Jump to content
Dante Unbound: Share Bug Reports and Feedback Here! ×

Warframe - Math and statistics - Quantifying the Grind


master_of_destiny

Recommended Posts

1 minute ago, master_of_destiny said:

I did the grind for focus without buying affinity boosters and lenses.  I did it because despite being months of grind it was valuable.  I hate Eidolons because after months of grind I still had no idea of when I would get the rewards.  I had nothing but RNGesus to pray to, and cheetah blood to rub on a d-20 for luck.  That's hyperbole, but the point is that it's not great to be on the bad end of random loot drops and does not feel rewarding.

 

The point of citing maiming strike and the like is that nothing in this game is of constant value if traded between players.  It's always 20 platinum for a warframe slot.  It's always a constant price for the Xiphos....another fractional percentage drop item which is a miserable grind.  

My point here is that nothing is a constant unless DE makes it so.  Rivens, meta mods, pick your poison.  Circling back to the original point, trading platinum for arcanes is not a solution to a bad economy, but the admission that said bad economy is acceptable to DE.  That's a depressing state to be in.  DE should fix this, or they shouldn't be surprised that people don't want to invest in their game.  Paying for the next 70+ hour grind is just....frustrating.

absolutely agree on that part but

2 minutes ago, master_of_destiny said:

they aren't the only game on the market, and as such their asking price of 80 USD has to be justified by something more than the tag line of "a 205 USD value."  I know that Doom Eternal is going to provide me demon killing for a number of hours, and after that time I can maybe purchase DLC to extend it further.  It's also going to run on my system without massive technical issues, like regularly clipping out of the world.

The pricing and monetization systems of games with artificial value is kind of complex to handle.

In general with Prime Accesses you pay for the exclusivity of the items contained in it. So with 80 USD you not only get the (for a limited time) farmable frame and weapons you also get the glyphs exlcusive to this offer(and it's even bigger version). The reason for implementing this system of monetization dates all the way back to the first primes if not even the founder packs. If you were to "better" the value of these packs doesn't that lower the value of platinum in the game and by that making any purchase prior to that a way worse deal, doesn't it?

The tagline of "a 205 USD value" is in comparison of the default prices making it even more attractive to players.

Also choosing the 80 dollar pack is probably the worst option as the best value in prime accesses are the accessories and the biggest pack.

Link to comment
Share on other sites

10 minutes ago, (PS4)ozgurozacik said:

150 platinum a piece? For an arcane? Is this a pc thing? In ps4 both arcane energize and grace goes for 20p - 25p a piece and can get the max for 400-500

warframe.market says 50-60 plat for either grace or energize on pc (WTS)

Link to comment
Share on other sites

You could justify Eidolon rare arcanes - they are supposed to be those high-end rares, like winning a lottery -  grindans simply need such drops, every game of this sort has them, to motivate players to grind more for a chance of a 'big win'. While there are also *guaranteed* common and frequent uncommon rewards that make it worth running either way. Also they are totally optional with how many alternatives for the same effects you have.

But mech mods? even the basic ones have abysmal chance and they are bare necessity (unless you just give up on mechs of course ...) and yet they still have terrible chance - you could have 20 runs with no drops. DE completely messed this up, even mech scraps had better drops (before they got patched to drop noting). And frankly Vaults are not worth farming for these terrible chances. Inseatd I can just farm all the plat and buy all I need in a day.

As of overall grind in Warframe - yes, the game is insane timesink with waitwalls everywhere. Worse of the game never teaches players what to do and where to farm efficiently, even the affinity system is counter-intuitive and never explained (ie that all your weapons and frame share it, so you want to level up a weapon quickly - unequip all other weapons and DONT kill anything yourself, only leech to get most of the XP to that weapon! )

A lot of grind got reduced through the years, to be fair. Credits and endo are trivial to make now compared to what it was ~3-4 years ago. But there are still many problems and with how vast the game is - it might present an impossible wall for new players. Fancy ranking up all these ~400 weapons?

Link to comment
Share on other sites

4 hours ago, uAir said:

Now, is it still a grind? Yeah, kind of. You still gotta put your work in and do what needs to be done. But what do you want? You want a game where skill ceiling is extremely high and there's zero RNG in any loot and however good you are reflects the time and effort and talent you have in the game instead of the amount of grind you did? Well, go play fighting games.

Otherwise, there's Warframe. It is what it is. >_>

Sorry, maybe I was a bit misleading. As a "mostly f2p player", I meant I only ever buy plat if I have a 75% off coupon, which usually only happens like once a year. That's how I got most of my rare mods since farming them was just too tedious. Even though I could just do the same with arcanes, they're prices are just far too high for a maxed one.

Link to comment
Share on other sites

1 minute ago, Buff00n said:

When a squad kills the Hydrolyst, that is a single event that has a 5% chance to reward an Arcane Energize to each member of that squad.  One event = one drop.  There's no coordination with some "population".  It doesn't matter how many other squads are currently doing an Eidolon run.  It doesn't matter what region the squad is in.  It doesn't matter what is happening anywhere else in the Warframe ecosystem.  One event = one drop = one roll with a 5% chance.  A random number N between 0 and 1 is generated just for that squad, and if 0<N<0.05 (for example), then that squad gets an Arcane Energize.  The "population" doesn't matter.  Each squad gets its own event, its own randomly generated number, and its own drop.

I don't know how many other ways I can say it.  I honestly don't understand why you're adding complexity where none exists.

This statement in particular I'm really struggling to understand:

Okay, but 5% of what in this case?  If it's not 5% of the population itself, then what is the 5% measuring?  If there is some set amount of an item that can drop that is independent of the population, then the drop rate cannot always be 5% and the drop tables would be straight-up lies. 

When an item is defined as having "a 5% drop rate", what exactly do you think that means?

 

Since you asked: In the early days of Sorties the drop rate for Ayatans was much higher than Rivens, something like twice as much but they were't publishing drop rates at that time.  Over the years they have been adjusted, and when the drop rates were first published around U21 they were 28% Ayatan vs 24.9% Riven.  Since then the Riven drop rate has increased as more Riven types were added.  My results are within expected tolerances considering this variation and the fact that it's still a pretty limited statistical sample.

If you would prefer another anecdote: It took me exactly 99 runs of EOS to obtain all the parts for the Braton Vandal and Lato Vandal, which was shockingly close to the expected average of 103 runs

Even my relic notes show I average about 3 radshares per rare prime part going back to when relics were first a thing with Nekros Prime, matching the expected average of 2.91.

There's no reason to suspect anything other than a simple binomial process to RNG.  I have yet to see compelling evidence to the contrary.  There are plenty of things in the official drop tables to be concerned about without inventing new ones.

The Binomial Distribution, and its inadequacies.

OK, simplistic overview of this, with a server called for rewards you're working with a pseudo random value.  That's means that you have a binomial distribution dependent upon seed generation.  You also are not accounting for people leaving the eidolon hunt because 67 runs without a desired reward basically will have them giving up due to frustration.  I made a large conceit relating to that to make my math easier, and this is where my variable population comes into play.

 

Why would DE do this?  Well, imagine there's a seed function on the client computer, like the original Doom.  Find and screw with the seed file, and suddenly you get constant rare drops.  Can't have that, so move the seed and function to a server and have the client request the rewards.  You also cannot have a truly random call function because it takes a lot longer to process on the server.  The simpler result is to have a pseudo random with an input seed and algorithm that is almost random.  How so?  Well, even Excel cheats and utilizes a pseudo random number.  Do you believe DE would be less efficient and require a true random call, or would they use the same short cut, creating a new functional distribution each time a new seed is implemented?

 

How do I prove this in-game?  Well, have you gotten to the end of mission and not gotten rewards?  Then, suddenly the list populates.  This is client to server issues, and the rewards not processing in time.  It happens a lot on poorer connections to DE's servers, or when network connectivity is a problem.  This heavily implies the client is not calculating rewards, thus the semi-random seed, thus the dependence not on a true distribution but on a defined function where 5% is overall and not individual chance.

 

In practice, 3% don't get the reward on the first 67 runs.  The math says 3% of the 97% and 3% of the 3% don't get anything on the second run.  So here's my conceit, I simplified the math.  If you run the eidolon hunt 67 times and never see a rare drop it's the end for you.  Who in their right mind would keep grinding?  I assume that 3% of the remainder are lost each time and do not come back.  Thus round two is not 0.97*0.03+.03^2 but  0.97*0.03+.03.  This conceit allows you to generate a simple x^y rather than the much longer binomial distribution you've decided on.  

Why did I call this conceit variation in the population?  Well, humans aren't machines.  We wouldn't keep grinding endlessly, and there is a point of not getting desired rewards where we stop grinding.  See above for all of the people saying "just buy it with platinum."  So I cheated a bit and did the much simpler math.  It's basically saying that with a 3% bleed off each time after 1407 runs you have everyone remaining guaranteed to get their desired reward.  The 50% that have bled off are likely going to either skip the content or purchase it from a grinder.  This means basically for each person who is assured to get the reward there's 1407 runs completed (but not just by them) and a bunch of people with partial arcanes.  That total is soaked to multiple players, some quitting after a single round of no rewards, other quitting after a few rounds with rewards and eventually reaching a round where there is enough non-reward to remove them from the population by burn-out, and still other grinding endlessly so they can sell the arcanes.

Is my cheat fair?  Well, I can only offer anecdotal evidence.  1 in 200 is pretty much where I gave up eidolons.  I'd suggest at that rate getting 21 would have definitely taken me 1407 runs or more...but that's bad math with a sample size of one.  I'd suggest other respondents have already suggested they reached the point of burn-out and paid for arcanes, so there's that.  I'm not really equipped to tell you the cheat is mathematically fair, but it's justifiable.  It's justifiable entirely based off of humans performing an action and simply fading out when rewards are not present.  A binomial distribution doesn't address that population shift....so I'm going to call it not a less accurate model, but as not factoring in all phenomena.  It's mathematically more correct, but assumes humans will infinitely grind.  That's a bad assumption.

 

Your experimental graph....and its validity as anything more than anecdote

Regarding your graph....I don't see your retort strengthening the argument.

If they changed the percentages then your data is even smaller in the sample windows for any particular drop rate, making it even less relevant.

If you graphed all of it with the intention to say it's good today, and included different chances in the past then it's useless because the target is moving.

I don't see how this data supports your claims when the underlying assumptions have to be that the rates changed over time, there are no numbers, and the population for the data is a grand total of one and therefore insignificant.  Put simply, this is irrelevant data that may look good but is not viable as any sort of indicator.

 

Radiant relics, expected drops, and the wonders of sigma in a statistical world

I'm just going to ask you to share the work on the radiant relics.  Your link shows 2.91....what?  2.91 runs to unlock a rare?  If you're calling the server for 12 rewards then at 10% it's basically showing a straight forward probability calculation.  It is not accounting for population variance between runs, because there is none.  It also is not accounting for each Eidolon hunt being linked to a group rather than individual call, as you don't stop running relics ever.  

Is the seed argument valid here?  Well, yes and no.  The seed argument is more of a problem when you decrease the amount of calls.  It also is not calculating the need to have 21 rare drops.  It's effectively changing back down to a simple calculation of input x number of rolls to get the appropriate values.  

Let's have some fun.  1 sigma is 68%.  When you say that the expected result for drop is 2.91 that is easy to calculate.  1-(1-0.1)^(2.91*4) = 0.7066.  By golly, it's almost like a rounding error has produced exactly one sigma as the value you have as expected (I cannot see more than two digits, so have to assign this as rounding rather than significant figures), and it's exactly what I'm calculating.

-shocker, I know a bit here and the 1 sigma value was blindingly apparent to me as hopefully it was to you-

The difference in our little example is 12 calls to the server, instead of 1.  Much larger pool, soaks up much more of the problematic semi-randomness and you don't have to factor in burn-out because there are always new relics.  Eidolons have a smaller percentage chance and a single roll.  See above for my commentary on insignificant sample sizes leading to error.  Error that has to be accounted for with such small sample pools, and the non-infinite grind players will endure.  

 

 

For people asking what the heck a sigma is, it's basically saying that in a normal distribution 68% of values fall into 1 sigma from a median value, 95 into 2 sigma, and so on.  See: Bell Curve (though that's a regular and not binomial distribution).  Most of the results, or what you would expect, fall into this value and thus your expected number of runs would be 2.91 (rounded) with 4 relics each at radiant values offering 10% individual drop rates.

Now, you've shown me one drop.  That's actually a 30% chance that you missed it after 12 relics.  Tell me how many runs it would take to crack 21 rares?  How many relics do people get dropped, need to enrich to be radiant, and then crack without a reward before they buy things from people who already got the drop?  A binomial distribution still hasn't accounted for people giving up after 20+ relics and just buying the thing.  It definitely doesn't account for the grind of getting the right relic, burning through a bunch of non-radiants to get void traces, enriching, and then running the enriched radiants to make what should be a simple 10% chance effectively require dozens of random rolls simply to be a 10% chance.

 

The short of it all

How do you shut me up?  Well, prove that the seed and pseudo random generation is not reset at server reset.  Not sure how you'd do it.  Once you've done that, demonstrate exactly how much grind people will perform before burning out.  Take note that nowhere in that distribution curve is factored in that real humans are doing the grind.  Now that you've demonstrated the binomial distribution is good for the individual player instead of the population as an unknown whole, and that you can account for player bleed due to grind, I'll happily admit that I'm wrong.  

For the record, the assumptions I made are cataloged above.  From what I am seeing the assumptions you made are; players will infinitely grind, players do not stop once they have 21 arcanes, and the binomial distribution is based off of a true random string rather than a pseudo random string controlled by an unknown function.  Neither of our points are bullet proof.  As such I'm happy to admit that you modeled an ideal system better than I have.  What I am not satisfied with is that this represents reality.  My garbage in is to require a drop each time, while your garbage in is to assume players can tolerate infinite grind.  I'm happier with my garbage because people don't do a binomial distribution, they run a thing and see rewards or not.  If I ran 67 eidolon hunts without a specific reward I'd be done....oh wait, that's exactly what happened.

Likewise, Steel Path requires 80+ steel essence for a reward....and after clearing Earth I received 0 drops.  Yep, steel path is done.  Isolation Vaults....yep, I've done a couple dozen and it's not fun anymore.  I consider that as infinitely more valid than assuming everyone will just keep grinding.  Take it for what you will.

Link to comment
Share on other sites

6 hours ago, (PS4)ozgurozacik said:

150 platinum a piece? For an arcane? Is this a pc thing? In ps4 both arcane energize and grace goes for 20p - 25p a piece and can get the max for 400-500

In the WF.market it's 1170 for maxed....

9 hours ago, uAir said:

It's that simple. There's no need to rush anything. There's no need to compete with anyone. There's no need to sit there and grind for 18 days trying to get Condition Overload.
Just run 1-2 hours a day for a week or so for prime parts. Sell. Buy the Condition Overload.

For simple stuffs or even frames/weapons (~300 plat) it's enough (that's what I do with frame past Octavia because grind is bad in most cases) however for arcanes it would take too much time. I am not going to buy arcane for more than a frame. And even I want to earn plat for it it would takes a lot of time grinding for void tears, then relics and selling stuffs. And, you know, I want to do other stuffs in this game.
As for now I prefer pizzas, 100x costs only 90k credits and some resources. Not like 1000+ plat...

Link to comment
Share on other sites

6 hours ago, OggerAZ said:

absolutely agree on that part but

The pricing and monetization systems of games with artificial value is kind of complex to handle.

In general with Prime Accesses you pay for the exclusivity of the items contained in it. So with 80 USD you not only get the (for a limited time) farmable frame and weapons you also get the glyphs exlcusive to this offer(and it's even bigger version). The reason for implementing this system of monetization dates all the way back to the first primes if not even the founder packs. If you were to "better" the value of these packs doesn't that lower the value of platinum in the game and by that making any purchase prior to that a way worse deal, doesn't it?

The tagline of "a 205 USD value" is in comparison of the default prices making it even more attractive to players.

Also choosing the 80 dollar pack is probably the worst option as the best value in prime accesses are the accessories and the biggest pack.

So, regarding the prime packs my view is as follows:

 

A glyph holds no value.  There are literally hundreds and they tell you nothing about a player.

The "base" prime access is just the weapons...or two weapons, a pair of weapon slots (sold as 1 item on the market), and 2 catalysts.  The "medium" is a $30 increase and adds platinum plus a frame, frame slot, and reactor.  The "premium" is $90 more than the base and includes two cosmetics and two boosters along with more platinum.  Taking this into account:

50 USD = 2 items, 1 slot pack, 2 catalysts, and 1050 platinum

80 USD = 3 items, 2 slot packs, 2 catalysts, 1 reactor, 2 glyphs, and 2625 platinum

150 USD =  3 items, 2 slot packs, 2 catalysts, 1 reactor, 2 glyphs, 2 cosmetics, 2 boosters, and 3990 platinum

This means 

B-M is a 60% increase in price and a 150% platinum increase.  

B-P is a 200% increase in price and a 280% platinum increase.

M-P is a 87.5% increase in price and a 52% platinum increase.

This means that the valuation placed on the cosmetics and boosters is functionally more than getting a warframe.  It's stating that the content isn't as valuable as the fashion....and I'm having a real problem not joking about "end game."

It's also an artificial currency, so the listed "100," "205," and "380"  values mean that the frame is a disproportionate segment of the pack.  What does this tell us?  Well, DE wants us to purchase the premium pack because it's the most costing, and to make it valuable they have to throw in cosmetics and boosters to make it exclusive.  They know the majority of sales are in the medium class.  The base is offered as a deal to get people to spend money, because regular platinum pricing has no in-built "deal" unless you get a market discount from the daily.  

 

I wouldn't call the premium pack the best deal.  I view it as the worst deal because the pricing gap between medium and premium is not filled in with platinum, but with a 90 day booster designed to make the game less grindy and cosmetics.  Ouch.  If you want cosmetics wait two years and get them for 20 USD in a twin pack from an unvaulting.  It's so much cheaper as to be frighteningly preying upon people without impulse control.

Link to comment
Share on other sites

7 hours ago, (PS4)ozgurozacik said:

150 platinum a piece? For an arcane? Is this a pc thing? In ps4 both arcane energize and grace goes for 20p - 25p a piece and can get the max for 400-500

 

7 hours ago, OggerAZ said:

warframe.market says 50-60 plat for either grace or energize on pc (WTS)

 

To everyone here calling out pricing...I'd ask you do the math yourself.  It's simple.

 

I quote 150 because there was a time where it sold for that.  If it's 150 platinum and you're grinding at $1.22 an hour, but the price you want is 50 platinum, then divide the $1.22 by three (50/150).  This effectively means that you need about 2 packs instead of 4 to purchase it.  

As I'm not writing a dynamic calculation, I cited my assumed expenses.  In two months it'll be different than today, as the depreciation from Scarlet Spear will be lifting.  Likewise, two months ago the arcanes were cheaper.  It's a dynamic market based on supply and demand, so please keep this consideration in mind.  This is why the warframe marketplace only has 90 day histories....and Scarlet Spear was more than 90 days ago.

Link to comment
Share on other sites

Yea I'm not reading all that sorry lol. 

I mean if you have so much data and clearly thought out posts, take it to feedback. We can't do anything about it. You're either gonna be the hero that takes down the gaming industry, or get a few adjustments made to high end items, or nothing is gonna happen at all. 

I personally have stuff to do lol.

Link to comment
Share on other sites

9 minutes ago, (PS4)Madurai-Prime said:

I personally have stuff to do lol.

You sure? You took the time to post nothing on this thread. If you don't want to read the post, don't. I for one appreciate any statistical analysis of the way im spending my time in Warframe. It's an information post, what you choose to do with it is your business.

Don't disparage someone for giving you information.

Link to comment
Share on other sites

Honestly. This is the reason I play Warframe for a few weeks, maybe a month, and then put it down for 6-10 months. The grind over this game's life time has just burnt me out and its not really sustainable. The pool of Warframe players that aren't burnt out grows more shallow every day.

Link to comment
Share on other sites

2 hours ago, Skaleek said:

You sure? You took the time to post nothing on this thread. If you don't want to read the post, don't. I for one appreciate any statistical analysis of the way im spending my time in Warframe. It's an information post, what you choose to do with it is your business.

Don't disparage someone for giving you information.

The information is already on the wiki.....And I also got to around the 210 hydrocap mark and realized I got about 9 +/- energize. It happens....but guess what I did? I took all those Prime warframes and weapons I farmed and sold them. I took all those extra arcanes I farmed and sold those. I took all the extra fish and gems I farmed and sold those. I took the extra arcanes from the Quills and Vox Solaris that I had and sold those.....I could have bought multiple Energize and Graces......but here's the crazy part...you ready?! 

You only need 1 Energize and 1 Grace. It's a one-time investment and it's completely done with. If this guy cares so much he needs to go to feedback. 

Don't you people say all the time that DE doesn't read General Discussion?? 

Link to comment
Share on other sites

And in warframe you get to keep what you get. DE isn't gonna make another Energize that's better than the current one and force you to farm a new one every 3 months..... They're not gonna repeatedly make different versions of the same Condition Overload and force you to constantly upgrade your mods. Once you acquire something in warframe. It's useful for a really long time. You can leave the game, come back and still use Weeping wounds CO and BR without having to farm a new Bloodrush 2.0 that made the previous Bloodrush completely useless. 

New weapons and mods will come out, but you still complete all content with mods that probably came out before I even started playing. 

If new people need Energize, they can wait for SS again and get one in 2 weeks of farming (which people would still complain about) or they can build a few frames and weapons to do eidolons, or they can support the game with a 1 time purchase, never to be made again.....and play the game for years without ever having to touch their wallets, ever again.

Link to comment
Share on other sites

6 hours ago, master_of_destiny said:

OK, simplistic overview of this, with a server called for rewards you're working with a pseudo random value.  That's means that you have a binomial distribution dependent upon seed generation.

...

Why would DE do this?  Well, imagine there's a seed function on the client computer, like the original Doom.  Find and screw with the seed file, and suddenly you get constant rare drops.  Can't have that, so move the seed and function to a server and have the client request the rewards.  You also cannot have a truly random call function because it takes a lot longer to process on the server.  The simpler result is to have a pseudo random with an input seed and algorithm that is almost random.  How so?  Well, even Excel cheats and utilizes a pseudo random number.  Do you believe DE would be less efficient and require a true random call, or would they use the same short cut, creating a new functional distribution each time a new seed is implemented?

The link I provided earlier addressed the seed issue.  Back in 2013 this was a problem but it was quickly fixed.  The PRNG now used by Warframe to calculate drops is sufficiently random enough that any reasonable subset of its output is still random.  PRNG has been well understood mathematically for 70 years, and modern algorithms will take an astronomical number of iterations before they start repeating or showing any kind of pattern.

6 hours ago, master_of_destiny said:

How do I prove this in-game?  Well, have you gotten to the end of mission and not gotten rewards?  Then, suddenly the list populates.  This is client to server issues, and the rewards not processing in time.  It happens a lot on poorer connections to DE's servers, or when network connectivity is a problem.  This heavily implies the client is not calculating rewards, thus the semi-random seed, thus the dependence not on a true distribution but on a defined function where 5% is overall and not individual chance.

I have noticed the "pause" in the new end of mission reward display updated a few weeks ago, too.  I'm not convinced this isn't just a quirk of the new UI update, but even if this is a DE server round trip it doesn't mean the server is doing anything other than a simple PRNG calculation and updating accounts.

There is no reason to expect some complicated server-side rationing system that makes sure exactly one out of every 20 rolls turn out a certain way.  That is impossible to balance on a per-user basis, which is the entire point of the published drop rate.  Just a basic, commodity PRNG is by far the simpler and most effective solution, and it will statistically approach a specific drop rate with enough drop events.

The UI pause is not proof of anything other than possibly a server round trip.  You will need to show a discrepancy in published drop rates versus actual drop rates beyond a statistically significant threshold, and I have not seen that proof.  Extraordinary claims require extraordinary evidence.

 

6 hours ago, master_of_destiny said:

You also are not accounting for people leaving the eidolon hunt because 67 runs without a desired reward basically will have them giving up due to frustration.

This is irrelevant, as we are only considering drop events that actually happen.  If a player gives up then they are no longer participating in Eidolon hunts.  They no longer count when talking about drop rates for an event they are not experiencing.  If a player does 67 runs without success and then gives up, that does not mean the drop rate is zero for that player.  And it does not affect the drop rate for any other player unless that other player happened to be in the same unlucky squad the whole time.

 

6 hours ago, master_of_destiny said:

This means basically for each person who is assured to get the reward there's 1407 runs completed (but not just by them)

If you're going to include a whole population then you need to consistently count that whole population.  In 1407 Hydrolyst runs, across any number of players and squads, I would expect around 70 Energizes to be rewarded, distributed across that same group of players/squads. 

If that population is a single squad running 1407 Hydrolysts over and over again, then I would expect every member of that squad to have around 70 Energizes. 

If that population is 1407 different squads doing one Hydrolyst run each, then I would expect the members of 70 of those squads to have one new Energize.

If that population is 100 different squads running 14 Hydrolysts each, then all we can say about the population as a whole is that 70 Energizes were rewarded.  We could drill down to one squad doing 14 runs and say that we expect each member to have about 0.51 Energizes, and use that to infer that across the whole population, about half of them received at least one Energize.  However, because we expect 70 Energizes to be awarded, that means some of those 50 squads received more than one Energize.

But to say that 1407 runs across some population somehow counts towards an individual player's result is meaningless.  It's comparing apples to oranges.  They aren't the same thing.

 

6 hours ago, master_of_destiny said:

1 in 200

So now the real reason for your original post is revealed.  You did 200 Hydrolysts and received one Arcane Energize.  That's about a 1 in 2700 chance.  I'm sorry, that sucks.  But, it's not outside the realm of possibility given the size of the player base.  My original advice that you're better off waiting for Scarlet Spear to return still stands.

Still, you probably have a fair number of Arcane Barriers and Arcane Graces, right?  Probably more than the expected average, given that 199 of those runs had to have given you something other than Energize.  I think what people are trying to tell you here is that you can trade extras of what you don't want for more of what you want.

 

6 hours ago, master_of_destiny said:

I'm not really equipped to tell you the cheat is mathematically fair, but it's justifiable.  It's justifiable entirely based off of humans performing an action and simply fading out when rewards are not present.  A binomial distribution doesn't address that population shift....so I'm going to call it not a less accurate model, but as not factoring in all phenomena.  It's mathematically more correct, but assumes humans will infinitely grind.  That's a bad assumption.

Again, the population shift is entirely irrelevant to talking about drop rate.  We can only do math with events that actually happen. 

We can use probability to gauge how likely a player is to give up before achieving success, but for every one of those players there will be players that have good luck, and succeed either much faster or multiple times with the same number of runs.   You cannot treat the discouraged players differently from the lucky players, you have to quantify the population as a whole.  And the population as a whole gets an Arcane Energize for about 1 out of every 20 Hydrolyst kills.

 

6 hours ago, master_of_destiny said:

Your experimental graph....and its validity as anything more than anecdote

Okay, fair enough.  Here are my numbers since the Sortie drop table was last changed in U24:

Spoiler
Reward Number Actual % Drop Table % (U24)
Ayatan/2K Endo 191 29.20% 28.00%
4K Endo 87 13.30% 12.10%
Riven 186 28.44% 27.90%
Lens/Kuva 77 11.77% 12.00%
Exilus 15 2.29% 2.50%
Catalyst 11 1.68% 2.50%
Reactor 2 0.31% 2.50%
Booster 67 10.24% 9.81%
Forma 17 2.60% 2.50%
Legendary 1 0.15% 0.18%
Total 654    

I don't have a graph prepared but I think the raw numbers are clear enough.

 

6 hours ago, master_of_destiny said:

Your link shows 2.91....what?  2.91 runs to unlock a rare?

One radshare gives (1-(1-0.10)^4) ~= 34% chance to get the rare reward.  I don't think that's controversial.  With P=0.34, the expected average number of radshares is 1/0.34 ~= 2.9078.  It has nothing to do with the standard deviation of the normal distribution.

I tried to munge my relic data into something I can show but LibreOffice Calc keeps crashing on me (I should really start using something else), so I had to call time on getting you hard data.

 

6 hours ago, master_of_destiny said:

A binomial distribution still hasn't accounted for people giving up after 20+ relics and just buying the thing.

I can't say it enough times, this is irrelevant when talking about drop rates.  Those people who give up are part of a larger population that includes people who are unusually lucky.  The overall drop rate across the whole population remains the same.

6 hours ago, master_of_destiny said:

It definitely doesn't account for the grind of getting the right relic, burning through a bunch of non-radiants to get void traces, enriching

This is also irrelevant when talking about a rare prime part's drop rate.  You seem to be trying to take some kind of wholistic approach but you're not explicitly quantifying it that way.

 

6 hours ago, master_of_destiny said:

How do you shut me up?  Well, prove that the seed and pseudo random generation is not reset at server reset.  Not sure how you'd do it. 

I'm not sure how you'd prove that they are.  I believe your assertion to be the more extraordinary claim, considering how it vastly complicates the simple job of generating random drops, and such claims require extraordinary evidence.

6 hours ago, master_of_destiny said:

Once you've done that, demonstrate exactly how much grind people will perform before burning out.  Take note that nowhere in that distribution curve is factored in that real humans are doing the grind.  Now that you've demonstrated the binomial distribution is good for the individual player instead of the population as an unknown whole, and that you can account for player bleed due to grind, I'll happily admit that I'm wrong.

Your demand, again, is irrelevant to a discussion of the mathematics of drop dates.  One event = one drop, and that's the only thing you can work with statistically given the published drop rate data.  If you're trying to make some kind of wholistic statement about discouraged players' runs counting towards other players' runs, then I don't think you've made that case in any statistically meaningful way.

If you personally kill 1407 Hydrolysts, then I guarantee that you will have at least 21 Arcane Energizes.  There's virtually no chance that you won't. 

If you are a member of a population of players that kill 1407 Hydrolysts in total, then all you can say is there were about 70 Arcane Energizes distributed among those players.  If we wanted to we could probably work out the probability that 21 of those 70 went to a single player, which would depend on the size of the population and distribution of how many runs each member did.  But at that point we're just making up very specific fantasy scenarios and we're no longer talking about the average player or population's experience.

The published drop rates are defined in terms of a player's experience.  You have to be consistent whether you're talking about a single player or a whole population of players, otherwise the drop rate does not apply and you're talking about something completely and mathematically different.

This conversation has been both fun and exasperating, but I need to go do my actual job now.  Talk to ya later.

Link to comment
Share on other sites

On 2020-09-07 at 4:58 PM, master_of_destiny said:

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 you need to capture a Hydrolyst 1407 times.

 

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 a 50% chance of getting the reward.

 

 

 

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.

Don't forget kuva grinding and the actual chance of getting a decent roll on a riven.

Link to comment
Share on other sites

5 hours ago, (PS4)Madurai-Prime said:

And in warframe you get to keep what you get. DE isn't gonna make another Energize that's better than the current one and force you to farm a new one every 3 months..... They're not gonna repeatedly make different versions of the same Condition Overload and force you to constantly upgrade your mods. Once you acquire something in warframe. It's useful for a really long time. You can leave the game, come back and still use Weeping wounds CO and BR without having to farm a new Bloodrush 2.0 that made the previous Bloodrush completely useless. 

New weapons and mods will come out, but you still complete all content with mods that probably came out before I even started playing. 

If new people need Energize, they can wait for SS again and get one in 2 weeks of farming (which people would still complain about) or they can build a few frames and weapons to do eidolons, or they can support the game with a 1 time purchase, never to be made again.....and play the game for years without ever having to touch their wallets, ever again.

you don't always keep what you get. think about the riven disposition nerfs that make you endless grueling farm for kuva seem like a waste of your time.

Link to comment
Share on other sites

В 08.09.2020 в 00:58, master_of_destiny сказал:

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. 

I can and will argue about "insane levels of grind". I was done in about a week? Maybe 2, I don't quite remember. I did miss 2 initial weeks of operation due to covid stuff. I got every arcane set I wanted from 0 to max - with exclusion of Energize, which I had beforehand. 2 legendaries, 1 gold, 1 silver. If that's "insane grind" for you - you're better off playing some other game. Because in WF, people somehow manage to enjoy grinding Plaguestar - a literal piece of garbage - and call it good operation.

The only reason SS was "poorly received", bugs aside, was exactly because it bricked the arcane mafia economy. Good riddance.

Link to comment
Share on other sites

2 hours ago, Buff00n said:

The link I provided earlier addressed the seed issue.  Back in 2013 this was a problem but it was quickly fixed.  The PRNG now used by Warframe to calculate drops is sufficiently random enough that any reasonable subset of its output is still random.  PRNG has been well understood mathematically for 70 years, and modern algorithms will take an astronomical number of iterations before they start repeating or showing any kind of pattern.

I have noticed the "pause" in the new end of mission reward display updated a few weeks ago, too.  I'm not convinced this isn't just a quirk of the new UI update, but even if this is a DE server round trip it doesn't mean the server is doing anything other than a simple PRNG calculation and updating accounts.

There is no reason to expect some complicated server-side rationing system that makes sure exactly one out of every 20 rolls turn out a certain way.  That is impossible to balance on a per-user basis, which is the entire point of the published drop rate.  Just a basic, commodity PRNG is by far the simpler and most effective solution, and it will statistically approach a specific drop rate with enough drop events.

The UI pause is not proof of anything other than possibly a server round trip.  You will need to show a discrepancy in published drop rates versus actual drop rates beyond a statistically significant threshold, and I have not seen that proof.  Extraordinary claims require extraordinary evidence.

 

This is irrelevant, as we are only considering drop events that actually happen.  If a player gives up then they are no longer participating in Eidolon hunts.  They no longer count when talking about drop rates for an event they are not experiencing.  If a player does 67 runs without success and then gives up, that does not mean the drop rate is zero for that player.  And it does not affect the drop rate for any other player unless that other player happened to be in the same unlucky squad the whole time.

 

If you're going to include a whole population then you need to consistently count that whole population.  In 1407 Hydrolyst runs, across any number of players and squads, I would expect around 70 Energizes to be rewarded, distributed across that same group of players/squads. 

If that population is a single squad running 1407 Hydrolysts over and over again, then I would expect every member of that squad to have around 70 Energizes. 

If that population is 1407 different squads doing one Hydrolyst run each, then I would expect the members of 70 of those squads to have one new Energize.

If that population is 100 different squads running 14 Hydrolysts each, then all we can say about the population as a whole is that 70 Energizes were rewarded.  We could drill down to one squad doing 14 runs and say that we expect each member to have about 0.51 Energizes, and use that to infer that across the whole population, about half of them received at least one Energize.  However, because we expect 70 Energizes to be awarded, that means some of those 50 squads received more than one Energize.

But to say that 1407 runs across some population somehow counts towards an individual player's result is meaningless.  It's comparing apples to oranges.  They aren't the same thing.

 

So now the real reason for your original post is revealed.  You did 200 Hydrolysts and received one Arcane Energize.  That's about a 1 in 2700 chance.  I'm sorry, that sucks.  But, it's not outside the realm of possibility given the size of the player base.  My original advice that you're better off waiting for Scarlet Spear to return still stands.

Still, you probably have a fair number of Arcane Barriers and Arcane Graces, right?  Probably more than the expected average, given that 199 of those runs had to have given you something other than Energize.  I think what people are trying to tell you here is that you can trade extras of what you don't want for more of what you want.

 

Again, the population shift is entirely irrelevant to talking about drop rate.  We can only do math with events that actually happen. 

We can use probability to gauge how likely a player is to give up before achieving success, but for every one of those players there will be players that have good luck, and succeed either much faster or multiple times with the same number of runs.   You cannot treat the discouraged players differently from the lucky players, you have to quantify the population as a whole.  And the population as a whole gets an Arcane Energize for about 1 out of every 20 Hydrolyst kills.

 

Okay, fair enough.  Here are my numbers since the Sortie drop table was last changed in U24:

  Reveal hidden contents
Reward Number Actual % Drop Table % (U24)
Ayatan/2K Endo 191 29.20% 28.00%
4K Endo 87 13.30% 12.10%
Riven 186 28.44% 27.90%
Lens/Kuva 77 11.77% 12.00%
Exilus 15 2.29% 2.50%
Catalyst 11 1.68% 2.50%
Reactor 2 0.31% 2.50%
Booster 67 10.24% 9.81%
Forma 17 2.60% 2.50%
Legendary 1 0.15% 0.18%
Total 654    

I don't have a graph prepared but I think the raw numbers are clear enough.

 

One radshare gives (1-(1-0.10)^4) ~= 34% chance to get the rare reward.  I don't think that's controversial.  With P=0.34, the expected average number of radshares is 1/0.34 ~= 2.9078.  It has nothing to do with the standard deviation of the normal distribution.

I tried to munge my relic data into something I can show but LibreOffice Calc keeps crashing on me (I should really start using something else), so I had to call time on getting you hard data.

 

I can't say it enough times, this is irrelevant when talking about drop rates.  Those people who give up are part of a larger population that includes people who are unusually lucky.  The overall drop rate across the whole population remains the same.

This is also irrelevant when talking about a rare prime part's drop rate.  You seem to be trying to take some kind of wholistic approach but you're not explicitly quantifying it that way.

 

I'm not sure how you'd prove that they are.  I believe your assertion to be the more extraordinary claim, considering how it vastly complicates the simple job of generating random drops, and such claims require extraordinary evidence.

Your demand, again, is irrelevant to a discussion of the mathematics of drop dates.  One event = one drop, and that's the only thing you can work with statistically given the published drop rate data.  If you're trying to make some kind of wholistic statement about discouraged players' runs counting towards other players' runs, then I don't think you've made that case in any statistically meaningful way.

If you personally kill 1407 Hydrolysts, then I guarantee that you will have at least 21 Arcane Energizes.  There's virtually no chance that you won't. 

If you are a member of a population of players that kill 1407 Hydrolysts in total, then all you can say is there were about 70 Arcane Energizes distributed among those players.  If we wanted to we could probably work out the probability that 21 of those 70 went to a single player, which would depend on the size of the population and distribution of how many runs each member did.  But at that point we're just making up very specific fantasy scenarios and we're no longer talking about the average player or population's experience.

The published drop rates are defined in terms of a player's experience.  You have to be consistent whether you're talking about a single player or a whole population of players, otherwise the drop rate does not apply and you're talking about something completely and mathematically different.

This conversation has been both fun and exasperating, but I need to go do my actual job now.  Talk to ya later.

You seem to selectively quote, cut context, and then assume.  Let's go point by point.

 

1) The equation currently used is PRNG, but it's random enough.

It's interesting you make this claim, then later state that claims must be supported.  What was fixed?  What is the new equation?  When the the random seed refreshed?  All of these questions are not addressed in the post.  In fact, there's no evidence anything was changed.  Apparently only I have to provide evidence?

Well the last two weeks I can use Scintillant as a prime example.  I could also suggest that you've not provided any support that is viable given the already covered lack of statistically significant data.  Alternatively, I could simply suggest that I don't care.  It's as valid as your point, given as much factual basis on either side.  The difference is that DE has a history of screwing things up....and I'm going to bet on human error when they define "common" as a 3% drop rate.

 

2) The status screen is a quirk of the "new" UI.

No.  Just no.  It's been around for years, and the relative slow refresh of the new UI is not a factor I am considering.  Four months ago I completed a mission, got no rewards at all, and after the mission decided to go to last mission summary.  Suddenly awards were there.  This is not new, and it's pretty apparent if you do a solo relic farm on a crap internet connection.  As you don't choose a reward there is not visual wait, and you could go through the rewards screen and be back on your orbiter prior to ever seeing the prime part drop.

 

3) You don't have to account for people leaving the reward grind.  The 67 runs is invalid because it's not counting those that get more.

Oh, I absolutely do.  While you may still have a normal distribution of rewards, there are suddenly less more people grinding harder and less casuals.  This means that disproportionately the hard grinders are going to get the arcanes, simply because they'll be pulling far more chances.  The 1407 number is based around the assumption that 50% of the population will be guaranteed to have the fully ranked arcane.  The remainder of the population will shake out to either purchasing the arcane, or dealing with not grinding.  We assume 1 sigma around the 420 mark, but that's not really touching on all of the people leaving before they can grind out a full 420 round because the rewards sucked.  Their RNG sucked.  Again, this is separate from the overall and ignores the hyper grinders.

Why does that matter?  Well, it's the platinum economy and what drives real money purchases. That 1407 represented what had to be done to have 50% get the reward.  It's not a measure of an individual's chances.  Why is that a more accurate measure than a binomial distribution?  Well, again, people aren't going to grind 420 eidolon hunts.  There is a subset of grinders that will, and even exceed this.  That's where you get the engagement...because players will say screw it and just pay someone to grind out those extra eidolon runs.  Your population will change based simply on the apparent outcomes, and this is where I say variability in the population will drive your outcome to be much higher than the binomial distribution would account for.  420 runs for you...then some unknown number of people cashing out before the 420 to simply buy arcanes instead of going through the grind.  The hyper grinders then put in more than 420 so they can sell the arcanes...because platinum buys them stuff that they want and they value their time at less than what it would cost to fork over real money for that platinum.

Is the assumption of 97% fair?  It's arguable.  I'm of the mind that 67 runs without an arcane is enough to make people quit.  In that same 67 runs there are people who got all 21 arcanes.  This is the disparity people see, due to that distribution, which makes the core mechanic of RNG not suitable as an integral rewards system long term.  You stretch it too far and it simply makes people quit.  I've pegged that loss at 3% per arcane, you can argue more or less.  That is something I literally cannot produce data on because I'd have to work at DE to have it.  I give it that because the game has things that are 3% drops for similar grinds....and they are frequently in trade for a significant enough platinum quantity to make me believe it's about skipping grind rather than expediting things.  Looking at you Braton Vandal.  

All of this still boils down to a binomial distribution assuming that people will grind infinitely.  They do not.  That's psychology 101, and not accounted for with pure math.   It's why people in economics use both statistics and psychology to develop models.  If you believe the economics are not also riven by statistics then you're always going to wind up with an incomplete picture and motivations that do not make sense.  That last bit is bolded, because it is what mathematicians often miss when making models.  It's why people play the lottery, and join in gambling at all.  The math is simple, but the people are not.

 

4) 1 in 200.  That's my only motivation

Shenanigans.  Let's add the context back to what that came from.  I suggested that I had stopped killing eidolons because my personal results were to get 1 in 200.  This was not a criticism of the model, and you're intentionally leaving out the context to compose a straw man.

I stopped grinding because of my results.  That is a direct point as to why I stated humans will not simply continue grinding forever.  It's fantastic that you can take a personal statement about why people would stop grinding, and extrapolate that to invalidate any argument that the grind will stop people from playing.

You want someone unbiased, look earlier in the thread.  Somebody stated point blank that "nobody they knew had actually done enough grinding to get all of their arcanes to maximum rank."  That's a point blank assertion that somebody got the drop, sold it to someone else for platinum, and thus there was at least one person without a drop and another who had purchased it.  As none of this is magic, let's extrapolate.

10 people run 420 total eidolon hunts.  If the binomial is correct, 21 arcanes should drop.  Those ten people don't all get together and trade their arcanes to one person.  There will be a bunch of people with partials.  Now, the same group has to run that 420 again...and again....and again.  At some point there will be half of the population with a partial of some value, and half the population which will have gotten the full riven.  My approach is to weed out those with the partials as part of the half....which allows me to multiply the chances. 

What it doesn't give me is a specific distribution.  It's crazy... but you make different assumptions with different goals and models and have different results.  It's almost like why there's different schools of thought on economics...  Wow.

So, your answer is that on average 420 ish runs of the eidolon hunt will give most people the arcane (expected value).  My answer is that given player burnout and non-optimized aggregation of arcanes there have to be 1407 runs for 50% of the player base to have a full arcane.  It's almost like both answers are different perspectives on the same question....and why I've constantly asked you to explain your assumptions.  Well, here it is.  You assume humans grind.  I assume humans will burn out.  These fundamentally different assumptions lead to a different answer, as clearly outlined by the math I suggested and the...completely unsupported calculators you've whipped together with no transparency as to how they were made.  Again, it's generally nice to be able to check work instead of linking to theory and a calculator.  I've assumed everything is kosher as benefit of doubt.  That's a courtesy.

I will cop to a poor choice of words here.  Instead of stating "you'll have to capture 1407 Hydrolysts" it should be "1407 Hydrolysts will have to be captured."  That's fair criticism of a poor grammatical error.

 

5) Accounting for the shifting population is irrelevant.

Back to the argument of humans not being machines.  They don't grind forever, and they will not tolerate things that are not rewarding.  This is going back to the base assumption you make about average for a single player, versus average for 50% of the players to be guaranteed a full arcane.  People quitting, buying arcanes from people who are better off in that distribution, people accepting having a partial arcane, and grinders are not something that the binomial distribution accounts for.

I hate to say it, but psychology drives things like this and a large set of bad rolls will prevent many players from continuing.

 

6) 2.91 rad shares it 4 radiants relics basically 3 times.

Let's talk about the statistical angle.  It's not a normal distribution because of the tail....fine.  What it is is exceptionally close.  

Now let's take the lessons of continuous improvement and process improvement.  I'm a fan of this because it's exceptionally useful for people to understand.  The expected value of a process under control is to be 1 sigma, or 68%.  You even use that terminology, and then demonstrate that for a 10% process the expected results are about 12 relics, and low and behold the normal distribution agrees with basic statistical calculations that one sigma is the same as your expected value.

Let me boil all of that down.  This will always be the case for a distribution, because it's how sigma is defined (assuming you have a controlled process).  It's how you get things like the automotive and aerospace industries, where you aim for your processes to have 6 sigma inside the upper and lower tolerances such that 6 in a million parts are defective.  

So here's my point to all of this.  Your example of a rad share proves my math works, using an entirely different methodology.  Same answer, because it's the same question.  The question you and I sought to answer with Eidolons is more complex.  I answered with the appropriate tools for my question (average runs for 50% of people to have the max rank arcane), you used a binomial distribution to answer a different question (average number of runs a person has to do in order to get the max rank arcane).  Different question, different goals, different results  Hopefully that's clear.  When we are asking the same question, we got the same answer.  You get 2.91, I get 3.  They're both one sigma, which is the answer to average runs that have to be completed to get a rare. 

 

7) Radiant making is irrelevant to the drop rate.

I'm going to not mention the grind and burn out.  I already covered that.

What I will mention is that if there is a true binomial distribution then the amount of relics you crack absolutely will influence the amount of radiants you will attain.  It's required to run between 20 and 8 relics to get the void traces.  This variable quantity has a much lower rare spawn rate, but they are rolls.  

You seem to be willing to divorce there rolls from the subsequent rolls of the rares...and I am not.  If I need to crack 10 relics, then enrich one, and repeat that on average 3 times I've actually cracked more than just the 3 you're admitting to for the radiant relics only.  This is a question of scope for me.  It's also a question of layered grind that obfuscates actual time to get the rewards as advertised.  Yes, a radiant is 10% chances but you then have to grind 10 on top of the one you want.  This is DE adding more grind into the system....which would be fine if there weren't already other layers of grind.  Grind on missions to get a chance at a relic drop, grind other missions to get "trash" relics.  Grind the trash relics to get void traces.  Use the traces to enrich a single relic to still be a 10% chance at a reward....which is on average going to take you 12 relics before you get the rare reward.

You're welcome to say it's only 3 for me.  It's basically devaluing the time everyone else spent, the maybe 120 relics required to be cracked to enrich the 12 you actually wanted.  But none of that matters.  Again, I'm not arguing the math here.  10% isn't terrible.  I'm arguing the multiple layers of grind to get this 10% and the fact that any individual likelihood is equally reasonable to model with either a binomial or a percentage calculation as long as you're doing everything in a void.

 

8) Extraordinary claims require extraordinary proof

Excel does it.  DE can't?

Define the mathematical function being used as a random number generator.  Don't provide the seeds, and as a cautionary measure regenerate the potential seeds every 90 days along with the prime access.  If you want to be cheeky copy the old Doom seed list and have some fun with it.

Again, that forum post linked to had nothing of use.  It showed a matrix of 1 and 0 valued.  Old was linear based on call time, fast was linear based upon a repeating pattern, and new was apparently more random based only on visuals.  Oh boy.  No actual useful information, just a single block of what visually looks random...and no a visual matrix is not useful because human eyes may be detecting patterns but not when there's literally hundreds of thousands of data points.  I know I'm not a savant....so I really can't tell anything form a sample.

 

9) Grind and fallout are still not relevant.

Ask the Same Question.  GIGO.

One last time, what is your assumption?  Average runs one player will do and have the 21 arcanes.  What is my question?  How many runs are required to insure 50% of the player base has the reward.  It bears repeating, again, that it's two different questions.  As such, two different models.  As such, there is relevance in players burning out, trading, and all of the associated inconsistency.  

Care to rebut?  Fine, the obvious points are that 3% of players are shed per guaranteed drop.  I'm basing that off of the end goal of 50% having 21 drops or more.  If we assumed 10% will grind out the entire thing it'll require significantly less runs per guaranteed drop, and significantly less overall.  I also haven't accounted for players getting many more than 21, and trading.  I have no means to do this.  I have not inserted my personal experience as justification that the binomial distribution is wrong.  I have stated that I experienced burn out when my position in the distribution sucked, and that other people will likely experience that same burn-out.  

 

Please take note, I called out your sortie drop list for being an insufficient sample size for any relevant data.  My own experience was the same.  I don't think the 1 in 200 is an indication of a binomial distribution model being incorrect, only that if this rate of reward continued I would never have completed the arcane without the Scarlet Spear and being able to grind for a direct reward.  I would appreciate it if you don't assume otherwise...I constantly say that my opinion is worthless, in the face of statistical realities.  It doesn't matter if I got Inaros Prime in 6 relics, when the average relic cracks for just the neuroptics is 12 radiants.  To suggest otherwise is to conflate bad RNG with bad grinds, something that I explicitly state was my goal to identify and separate.

Having 1407 dead eidolons, amongst a litany of people who stopped at only partial arcanes, points to a model of excess grind and player to player trade being functionally required.  That was never the deal.  I also presume that the extreme grinders fueling the economy and decreasing engagement time was not the goal....until DE verified that players were buying platinum and therefore supporting them simply by having such a frustrating grind.  That's my contention.  My backing for it is that DE has been profitable for the last three years in a way like never before...and it's largely been driven off of these long form grinds with player traded drops at terrible rates.  Before PoE DE was profitable, but not in the same way.  When Railjack and Old Blood failed to introduce such grind it was financially harmful.  Now mechs are here...and we have 0.201% drop chances on required 20-40 minute missions.  Almost like arcanes all over again...and somebody is willing to pay that 1200 platinum to not have to run 115 full vaults.  I wonder how much platinum will be sold to skip a potentially 80 hour grind?

Link to comment
Share on other sites

Eidolon arcane hunting hits close to me, I gave up on it already. Its not "random friendly" and if you go through recruitment chat for a squad chances are you get yelled at for doing something differently from what the host expects. 

Still, Ive done a lot of these and have have about 1 grace and guardian, and still zero energize.

Waiting for scarlet sphere I guess... 

Link to comment
Share on other sites

4 hours ago, Serafim_94 said:

I can and will argue about "insane levels of grind". I was done in about a week? Maybe 2, I don't quite remember. I did miss 2 initial weeks of operation due to covid stuff. I got every arcane set I wanted from 0 to max - with exclusion of Energize, which I had beforehand. 2 legendaries, 1 gold, 1 silver. If that's "insane grind" for you - you're better off playing some other game. Because in WF, people somehow manage to enjoy grinding Plaguestar - a literal piece of garbage - and call it good operation.

The only reason SS was "poorly received", bugs aside, was exactly because it bricked the arcane mafia economy. Good riddance.

 

That's....I'd like to say wrong but will instead say incomplete.  You forget release state, and presumably did not have to purchase everything.

 

Upon release there was a week before they even allowed all of the arcanes into the store.  Upon that release, you could only grind for the commons and the unique stuff to the event.  The following week they added the uncommon arcanes, and after that they slid the rare and legendary rewards into the drop table.

 

You had arcanes to start with....fine.  Let's look at the grind from the perspective of having nothing.  21 arcanes for a legendary.  Each legendary cost more than you could make in a single run, because they were capped for duration.  You could run multiple instances of the event...assuming your group didn't complete the limited quantity of Murexes being driven off.

Now, let's discuss the actual amount of standing required.  It's 1,123,500 event standing to get one of each arcane at maximum value.  If you did two runs during a session you'd get the maximum possible standing of 3960*2+10000= 17920.  That means simply to purchase the arcanes you needed to do 2 runs per timer at least 63 times in order to buy everything.  Each wave was 3 hours.  Let's say you only did one group per wave, because that second group was often impossible to get 2 full rotations in.  63 events * 3 hours/event = 189 hours.  That's not active game time, but the hours required in the real world.

Now tack on the 20k standing just for the Ceti Lacera, and the 15k for the Basmu.  Then tack on 21k for the unique cosmetics.  If you're nuts tack on however many stance formas are required at 5k each.  By golly, looks like we're adding on 56k at a minimum, so that's another 4 rotations and 12 hours to get the event exclusive items. 

 

Maybe now you can understand how this might be described as an insane grind.  I spent a lot of time appreciating investment into a range/duration Limbo, because the maximum duration basically skirted the sentient adaptation thing eventually added to make things less....active.  Two casts and you could just sit in the bubble without much worry about being killed.

If you're like me then you only needed a few legendaries and rares....which cut that grind way down.  If you're trying to start arcanes, because DE sold this as an alternative to the Eidolon grind, there's a good reason this event lasted more than a month.  

 

 

Let's also not suggest that two frames ate a permanent nerf because of a temporary event.  Let's also not suggest that you ever did less than 2 rotations in a wave, because the bonus was score*2 maxed at 10k standing.  Let's then forget entirely that many of these waves ended very early because 100 Murexes per instance was all you got.  Once all that's factored in, even the much smaller grind left me...less than enthused.  It was better than RNG, but in the way that getting kicked in the shins is better than being smacked by a broom.  

Link to comment
Share on other sites

I grinded some of the original warframes when I started playing. Ember, frost and like that. After those I more or less gave up on every grind I ever read up on.

Skipped all planets, just shake my head at the kurva weapons, I laugh at the riven system, nope.

First you have to get a riven, then you have to unlock it, then you have to hope it isn't for a pistol, then you have to hope it's for a good weapon, it just goes on and on with these people lol, no way I am doing any of that.

For instance the other night I read how you have to max up the second planet rep TO MAX, to craft Gaurda, lol, no. No, no, no. No.

We are still laughing at it on our discord.

In that situation I am actually more inclined to stay away from the planet-grind frames simply out of spite, even though I easily have the plat to straight buy them.

The real math of anything, isn't the context of what you are doing in itself, but rather what you could have been doing instead.

Yeah the cost is 287 runs... but also the cost of losing 287 of running something else, you could have been doing.

I'd much rather level a warframe, while opening relics, while picking up resources, getting endo etc. etc. all at once. The more you can at the same time, the better.

I also learned a long, long time ago to quite honestly not give a flying f.

I play all video games unattached to whatever items they dangle in front of me. Out of share principle denying them power over me. I am running the show, I am calling the plays. The last thing you want is some pointless item having any kind of power over you. Let it go.

I look at those arcanes and laugh, what, you want to convince me those make and break the game, and make all the difference?

Nothing is worth getting stressed out over and at any time you aren't enjoying playing a video game is time to make some adjustments and reclaim power over the situation.

 

Link to comment
Share on other sites

2 hours ago, master_of_destiny said:

average runs for 50% of people to have the max rank arcane

We can continue to throw multi-page rebuttals at each other, but I think I finally understand what your mathematical thesis is.  Let me help you out.

You are modeling something that's far beyond a simple drop table.  The 5% drop chance and the 21 drop goal are the first parameters of your model.  The 67-run "bail" point is another parameter.  Let me see if I can I can flesh the rest in enough detail that I can write some code to simulate it.

The setup:

  • Some number of players all start performing runs with a random 5% drop
    • To simplify things, the first, second, third, runs, etc. all happen simultaneously for all players.
  • If a player hits the 21 drop goal then that player "succeeds", and stops doing runs.
  • If a player hits the 67 run bail point with no drop then that player is "fails", and also stops doing runs.
    • The 67 runs with no drop must be consecutive, if a drop occurs then the counter is reset for that player. 

The punchline:

  • At some point in time, 50% of the total players have "succeeded". 
    • Note that, depending on the drop chance, drop goal, and bail point parameters, this is not always guaranteed to happen.
    • Also note that, being a discrete model, we're not likely to hit exactly 50%.  Instead, let's look for the run where it crosses 50%.
  • At the point in time where 50% of the total players have succeeded, some number of other players have failed.
  • A third group of players may still in progress, hitting neither the success nor failure conditions by that point.
  • We can add up the total number of runs performed by succeeded, failed, and in progress players up to that point in time, divide that by the number of players that have succeeded, and I believe this is the number you are looking for.
    • Do we include the runs by players that are still in progress?  I wasn't sure, but I decided to include them because it made coding easier.

I have built the above model into a python program.  It's here if you want to play with it yourself: https://github.com/buff0000n/rngsim_mod/blob/master/rngsim_mod.py

It has four parameters:

  • --prob: the drop chance, 0.05 by default.
  • --num: the drop goal, 21 by default
  • --bail: the bail point, 67 by default
  • -- percentile: the percent success that we are looking for, 50% by default.

I didn't add a parameter for this, but by default it simulates 100,000 players.  It can take up to a minute to run that on my macbook.

The random drop is governed with the numpy library's PRNG.  We can continue our argument about PRNG offline if you like, but I have to use something and numpy's PRNG is very good.  If you want to try out other ideas then it's all factored out into a drop() function you can change.

Anyway, I tested it out using a very large bail point, basically preventing any players from giving up.  Here's a result:

Quote

python rngsim_mod.py --prob 0.05 --num 21 --bail 10000 --percentile 0.5

players: 100000, successes at t=413: 50134, failures: 0, in progress: 49866, total runs: 38063964, runs per success: 759.2445047273308

The `t=413` shows the number of runs where successful players crossed 50%, which matches my other simulation's number for the median.  Great, I think this is working. 

This shows that, if there is no bailing early, then the total number of runs across the entire population to get 50% of the players to success is about 760 runs per successful player.  Interesting.

Now let's try with a bail point of 67:

Quote

python rngsim_mod.py --prob 0.05 --num 21 --bail 67 --percentile 0.5

players: 100000, successes at t=563: 50003, failures: 49653, in progress: 344, total runs: 29907592, runs per success: 598.1159530428174

Three interesting things about this result:

  • There are a few in-progress players, but most have either succeeded or failed.
  • The total runs per success has decreased to about 600.  My guess is it's mostly because of players bailing and no longer adding to the run total.
  • More interestingly, the number of runs it takes for the successful players to pass 50% is much higher, at 560. 

This means that some of those players who gave up would actually have ended up part of the 50th percentile of successful players had they stuck with it.  This doesn't disprove the gambler's fallacy, but it's food for thought.  

I was playing around with this a little bit more and discovered something else interesting.  Here's what happens when you set the bail point to something low, like 20:

Quote

python rngsim_mod.py --prob 0.05 --num 21 --bail 20 --percentile 0.5

players: 100000, successes at t=256: 9, failures: 99991, in progress: 0, total runs: 3574278, runs per success: 397142.0

Basically, this is the simulation breaking down.  By bailing after only 20 failures, so few players make it to 21 that they're essentially a rounding error.  It's almost impossible to hit 50%.

I then asked the question, what is the minimum bail point you need to actually hit 50%?  The answer turns out to be 67.  Here's 66:

Quote

python rngsim_mod.py --prob 0.05 --num 21 --bail 66 --percentile 0.5

players: 100000, successes at t=1024: 48472, failures: 51528, in progress: 0, total runs: 29369105, runs per success: 605.8983536887275

It can't quite hit 50%.  I'm not sure exactly why, but your method for coming up with a bail point of 67 has produced the minimum failure tolerance that allows 50% of the player base to succeed.  That's pretty amazing!

Anyway, I hope you found this as interesting as I did.  We can resume arguing if you like, but I came here for interesting math and now I can leave satisfied.

Link to comment
Share on other sites

Archived

This topic is now archived and is closed to further replies.

×
×
  • Create New...