago, o0Despair0o said:

And that's where you lost me.

 

I knew I was bad at math but hory sheet I don't understand anything about this. Might as well be hieroglyphs right there.

p = probability

1 in both locations represents 100% chance of a drop

0.05 represents a 5% drop chance

n = number of runs

 

Putting this into words:

(probability of a drop) = (assured drop) - [(assured drop) - (drop rate)] ^ (number of runs)

 

This equation basically takes the likelihood of not getting a drop away from an assured result to find the chance of a drop.

What it doesn't do is find the chance of a specific outcome.  Basically, somebody gets 10 drops in 10 rolls and somebody else gets 1 drop in 10, but both fall into the "at least one" category.

 

 

Let me diverge, and give you an example.  Flip a coin.  The chances of getting heads is p = 1-(1-0.5)^1 = 1 - 0.5 = 50%.  Flip two coins.  The outcomes are H-H, H-T, T-H, and T-T.  This means the likelihood of getting at least one heads is 75%, but the chance of getting both heads is 25%.  This is how you get a specific result that is lower, but the chance of at least one instance as much higher.  It's a very simplified understanding, but if you want to go deeper investigate normal distribution curves in statistics.  They'll show you how bell curves represent actual outcomes in large scale systems.  

Now, imagine a coin with 500 faces.  That's effectively the results with a 0.201% chance.  There's how you can flip the coin 500+ times and not get your desired result.