Warframe - Math and statistics - Quantifying the Grind

[master_of_destiny]

44 minutes ago, Buff00n said:

Honestly I think you're given DE too much credit here.  I highly doubt this much thought goes into drop rates.  My impression from years of watching this game is they prefer to just make a decision, sometimes pulling it out of thin air, and then adjust it later as they monitor metrics and gauge reactions.  In the last year or so it seems they're preferring to err on the side of harsher grinds and weaker rewards, so that any adjustment they make is in the players' favor.  This happened most recently with Scintillant and Son Tokens.  In recent months the highest profile instance of this is the change to the Riven Dispositions of newly released weapons.  

That's why I expect something to be done about the Necramech mod situation.  The reaction has been pretty uniformly bad and their metrics can't be showing more than a pittance of them in circulation at this point.  The numbers are just way off base.

The Arcane situation is a little harder to figure out.  Eidolons have been dropping Arcanes for a couple of years, which should be plenty of time to collect data and adjust.  The simplest explanation is they don't see a need to adjust.  Eidolons were already a huge improvement over the previous method of obtaining arcanes, Trials, where you were explicitly limited to 2-3 drops a day.  The Scarlet Spear update recently increased arcanes to R6, but you could argue that didn't really change how many arcanes players were obtaining since a lot of players were doubling up on R4 Energizes anyway. 

Scarlet Spear also introduced a much, much easier path to obtain all the arcanes you want.  I think at this point, six months on, it's clear that's going to be the official answer.  Arcanes are technically obtainable at any time, but Scarlet Spear is going to be the preferred method for obtaining them.  Honestly, all we need from DE is when the next Scarlet Spear is going to be.  They usually like events to be a surprise, but considering the amount of premium currency flowing through the arcane market they need to make an exception in this case.

I wish that I could disagree.

 

 

That said, if I were designing the economy this is how I'd go about it.

Scintillant was borked in many ways.  The "common" was 3-8%, there were flags missing, and the hit box on the thing basically did not exist.  I'd chalk this up to releasing alpha an planning to patch later rather than developing an economy.  It's....really indicative of them needing this out the door to show higher player numbers after the rest of this year being so terrible.

 

The entire power scale for arcanes was idiotic.  They seem to have designed it for back in the days of Raids, where you'd never be able to get 10.  Even if you did, you either apply it to a syndana, or a single frame and it's gone.  The whole rework was botched and showed their utter lack of planning.  Personally, it seemed like the rework was simply to reinstate the older balance, but to fit that round peg into the square hole with a hammer.  When the community responded badly they instituted Scarlet Spear...which was fixing a busted leg with a band-aid.  In six months the Scarlet Spear will be the acolyte event all over again, with no lesson learned.

[Buff00n]

18 minutes ago, master_of_destiny said:

 

I'm going to use your work, so that there's no questions.  

 

4 player archetypes.  1 is the grinder, 1 is the stop at reward, and 2 are the various states of quitter.  Quitter 1 is basically a non-starter, and Quitter 2 reaches a break point before stopping.  1407/4 = 351.75 = 352.  This means on average to population will perform 352 runs each.  Can I say who makes how many runs?  Nope, no player data to work with.  

 

Does this check out?  Well, I'm not going to use my data, I'm going to use your binomial distribution:

 

 

352 appears to be where the 50% is reached rather than the expected 68% at 420.  You are welcome to give me a more exact figure, but I'm reasonably sure enough that I will stand on the point.

 

What does this prove for the economy.  Well, grinder runs more than 352.  Quitters run less.  Doesn't really matter though, the average per person is 352 despite the average required runs being 420.  This is psychology of rewards, and not math.  Math is reasonable, us squishy humans are not.

 

 

So, what are the flaws to my assumptions:

1. I cannot tell you who quits when.  I can only tell you the average between the archetypes.  To do better I need DE's data.
2. I assume that despite needing 420 runs on average people only run 352.  This is a fun little diversion which accounts for individual player luck without ever acknowledging it.  It's a trick a statistician taught me, that still isn't entirely reasonable.  It's the stupid human factor, associated with the bleed.
3. I'm doing 50% rather than an expected 68%.  Half versus one sigma is an argument to be made.  That said, I stated this assumption so it's not like I have changed the goal posts.
4. Where in hades do I get 1047/4?  Well, it's an average of the player base and not an average to be pulled from a data set.  It's again a short-cut I've been shown with regards to human behaviors.  You can alter this assumption with more data indicating the actual breakdown, but most of the time these archetypes in a large enough pool represent 4 sigma of all outcomes, and the remaining less than 1% can safely be ignored.  Gotta love a statistical model teacher who isn't tied to exact numbers but practically useful models.  

 

 

Is all of the above fair?  Well, I've stated my assumptions.  I've stated 50% was my goal.  I've stated that my model assumes an average of 3% bleed, and that the average bleed is definitely not representative of an actual figure.  I've also stated now that the 1407 actually represents 352 runs on average for a real player.  I don't know what else can be provided.

Does this actually jibe with your binomial distribution?  Well, yes.  If you have 1680 total runs (4*420) the likelihood of having the reward is 70.5%, which 100% matches with the above binomial distribution.  So we are clear, 0.70488=(1-(1-0.05)^80)^21

The conclusion therefore is that you and I got different results by coming at this problem with different goals.  Once my method has the same goal as you we get the same result.  I don't see the issue, only the difference in initial parameters leading to a reasonable discrepancy.

The distribution picture is just a summary; all the stats are available if you click the link.

The 50th percentile is around 413, and the expected average of 420 is roughly the 53rd percentile (You need to click to Query button to have it compute that number).  It's close to normal but not quite.

It looks like you're assuming there are an equal number of players in each of the four categories, and that one of each of these players types contributes some part of the 1407 runs that count towards a single complete set.  Is that a valid assumption?  Also, two out of the four categories, the grinder and the stop at reward, posses complete sets by definition.  Am I misunderstanding something?

I feel like this "human behavior shortcut" is the key to why I don't understand your math.  Can you elaborate on that?

 

35 minutes ago, master_of_destiny said:

If you have 1680 total runs (4*420) the likelihood of having the reward is 70.5%, which 100% matches with the above binomial distribution.  So we are clear, 0.70488=(1-(1-0.05)^80)^21

I don't think your equation matches your description, but your description is not precise enough to be sure. 

If you're considering 1680 runs as a whole then the probability of having at least 21 arcanes rewarded is so close to 100% that I can't find any daylight between them.

If you're considering four players that run 420 runs each, then each of their probabilities having a complete set is ~53%, and the probability that at least one of them has a complete set is 1-((1-0.53)^4) = about 95%

(1-(1-0.05)^80)^21 = the probability of doing 80 runs and seeing at least one arcane, 21 times in a row.  I don't understand how this relates to the first statement at all.

[DrivaMain]

2 hours ago, Chaemyerelis said:

Arcanes arent  needed if you like playing a gimp build.

A gimped build? You can solo the hydrolyst without energize or grace or any arcane at all. Arcanes are a luxury. Something that is nice to have. Gimped build means that build will struggle heavily in any content. Give me one mission that demands arcane energize.
 

If you really can’t stand arcane RNG you either wait for scarlet spear to return or just farm plat to get the arcanes you want.

[herflik]

You guys know it's an online game, you are not supposed to find in online games all things yourself, you are supposed to trade for stuff too.
Try to play other RPG's like Path of Exile and then whine about drop rates of stuff like mirror - people played for years and never seen any, it is probably at level of 0,00000001%.

[schilds]

23 minutes ago, herflik said:

you are not supposed to

Says who? Show me where it is written :-P. Or carved into stone tablets, if u can.

[Chaemyerelis]

1 hour ago, DrivaMain said:

A gimped build? You can solo the hydrolyst without energize or grace or any arcane at all. Arcanes are a luxury. Something that is nice to have. Gimped build means that build will struggle heavily in any content. Give me one mission that demands arcane energize.
 

If you really can’t stand arcane RNG you either wait for scarlet spear to return or just farm plat to get the arcanes you want.

Eidolons are a poor example but arcanes are important part of builds that can last a long time in steel path or arbitrations. So yeah if you dont have arcanes youre gimping yourself

[master_of_destiny]

4 minutes ago, Buff00n said:

The distribution picture is just a summary; all the stats are available if you click the link.

The 50th percentile is around 413, and the expected average of 420 is roughly the 53rd percentile (You need to click to Query button to have it compute that number).  It's close to normal but not quite.

It looks like you're assuming there are an equal number of players in each of the four categories, and that one of each of these players types contributes some part of the 1407 runs that count towards a single complete set.  Is that a valid assumption?  Also, two out of the four categories, the grinder and the stop at reward, posses complete sets by definition.  Am I misunderstanding something?

I feel like this "human behavior shortcut" is the key to why I don't understand your math.  Can you elaborate on that?

 

I don't think your equation matches your description, but your description is not precise enough to be sure. 

If you're considering 1680 runs as a whole then the probability of having at least 21 arcanes rewarded is so close to 100% that I can't find any daylight between them.

If you're considering four players that run 420 runs each, then each of their probabilities having a complete set is ~53%, and the probability that at least one of them has a complete set is 1-((1-0.53)^4) = about 95%

(1-(1-0.05)^80)^21 = the probability of doing 80 runs and seeing at least one arcane, 21 times in a row.  I don't understand how this relates to the first statement at all.

 

So, per the earlier statement I cannot provide you with a breakdown of the groups.  As such, I've assumed them to be of equal size.  In reality, the majority of people will be in the middle, with the non-engagement and the engagement until rewarded groups being disproportionately represented.  I cannot accurately model without actual data.

 

The basis on this short-cut, carving things into 4 groups, is that people respond to rewards in relatively predictable ways.  The outlier groups will do things with no direct reward, and not do things even with rewards respectively.  It was described that the moderate 2 groups largely represent 2 sigma (95%), while the outlier represent 4 sigma (99.4%), and the remainder is 0.6% so bears very little concern.  I cheated and called each group 25%, when in reality it should be 2.2%-47.5%-47.5%-2.2%.  This would mean Grinders represent 2% of the population but do about do about 2 times the grind to deal with the early quitters.  I didn't provide any of this and only offered the 352 average runs per player.  If I wanted to be more accurate we could do the math and find an average runs per group.

 

 

Now, let's account for the fun bit here.  In a binomial distribution you assume that people will grind forever.  If every single person aimed to get the arcane, there would average out to be 413 runs (I'll use the proper value instead of rounding).  That would then mean that for everyone to have an arcane they'd all have on average 413 runs, which would mean if you grabbed a person from each group their summed total should be 413*4 = 1652 runs, right?  Fantastic, numbers add up.

What the binomial distribution never accounted for was bleed.  I set my bleed at 3%, and aimed for 50% attainment.  You're assuming that there are enough arcanes generated for the 4 people with 1652 runs....and I am asserting that not everybody will earn them.  Our group will not actually earn 84 arcanes, they'll earn something less.  If you factor in 3% bleed for each of the individual earned arcanes the total runs goes from 1652 down to 1407.  

-Stating again bleed is something I have largely approximated, and would need more data to be reasonable with-

 

So let's discuss the differences here.  Your binomial distribution states average player runs 413.  My assertion with bleed indicates that average person runs 352.  This means in my simulation the people that attain and stop are everything to the left of 352 on average.  With bleed you're allowing for more but not a lot.  It also accounts for people existing who need more than those 352, but stop because the grind is not rewarding after some number of runs.  The grinders and non-starters divide up the remaining 704 runs amongst themselves.  How?  My model would require actual player data, so does not say.  It in fact doesn't say anything about who has what quantity.

How in hades am I getting to 1680 and 70% (rounding 413 to 420 is the source of the 1680)?  Let's fix that from rounding, and go for 1 sigma.  Well, let's figure out what 1 sigma is.  The value of a sigma is 68%.  You cannot run part of a drop, so utilizing my calculations and aiming for 1 sigma you require 1659 runs, which would be 414.75 runs per each of the 4 players.  Why am I using sigma instead of a flat 50%?  Well, it's not a consistent distribution.  Because you've got what can be closely approximated as a bell curve the average number of runs will in fact have to be one sigma.  

 

Hopefully that looks right.  You say with a binomial distribution you average is 413 runs.  I say that without bleed, the average runs to get 1 sigma would be 415.75 runs.  The error here is largely because I cannot have a partial run, and had to use 69.2% instead of 68%.  

So, take away my bleed but aim for the exact same outcome and we're good.  Is the bleed value accurate?  Is it realistic?  I cannot really mathematically justify that 3% bleed.  What I can tell you is if I went with a lot higher bleed then we'd have to assume that DE doesn't want people to get arcanes.  They would absolutely require the super grinders to be selling them.  That may be the case....but I've given them credit stating otherwise.

 

Per other discussions...I may be an idiot.  I may be optimistic.  I assume 50% and bleed to account for humanity doing the grinding.  If you want to assume greater bleed, go ahead.  If you want to assume even less arcanes in the actual pool, go ahead.  I just....I have to believe that DE isn't simply throwing out numbers because they look "about right."  It may be a stupid assumption, but it's been 7+ years.  If they can't get a handle on an economy we are in deep crap.

[master_of_destiny]

1 hour ago, herflik said:

You guys know it's an online game, you are not supposed to find in online games all things yourself, you are supposed to trade for stuff too.
Try to play other RPG's like Path of Exile and then whine about drop rates of stuff like mirror - people played for years and never seen any, it is probably at level of 0,00000001%.

 

I'm going to refrain from calling this stupid.  It's taking all of my will power, but I will call this completely inappropriate instead.

 

Being real here, your argument is that as long as there is any chance to drop it's acceptable.  Please, don't ever gamble.  This is the entire argument behind Vader/Luke in Battlefront 2 being a pain to earn.  The fact that people still use this argument is really baffling, as it is the admission that your time is not valuable.  If you aren't valuable, that's fine.  I think my time is valuable.  Please find some other argument that isn't devaluation of yourself, and come back to the table.

[ApocNizmith]

On 2020-09-08 at 2:51 AM, Buff00n said:

 

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?

To me it should mean if I fight it 100 times 5 of those times it is guaranteed to drop. No random chance no rng, means if I fight 100 times maybe 95 times ina row it wont drop but I know unequivocally that the next 5 kill are a 100% chance to drop that loot I was grinding for. I know that isn't how it works but to me that is how it should work.

Say a loot table has 20 items on it. The game should remember I gave him drop A from Table A, Remove drop A from their perspective loot pool for next mission. Now the mission only has 19 possible loot drops for that person and next time they run that very same mission it should now roll loot again so now that 19 drops produces say Loot C from table B, then strikes it from the list for the next run for that player and now only has 18 items in the loot pool, and that loot pool should be refreshed for that mission once all 20 items have been collected from it's pool. That way RNG still is a factor, you might get Item c from table b on your first try, you may get it on your 20th try, BUT YOU WILL ALWAYS get it within 20 tries. Otherwise you are simply gambling.

Fortuna Atmos systems is a perfect example of this. 10% drop rate (my left foot) is what it is listed as on the Wiki. So you run mission 2 of profit taker, and 10% of the time you should recieve this item meaning 1 in 10 runs will have it in theory. In practice it's RNG inside of RNG and I have ran that same mission over 700 times and I have been stuck at rank 2 with Vox Solaris for over 1.5 years because I gave up because the item i needed to progress refuses to drop for me but I have 492 radiant relics to show for that instead of being able to rank up because I need 2 more of a item that in 700 missions on the same exact mission dropped a 10% item exactly once. You see how this RNG inside of RNG is not rewarding in the least. 

[Morthal]

23 hours ago, master_of_destiny said:

 

 

Let's chalk this up as a friendly misunderstanding, so the moderators don't start eyeing things up.

I believe the "Tencent needs your support" was meant as a joke, commenting that the money was going to someone other than DE.  The retort that nobody's innocent is just as fair, given that in a global economy it's very difficult to actually identify where things came from, let alone the practices involved in making them at the price you purchased them.

 

Can we maybe agree to disagree?  It's not like there's some substantial love or hate here.

Yeah, chalk it up to cynical humor. No investors were hurt in the making of that joke.

[Buff00n]

19 hours ago, master_of_destiny said:

 

So, per the earlier statement I cannot provide you with a breakdown of the groups.  As such, I've assumed them to be of equal size.  In reality, the majority of people will be in the middle, with the non-engagement and the engagement until rewarded groups being disproportionately represented.  I cannot accurately model without actual data.

 

The basis on this short-cut, carving things into 4 groups, is that people respond to rewards in relatively predictable ways.  The outlier groups will do things with no direct reward, and not do things even with rewards respectively.  It was described that the moderate 2 groups largely represent 2 sigma (95%), while the outlier represent 4 sigma (99.4%), and the remainder is 0.6% so bears very little concern.  I cheated and called each group 25%, when in reality it should be 2.2%-47.5%-47.5%-2.2%.  This would mean Grinders represent 2% of the population but do about do about 2 times the grind to deal with the early quitters.  I didn't provide any of this and only offered the 352 average runs per player.  If I wanted to be more accurate we could do the math and find an average runs per group.

 

 

Now, let's account for the fun bit here.  In a binomial distribution you assume that people will grind forever.  If every single person aimed to get the arcane, there would average out to be 413 runs (I'll use the proper value instead of rounding).  That would then mean that for everyone to have an arcane they'd all have on average 413 runs, which would mean if you grabbed a person from each group their summed total should be 413*4 = 1652 runs, right?  Fantastic, numbers add up.

What the binomial distribution never accounted for was bleed.  I set my bleed at 3%, and aimed for 50% attainment.  You're assuming that there are enough arcanes generated for the 4 people with 1652 runs....and I am asserting that not everybody will earn them.  Our group will not actually earn 84 arcanes, they'll earn something less.  If you factor in 3% bleed for each of the individual earned arcanes the total runs goes from 1652 down to 1407.  

-Stating again bleed is something I have largely approximated, and would need more data to be reasonable with-

 

So let's discuss the differences here.  Your binomial distribution states average player runs 413.  My assertion with bleed indicates that average person runs 352.  This means in my simulation the people that attain and stop are everything to the left of 352 on average.  With bleed you're allowing for more but not a lot.  It also accounts for people existing who need more than those 352, but stop because the grind is not rewarding after some number of runs.  The grinders and non-starters divide up the remaining 704 runs amongst themselves.  How?  My model would require actual player data, so does not say.  It in fact doesn't say anything about who has what quantity.

How in hades am I getting to 1680 and 70% (rounding 413 to 420 is the source of the 1680)?  Let's fix that from rounding, and go for 1 sigma.  Well, let's figure out what 1 sigma is.  The value of a sigma is 68%.  You cannot run part of a drop, so utilizing my calculations and aiming for 1 sigma you require 1659 runs, which would be 414.75 runs per each of the 4 players.  Why am I using sigma instead of a flat 50%?  Well, it's not a consistent distribution.  Because you've got what can be closely approximated as a bell curve the average number of runs will in fact have to be one sigma.  

 

Hopefully that looks right.  You say with a binomial distribution you average is 413 runs.  I say that without bleed, the average runs to get 1 sigma would be 415.75 runs.  The error here is largely because I cannot have a partial run, and had to use 69.2% instead of 68%.  

So, take away my bleed but aim for the exact same outcome and we're good.  Is the bleed value accurate?  Is it realistic?  I cannot really mathematically justify that 3% bleed.  What I can tell you is if I went with a lot higher bleed then we'd have to assume that DE doesn't want people to get arcanes.  They would absolutely require the super grinders to be selling them.  That may be the case....but I've given them credit stating otherwise.

 

Per other discussions...I may be an idiot.  I may be optimistic.  I assume 50% and bleed to account for humanity doing the grinding.  If you want to assume greater bleed, go ahead.  If you want to assume even less arcanes in the actual pool, go ahead.  I just....I have to believe that DE isn't simply throwing out numbers because they look "about right."  It may be a stupid assumption, but it's been 7+ years.  If they can't get a handle on an economy we are in deep crap.

The negative binomial distribution I provided just assumes some will run until the goal is achieved, not quite forever, and the average is 420.  413 is the median.

Breaking up your four groups by standard deviations is just as arbitrary as breaking it up into quarters.  1 standard deviation = 68% is also only true for normal distributions, which is close to but not quite what we're looking at.  Approximations and hand-waving abound in your calculations and I think that's what bothers me the most.

Your original calculation did not start with the 3% bleed goal.  You started with 50%, and calculated the minimum failure tolerance that would just barely allow 50% of the player base to acquire 21 arcanes before giving up.  That failure tolerance worked out to be 67 runs (rounded from 66.8214726635389), which is around the 97th percentile for at least one arcane (96.7827741143869%).  The 3% bleed (3.2172258856131%) comes from your 50% goal, not the other way around.  (high precision numbers here are mainly for my future reference because I keep accidentally deleting the calculations)

So what does 67*21 actually mean?  It is the longest possible successful run for an individual player under this 3% bleed rule.  They get their next arcane on their 67th try, every single time.  They are the agonizing center of this population.  ~50% did fewer than 1407 runs and gave up, ~50% did fewer than 1407 runs and got a full set.  And in the middle, a "small number" of players did exactly 1407 runs and succeeded by the skin of their teeth.  The probability of actually making it to 1407 is on the order of 10^-32, so for all practical purposes this "small number" is zero.

Anyway, The point is that 1407 measures the worst case individual scenario under this 3% bleed rule.  I don't see a statistically rigorous way to take this number and apply it to the population as a whole.

 

We can probably calculate the average number of runs average analytically, but it's going to be messy.

One assumption we need to make is this:  With the players that get a full set in fewer than 1407 runs, there's no reason to count any additional runs they might do.  It's purely voluntary; and with no trading in this model they can't affect anyone else.  

With that in mind, I'm gonna need a spreadsheet  Here it is:  https://docs.google.com/spreadsheets/d/1GMmCZ7ePpH4dAXjswvaYRCob6y4y3PNARgvDM3ubNkY/edit?usp=sharing

The first thing we need is the expected average of a "truncated" negative binomial distribution.  This is a negative binomial distribution that only goes up to 67 trials instead of infinity.  You can see all the math on the first sheet, but the answer turns out to be about 17.2.  This is less than 20, which makes sense.  If we're not counting runs all the way up to infinity then we would expect the weighted average of runs to be less.

The next thing we need is the probability of going past 67.  On the first sheet I calculate this in two ways to double check myself.  It's about 3.22%, as mentioned above.

Now we have everything we need to calculate the expected average for the population.  We're going to have to do it for 22 separate cases.

The first case is players that do 67 runs, fail and leave empty handed.  This is 3.22% of the population.

The second case is players that get one arcane in 67 or fewer runs, but then go 0 for 67 and bleed out.  This is 3.22% * (1 - 3.22%) = 3.11% of the population, and they do an average of 17.2 + 67 = 84.2 runs.

The third case is players that get two arcanes but bleed out before the third.  This is 3.22% * (1 - (3.22% * (1 - 3.22%))) =3.01% of the population, and they do an average of (2 * 17.2) + 67 = 101.4 runs.

And so on.  This is why I need a spreadsheet.

The 21st case is players that make it all the way to 20 arcanes, but bleed out on the 21st.  These unlucky players do an average of (20 * 17.2) + 67 = 411 runs, and comprise 1.67% of the population.

The last case is everyone else.  They run the gauntlet and make it to 21 arcanes without bleeding out.  They are 50.3% of the population, a little more than 50% because we have to use 67 instead of 66.8.  They do an average of (21 * 17.2) = 361 runs. 

Adding up and weighting the runs by these 22 population buckets, we get 290 runs per player.  However, only 50.3% of the population got a full set, so the number of runs per full set is (290 / 0.503) = 577 runs.

This is kind of close to the answers I get from my simulation, which are like this:

Quote

players: 100000, successes at t=739: 50435, failures: 49565, in progress: 0, total runs: 29831776, runs per success: 591.4895608208585

591 and 577 are far enough apart that I probably have a small off-by-one error on one side or the other.  But they're in the same ballpark.  The true answer in your 3% bleed scenario is is likely somewhere between 575 and 600 runs per successfully completed arcane set. 

There, you finally made me do the thing I've been trying very hard not to do: Use a spreadsheet.  :)

We can adjust the spreadsheet to look at values for the failure tolerance other than 67, but I think my simulation is easier for that.  If we want to have a variable fault tolerance depending on how many arcanes a player has accrued then that's also doable, but we will need a different truncated negative binomial average for each bucket and that's a pain in the neck.

 

Anyway, this has been a fun academic exercise, but I think I've done enough homework considering I'm not in school anymore.  

For our other discussion, I flippantly said DE might pull numbers out of thin air, but I'm sure that's not exactly the case.  We know they have "buckets" they like to put things in, "common", "uncommon", "rare", "ultra rare", "legendary", etc.  They may even do some analysis with some numbers, but I still feel their primary method is trial and error. 

Clearly, they can't have done any binomial/time analysis on the Necramech mod drop rates.  It looks like they copy/pasted a drop table template from a regular grunt enemy that you can kill thousands of in a day and just applied it to the Necramechs.  I feel like the changes they dropped today, moving some mods to Loid's store without changing the drop rates substantially, is a trial to see if there's any bellyaching from tryhards that have already done the hundreds of runs necessary to get those mods, or the suckers who already bought them for hundreds of plat from the aforementioned tryhards.  We've all been here long enough to know that there are always those players, but in this case I doubt there are enough that they can't be safely ignored.  As I sit here with my glass half full, I'm going to assume that an actual drop table change is still a possibility.

Just like your luck with Arcane Energize will tend towards 1 in 20 with enough runs, Warframe tends towards a playable game on a long enough timeline.

[master_of_destiny]

5 minutes ago, Buff00n said:

The negative binomial distribution I provided just assumes some will run until the goal is achieved, not quite forever, and the average is 420.  413 is the median.

Breaking up your four groups by standard deviations is just as arbitrary as breaking it up into quarters.  1 standard deviation = 68% is also only true for normal distributions, which is close to but not quite what we're looking at.  Approximations and hand-waving abound in your calculations and I think that's what bothers me the most.

Your original calculation did not start with the 3% bleed goal.  You started with 50%, and calculated the minimum failure tolerance that would just barely allow 50% of the player base to acquire 21 arcanes before giving up.  That failure tolerance worked out to be 67 runs (rounded from 66.8214726635389), which is around the 97th percentile for at least one arcane (96.7827741143869%).  The 3% bleed (3.2172258856131%) comes from your 50% goal, not the other way around.  (high precision numbers here are mainly for my future reference because I keep accidentally deleting the calculations)

So what does 67*21 actually mean?  It is the longest possible successful run for an individual player under this 3% bleed rule.  They get their next arcane on their 67th try, every single time.  They are the agonizing center of this population.  ~50% did fewer than 1407 runs and gave up, ~50% did fewer than 1407 runs and got a full set.  And in the middle, a "small number" of players did exactly 1407 runs and succeeded by the skin of their teeth.  The probability of actually making it to 1407 is on the order of 10^-32, so for all practical purposes this "small number" is zero.

Anyway, The point is that 1407 measures the worst case individual scenario under this 3% bleed rule.  I don't see a statistically rigorous way to take this number and apply it to the population as a whole.

 

We can probably calculate the average number of runs average analytically, but it's going to be messy.

One assumption we need to make is this:  With the players that get a full set in fewer than 1407 runs, there's no reason to count any additional runs they might do.  It's purely voluntary; and with no trading in this model they can't affect anyone else.  

With that in mind, I'm gonna need a spreadsheet  Here it is:  https://docs.google.com/spreadsheets/d/1GMmCZ7ePpH4dAXjswvaYRCob6y4y3PNARgvDM3ubNkY/edit?usp=sharing

The first thing we need is the expected average of a "truncated" negative binomial distribution.  This is a negative binomial distribution that only goes up to 67 trials instead of infinity.  You can see all the math on the first sheet, but the answer turns out to be about 17.2.  This is less than 20, which makes sense.  If we're not counting runs all the way up to infinity then we would expect the weighted average of runs to be less.

The next thing we need is the probability of going past 67.  On the first sheet I calculate this in two ways to double check myself.  It's about 3.22%, as mentioned above.

Now we have everything we need to calculate the expected average for the population.  We're going to have to do it for 22 separate cases.

The first case is players that do 67 runs, fail and leave empty handed.  This is 3.22% of the population.

The second case is players that get one arcane in 67 or fewer runs, but then go 0 for 67 and bleed out.  This is 3.22% * (1 - 3.22%) = 3.11% of the population, and they do an average of 17.2 + 67 = 84.2 runs.

The third case is players that get two arcanes but bleed out before the third.  This is 3.22% * (1 - (3.22% * (1 - 3.22%))) =3.01% of the population, and they do an average of (2 * 17.2) + 67 = 101.4 runs.

And so on.  This is why I need a spreadsheet.

The 21st case is players that make it all the way to 20 arcanes, but bleed out on the 21st.  These unlucky players do an average of (20 * 17.2) + 67 = 411 runs, and comprise 1.67% of the population.

The last case is everyone else.  They run the gauntlet and make it to 21 arcanes without bleeding out.  They are 50.3% of the population, a little more than 50% because we have to use 67 instead of 66.8.  They do an average of (21 * 17.2) = 361 runs. 

Adding up and weighting the runs by these 22 population buckets, we get 290 runs per player.  However, only 50.3% of the population got a full set, so the number of runs per full set is (290 / 0.503) = 577 runs.

This is kind of close to the answers I get from my simulation, which are like this:

591 and 577 are far enough apart that I probably have a small off-by-one error on one side or the other.  But they're in the same ballpark.  The true answer in your 3% bleed scenario is is likely somewhere between 575 and 600 runs per successfully completed arcane set. 

There, you finally made me do the thing I've been trying very hard not to do: Use a spreadsheet.  :)

We can adjust the spreadsheet to look at values for the failure tolerance other than 67, but I think my simulation is easier for that.  If we want to have a variable fault tolerance depending on how many arcanes a player has accrued then that's also doable, but we will need a different truncated negative binomial average for each bucket and that's a pain in the neck.

 

Anyway, this has been a fun academic exercise, but I think I've done enough homework considering I'm not in school anymore.  

For our other discussion, I flippantly said DE might pull numbers out of thin air, but I'm sure that's not exactly the case.  We know they have "buckets" they like to put things in, "common", "uncommon", "rare", "ultra rare", "legendary", etc.  They may even do some analysis with some numbers, but I still feel their primary method is trial and error. 

Clearly, they can't have done any binomial/time analysis on the Necramech mod drop rates.  It looks like they copy/pasted a drop table template from a regular grunt enemy that you can kill thousands of in a day and just applied it to the Necramechs.  I feel like the changes they dropped today, moving some mods to Loid's store without changing the drop rates substantially, is a trial to see if there's any bellyaching from tryhards that have already done the hundreds of runs necessary to get those mods, or the suckers who already bought them for hundreds of plat from the aforementioned tryhards.  We've all been here long enough to know that there are always those players, but in this case I doubt there are enough that they can't be safely ignored.  As I sit here with my glass half full, I'm going to assume that an actual drop table change is still a possibility.

Just like your luck with Arcane Energize will tend towards 1 in 20 with enough runs, Warframe tends towards a playable game on a long enough timeline.

 

Let's cut all of this down, and summarize as the argument I'm seeing here.

 

You start from the point of how many runs does the average player require to get 21 arcanes.  You answer with a binomial distribution, looking for an average player at the 50% range.  This comes to 413 runs.  That's a valid answer assuming the there is no market, people never bleed off, and that the 50% is an average.  All reasonably solid assumptions assuming that this was a mechanical process and not a lottery with people.

 

 

The work you've done above appears to still be calculating that the group of 4 people still earns 21 arcanes for each player.  The conclusion there is that with people who don't engage, there will have to be between 575 and 600 runs.  I'm fine, as the math seems to agree with you.  This still works under the assumption that there will be 84 arcanes in the pool.  If that's not the case, I'm not seeing the accounting for it.

 

 

What I have assumed is that at the end there are 50% of people left grinding and assured to have the reward.  How do I come to this conclusion?  The following things are my assumptions and why.

I assume a 3% bleed because 0.97^21=0.5 (rounded of course).  I set the 50% because you aim for half of people to have a thing to spur the other half to get it, and DE chose 21 by having that as their costing.  I assume that any reasonable market is centered around people who have, people that do not, and outliers which either will have a great excess or a significant lack thereof.  If DE was going to completely restructure the arcane system they could have chosen any number for the amount of required arcanes, but they chose 21.  This sets the expectations for bleed, assuming they aren't just picking a random number.  If this is all based off of their own data then the figure of 21 is what they believe to be viable.  If it's a random number then all bets are off.  I assume they are not idiots....take of that what you will.

I assume 4 archetypal groups for my distribution of the calculated runs because it's largely how a "random" population is divided.  I assume that the population of warframe is random, because there's no demographic bias.  The joke would be that the PC master race, console peasants, and the 99% of people between those two insults represent all walks of life.  As I have no demographic data I cannot do better.  If I could I might be able to say that the grinders represented more than 2.2% of the population, or even model the bleed as something more accurate than a constant percentage.  Who knows, maybe DE's data shows that 60% of the community managed to grind out 10+ arcanes and the rebalance was simply to force more transactions to get to 21, because they're actually aiming for 20% of the community to have full arcanes because the 5% of grinders ran on average 2000+ eidolon kills over the last nearly 1000 days of being available.  Again, no data means large assumptions.  

I assume a roughly equal distribution of players from each archetype, to get an average per player.  I assume this because I have no data.  I cannot tell person x that because they are a hard grinder they'll run on average 800, while the corresponding casual will only run 60 before simply buying their way out of the grind.  Again, hands are tied so I have to provide a per person average for that 50% earning the arcane figure.

I base my assertion that our math is the same because this is statistics and not simple math.  The "average" in a controlled system is not 50%, but one sigma.  One sigma is 68%.  If I am to work backwards from the assumption of 1 sigma, and completely ignore player bleed, we come to the same conclusion.  It's demonstrating that, within a quantity of 2 runs, which demonstrates we have the same conclusion with the same initial parameters set.  

 

I entirely support questioning the 3% bleed, but it is based off the assumption DE designed an economy rather than just chose a number.

I never explicitly stated the bleed.  I showed the .97^21=50 calculation, but never clarified it was a DE driven assumption from their economic structure.

I assume with the 352 run figure that a lot of the community will not have the 21 arcanes ever.  This drives an economy.

I assume that for the 4 archetypes, 84 arcanes will not be earned.

I assume that a significant percentage of the player base will never get a full arcane exclusively through the arcane grind, hence 1407<1652 (413*4).

I contest that 2400 (600*4) runs will ever be made over the 4 archetypes.  Put simply, the regular distribution assumed for players will never support this amount of grind.

Wrapping all of this up, DE set the goal posts.  I'm happy to be wrong on assumptions, but I based them upon assuming DE planned for things.

 

 

 

Regarding the recent changes...I believe Deimos is alpha or pre-alpha.  They screwed up Scintillant.  Their economy for Son tokens was insane.  The mech mods are basically standard mod drop rates, and the endless missions are basically a filler to give people bunches of ayatan stars while hiding away the mods that are actually desired.  

I don't think there are people who have run this hundreds of times.  30-40 minutes, time gated, and only two weeks.  I can definitely see 40-80 runs made by people who have nothing else in their lives....but even then that's below a 50% chance for the tier 3 rare mod.  I won't refer to that as a try-hard, but someone who genuinely wants to experience all of warframe.  In my experience these people also include streamers/partners, who want the content so they can make money.  That's...well that's DE creating friction between the people selling their crap and their insane design choices to try and make content last for the months between releases.

My money is that they removed their heads from their behinds and checked total drops.  Their internal goals did not meet actual numbers, so they "fixed" it by removing enough mods from the pool to bouy the mech drop chances.  They'll simply run this new mix for another two weeks, and then determine if it's hitting the numbers or not.  After 7+ years it's like they have to reinvent the wheel for everything...and it points to either stupidity or a lack of someone designing the economics. The constant iteration on already easily copied systems points to some substantial management and vision issues.  That's....discouraging.  

To whit, K-drives were a great solution.  Arguably useless, but they were an internally contained system that was a diversion.  Instead of copying that the mechs had to have enemy drops....because.  If k-drives weren't so useless the mechs would have been 100% the same.  I call them useless because it took almost 2 years to get a gun, and the drives are still devoid of meaning for each component.  DE just never learns....but is always capable of making a bad copy.  Sigh... 

I don't think we're on different pages.  I'm just tired of DE plumbing new lows.

[schilds]

32 minutes ago, master_of_destiny said:

they chose 21.  This sets the expectations for bleed, assuming they aren't just picking a random number.

I'm pretty sure they simply continued the sequence 1 + 2 + 3 + 4 (old arcanes stopped here at 10) + 5 + 6 (to get 21 for current max rank) without much extra thought :-P.

[master_of_destiny]

39 minutes ago, schilds said:

I'm pretty sure they simply continued the sequence 1 + 2 + 3 + 4 (old arcanes stopped here at 10) + 5 + 6 (to get 21 for current max rank) without much extra thought :-P.

 

Very short answer, why continue?

 

Slightly longer answer, why must they set this to rank 5 if the former maximum rank was 3 (rank 0 being the start)?

 

DE decided what to do.  DE could have reworked everything at once, and did not have to do any of this.  It's functionally arguing that they just kept going, but that's the argument that you can never fix things.  They burned down the progression house for a lot of the arcanes, so setting new goals or structure would have been trivial.

Logically, I think DE is really set on the whole diminishing returns garbage.  Think of this like railjack, where each step is about the same power but the cost doubles each time.  Alternatively, they could simply have linear progression for linear power.  This adherence to decaying benefits to consistent input is a design choice that makes me believe DE is running a psychology 101 level understanding of rewards...and hammering it home with a high school level commitment to mathematics.

[Buff00n]

20 minutes ago, master_of_destiny said:

 

Let's cut all of this down, and summarize as the argument I'm seeing here.

 

You start from the point of how many runs does the average player require to get 21 arcanes.  You answer with a binomial distribution, looking for an average player at the 50% range.  This comes to 413 runs.  That's a valid answer assuming the there is no market, people never bleed off, and that the 50% is an average.  All reasonably solid assumptions assuming that this was a mechanical process and not a lottery with people.

 

 

The work you've done above appears to still be calculating that the group of 4 people still earns 21 arcanes for each player.  The conclusion there is that with people who don't engage, there will have to be between 575 and 600 runs.  I'm fine, as the math seems to agree with you.  This still works under the assumption that there will be 84 arcanes in the pool.  If that's not the case, I'm not seeing the accounting for it.

 

 

What I have assumed is that at the end there are 50% of people left grinding and assured to have the reward.  How do I come to this conclusion?  The following things are my assumptions and why.

I assume a 3% bleed because 0.97^21=0.5 (rounded of course).  I set the 50% because you aim for half of people to have a thing to spur the other half to get it, and DE chose 21 by having that as their costing.  I assume that any reasonable market is centered around people who have, people that do not, and outliers which either will have a great excess or a significant lack thereof.  If DE was going to completely restructure the arcane system they could have chosen any number for the amount of required arcanes, but they chose 21.  This sets the expectations for bleed, assuming they aren't just picking a random number.  If this is all based off of their own data then the figure of 21 is what they believe to be viable.  If it's a random number then all bets are off.  I assume they are not idiots....take of that what you will.

I assume 4 archetypal groups for my distribution of the calculated runs because it's largely how a "random" population is divided.  I assume that the population of warframe is random, because there's no demographic bias.  The joke would be that the PC master race, console peasants, and the 99% of people between those two insults represent all walks of life.  As I have no demographic data I cannot do better.  If I could I might be able to say that the grinders represented more than 2.2% of the population, or even model the bleed as something more accurate than a constant percentage.  Who knows, maybe DE's data shows that 60% of the community managed to grind out 10+ arcanes and the rebalance was simply to force more transactions to get to 21, because they're actually aiming for 20% of the community to have full arcanes because the 5% of grinders ran on average 2000+ eidolon kills over the last nearly 1000 days of being available.  Again, no data means large assumptions.  

I assume a roughly equal distribution of players from each archetype, to get an average per player.  I assume this because I have no data.  I cannot tell person x that because they are a hard grinder they'll run on average 800, while the corresponding casual will only run 60 before simply buying their way out of the grind.  Again, hands are tied so I have to provide a per person average for that 50% earning the arcane figure.

I base my assertion that our math is the same because this is statistics and not simple math.  The "average" in a controlled system is not 50%, but one sigma.  One sigma is 68%.  If I am to work backwards from the assumption of 1 sigma, and completely ignore player bleed, we come to the same conclusion.  It's demonstrating that, within a quantity of 2 runs, which demonstrates we have the same conclusion with the same initial parameters set.  

 

I entirely support questioning the 3% bleed, but it is based off the assumption DE designed an economy rather than just chose a number.

I never explicitly stated the bleed.  I showed the .97^21=50 calculation, but never clarified it was a DE driven assumption from their economic structure.

I assume with the 352 run figure that a lot of the community will not have the 21 arcanes ever.  This drives an economy.

I assume that for the 4 archetypes, 84 arcanes will not be earned.

I assume that a significant percentage of the player base will never get a full arcane exclusively through the arcane grind, hence 1407<1652 (413*4).

I contest that 2400 (600*4) runs will ever be made over the 4 archetypes.  Put simply, the regular distribution assumed for players will never support this amount of grind.

Wrapping all of this up, DE set the goal posts.  I'm happy to be wrong on assumptions, but I based them upon assuming DE planned for things.

 

 

Regarding the recent changes...I believe Deimos is alpha or pre-alpha.  They screwed up Scintillant.  Their economy for Son tokens was insane.  The mech mods are basically standard mod drop rates, and the endless missions are basically a filler to give people bunches of ayatan stars while hiding away the mods that are actually desired.  

I don't think there are people who have run this hundreds of times.  30-40 minutes, time gated, and only two weeks.  I can definitely see 40-80 runs made by people who have nothing else in their lives....but even then that's below a 50% chance for the tier 3 rare mod.  I won't refer to that as a try-hard, but someone who genuinely wants to experience all of warframe.  In my experience these people also include streamers/partners, who want the content so they can make money.  That's...well that's DE creating friction between the people selling their crap and their insane design choices to try and make content last for the months between releases.

My money is that they removed their heads from their behinds and checked total drops.  Their internal goals did not meet actual numbers, so they "fixed" it by removing enough mods from the pool to bouy the mech drop chances.  They'll simply run this new mix for another two weeks, and then determine if it's hitting the numbers or not.  After 7+ years it's like they have to reinvent the wheel for everything...and it points to either stupidity or a lack of someone designing the economics. The constant iteration on already easily copied systems points to some substantial management and vision issues.  That's....discouraging.  

To whit, K-drives were a great solution.  Arguably useless, but they were an internally contained system that was a diversion.  Instead of copying that the mechs had to have enemy drops....because.  If k-drives weren't so useless the mechs would have been 100% the same.  I call them useless because it took almost 2 years to get a gun, and the drives are still devoid of meaning for each component.  DE just never learns....but is always capable of making a bad copy.  Sigh... 

I don't think we're on different pages.  I'm just tired of DE plumbing new lows.

Again, the expected average in the simple scenario with no other conditions is 420 runs, not 413.  413 is the median, which is different from the average.  Am I making any sense?  I can't make sense of statements like: "The "average" in a controlled system is not 50%, but one sigma.".  That is gibberish to me.

I feel like we're still kind of speaking two different languages.  One or both of us are not sufficiently defining our terms.

I don't understand the insistence on separating "mechanical" processes from "people" processes.  The whole point of statistics and probability is taking a messy process and mechanizing it in a way that can be understood numerically.  It's reductive by definition.  You assign some numbers and follow a handful of rules to see where those numbers lead.  If there's something you can't assign a number to then you can't derive any numbers from it. 

In this case, the numbers were 5% drop rate, a goal of 21, and a flat failure tolerance of 67 runs, derived to ensure just barely 50% of the population reaches the goal.  The question, as I understood it, was how many total runs would have to be performed across an entire such population for each complete arcane set acquired.   That is what I solved with my spreadsheet.  This counts runs by players that give up before acquiring a full set, ~50% of the population.  This does not count extra runs by players that have already obtained 21, there is no trading in this model so those runs are meaningless.  This also does not count players that never participate in Tridolon hunts.  We are counting runs, and those players contribute zero runs. 

All those numbers lead to 577 total runs per complete set, give or take spreadsheet errors.  We didn't have to care about demographics, we didn't have to consider any behavioral groupings, unless you count the 22 possible bail scenarios.  We didn't even have to care about how big the population actually is; everything in the spreadsheet is in terms of some percentage of the total population.  Our statistical model reduces human behavior to a basic 67-run fault tolerance, and that's enough to come up with a meaningful numerical answer.  

 

We can take that 577 and talk about things like how much time players will spend in Tridolon hunts and how many extra arcanes are floating out there in incomplete sets.  If we assume Tridolons run about 15 minutes on average, then that's about 144 hours and 9 extra arcanes spread around the population for each player who farmed a complete set. These are a useful numbers.

The 67 run fault tolerance is the only real variable here, and now that we know how to derive the solution, we can adjust that variable and see where it leads. 

For example, if we increase the failure tolerance to 100, then 89% of our population will acquire a full set, and each full set represents about 450 runs across the population, getting closer to the ideal of 420.  That's about 110 hours and 1-2 extra arcanes spread around the population for each complete set.  I guess the conclusion here is that a more hardcore population is more efficient, given the assumption of no trading, which makes a certain kind of sense.

(I'm using my simulation to get these numbers because I am lazy.)

On the other hand, if we reduce that failure tolerance to 50, then only 19% of the population will acquire a full set, and each full set represents about a thousand runs across the population.  That's about 250 hours and 30 extra arcanes spread around the population for every complete set.  It's crazy that just going from 67 to 50 makes that much of a difference.

Personally, I feel like if someone's only goal is a full Arcane Energize set then 50 failures in a row would be pretty tough to swallow.  And now we know that if the population as a whole feels that way, then less than 20% of the player base will end up farming a complete set on their own.  Your model plus my solution is already providing some useful insight.

Given the name of this thread, this is the kind of stuff we can quantify about the grind, and we can use it do draw some useful conclusions.  All this other stuff about archetypes, guessing DE's thought processes, if it's not quantifiable then we can only speculate in vague terms.  That's fun, too, but you can't draw any numerical conclusions from it.

Anyway, I think we're probably about as close to agreement as we're going to get.  I may have to see if I can include a "quit factor" in my rng app, but its already pretty damn complicated.

[master_of_destiny]

18 minutes ago, Buff00n said:

Again, the expected average in the simple scenario with no other conditions is 420 runs, not 413.  413 is the median, which is different from the average.  Am I making any sense?  I can't make sense of statements like: "The "average" in a controlled system is not 50%, but one sigma.".  That is gibberish to me.

I feel like we're still kind of speaking two different languages.  One or both of us are not sufficiently defining our terms.

I don't understand the insistence on separating "mechanical" processes from "people" processes.  The whole point of statistics and probability is taking a messy process and mechanizing it in a way that can be understood numerically.  It's reductive by definition.  You assign some numbers and follow a handful of rules to see where those numbers lead.  If there's something you can't assign a number to then you can't derive any numbers from it. 

In this case, the numbers were 5% drop rate, a goal of 21, and a flat failure tolerance of 67 runs, derived to ensure just barely 50% of the population reaches the goal.  The question, as I understood it, was how many total runs would have to be performed across an entire such population for each complete arcane set acquired.   That is what I solved with my spreadsheet.  This counts runs by players that give up before acquiring a full set, ~50% of the population.  This does not count extra runs by players that have already obtained 21, there is no trading in this model so those runs are meaningless.  This also does not count players that never participate in Tridolon hunts.  We are counting runs, and those players contribute zero runs. 

All those numbers lead to 577 total runs per complete set, give or take spreadsheet errors.  We didn't have to care about demographics, we didn't have to consider any behavioral groupings, unless you count the 22 possible bail scenarios.  We didn't even have to care about how big the population actually is; everything in the spreadsheet is in terms of some percentage of the total population.  Our statistical model reduces human behavior to a basic 67-run fault tolerance, and that's enough to come up with a meaningful numerical answer.  

 

We can take that 577 and talk about things like how much time players will spend in Tridolon hunts and how many extra arcanes are floating out there in incomplete sets.  If we assume Tridolons run about 15 minutes on average, then that's about 144 hours and 9 extra arcanes spread around the population for each player who farmed a complete set. These are a useful numbers.

The 67 run fault tolerance is the only real variable here, and now that we know how to derive the solution, we can adjust that variable and see where it leads. 

For example, if we increase the failure tolerance to 100, then 89% of our population will acquire a full set, and each full set represents about 450 runs across the population, getting closer to the ideal of 420.  That's about 110 hours and 1-2 extra arcanes spread around the population for each complete set.  I guess the conclusion here is that a more hardcore population is more efficient, given the assumption of no trading, which makes a certain kind of sense.

(I'm using my simulation to get these numbers because I am lazy.)

On the other hand, if we reduce that failure tolerance to 50, then only 19% of the population will acquire a full set, and each full set represents about a thousand runs across the population.  That's about 250 hours and 30 extra arcanes spread around the population for every complete set.  It's crazy that just going from 67 to 50 makes that much of a difference.

Personally, I feel like if someone's only goal is a full Arcane Energize set then 50 failures in a row would be pretty tough to swallow.  And now we know that if the population as a whole feels that way, then less than 20% of the player base will end up farming a complete set on their own.  Your model plus my solution is already providing some useful insight.

Given the name of this thread, this is the kind of stuff we can quantify about the grind, and we can use it do draw some useful conclusions.  All this other stuff about archetypes, guessing DE's thought processes, if it's not quantifiable then we can only speculate in vague terms.  That's fun, too, but you can't draw any numerical conclusions from it.

Anyway, I think we're probably about as close to agreement as we're going to get.  I may have to see if I can include a "quit factor" in my rng app, but its already pretty damn complicated.

Terminology

420 - the average you've calculated.  This is a no brainer, as a 5% chance means with infinite runs you get 1 every 20.  21*20=420.  You'll note a discrepancy in your value and the simple calculation because of the very nature of calculating your way.  Want to demonstrate?  Well, run multiple instances of your calculator and note that the returned values vary....this is kind of the issue with this methodology.

413 - your median value.  As the expected with this calculation, the value is shifted to a lower value than the mean.  Why?  Well, the thing isn't a normal distribution, so has a much longer tail to one side.  Basically you need 21 at a minimum so cannot have a value less than that, creating compaction between 21 and 420 which moves the median lower.  This is why a binomial distribution rather than a normal one is accurate....but when you're looking at (420-413)/420 = 1.67% of an error I really don't have an issue with this being modeled as a normal distribution.  Especially not when the standard deviation it more than 10x the shift between the average and median values.

Standard deviation - 89.  You're already calculating it....and never applied it.  I believe this is a function of the function you used.  I hate to point this out, but did you include it intentionally?  If so you've provided the whole statistical argument for using 68% instead of 50%.  If it was accidental, then you've now got a justification for why it's there.  

Expected Value (statistical) - 68%.  Long bit of story, but when you're looking at a controlled system the 50% average isn't statistically useful.  What you need is the standard deviation, which is 1 sigma.  This will show you what is expected for you population.  In this instance your one sigma is between (420-89) and (420+89).  My expectation therefore is that players will run between 331 and 509 eidolons.  Please note that this is assuming they earn the thing....and the 352 value includes a bleed.

Guaranteed Value (statistical) - 99.7% coverage or 3 sigma.  The range here is 420-89*3 and 420+89*3.  This means 99.7% of the population runs between 153 and 687 runs to get 21 arcanes.

 

Note all of the above is exceptionally hard to express to someone not versed in statistics.  It is how I can come to any number between 331 and 509 and technically be correct expressing a single value....despite the fact that no single value is actually the full picture.  Try explaining to people that they will have to run a 5% drop rate between 153 and 687 times for a relatively guaranteed drop though and they'll simply glaze over.

 

 

Inadequacies of a purely mathematical model

OK, show me your mathematical model accounting for:

Player burn-out

A market to allow people to purchase the rewards rather than get them in a random drop

Any indication of what population will quit without getting the full 21 arcanes, and what that quantity is

 

I am unaware of any purely mathematical model accounting for the above.  

 

The end game 

So, I could spend a huge amount of time explaining the history.  Perhaps covering the decrease of 4 sources to 3, perhaps covering the motivations of DE to create platinum sales.  Perhaps even touching on what they seem to find as acceptable burn varying wildly between game modes.  It almost seems like each new piece of content is bolted on without regards for any other, and they have not a single person responsible for economics.

 

The problem is that if nobody drives the economic ship it will crash.  This was demonstrated with the Riven black market.  It was demonstrated with the insane price for primed chamber mod.  It was demonstrated with the maiming strike insanity.  If DE wants a player economy it has to be balanced, controlled, and not based upon value which can disappear in an instant.  With variation between 18 hours (153 captures at 7 minutes each) and 80 hours (687 captures at 7 minutes each) how can you have a reasonable value on an arcane?   When you grind out a string of functionally worthless arcanes, that you cannot even use because there's a limit of 1 per type how can you feel anything but cheated of your time?

My net point is garbage drop rates are not acceptable for valuation of anyone's time.  We can argue how to express whatever you'd like.  If a thing is valued such that it could either be 58 platinum an hour or 13 platinum an hour (assuming a 50 plat per arcane price) the game doesn't want grinding for platinum.  It wants whales to buy the items with real money.  That points towards wanting to be a mobile game, and I cannot abide it.

[Felsagger]

Buffoon, sorry but master of destiny has a strong point here. Despite his binomial probability, despite all the scientific and mathematical reasoning behind his well constructed argument, his point is pretty simple. 

Warframe MUST NOT become a TENCENT PACHINKO machine. It's a video game that deserves more attention on playing instead of betting on probability chances. Arcanes are probability buffs, they are not that reliable since they happen sporadically not constantly. 

Warframe should focus on extrinsic game play instead of intrinsic gameplay. Time gates, XP gates, Gear check gates and the grind gates throws the game out of the main purpose. Those measure for profit are called ANTI FUN. We play games to have fun not to work another salary of time on the given entertainment. 

Master of Destiny thesis is exactly what we want out of DE and TENCENT. We want moderation on how these drop chances are handled. We want fun out of our game so we invest in it happily. One of the most important capital in this society is happiness. If customers are satisfied, the game will continue being profitable for DE and TENCENT. 

 

It's that simple. 

[master_of_destiny]

On 2020-09-10 at 11:43 AM, ApocNizmith said:

To me it should mean if I fight it 100 times 5 of those times it is guaranteed to drop. No random chance no rng, means if I fight 100 times maybe 95 times ina row it wont drop but I know unequivocally that the next 5 kill are a 100% chance to drop that loot I was grinding for. I know that isn't how it works but to me that is how it should work.

Say a loot table has 20 items on it. The game should remember I gave him drop A from Table A, Remove drop A from their perspective loot pool for next mission. Now the mission only has 19 possible loot drops for that person and next time they run that very same mission it should now roll loot again so now that 19 drops produces say Loot C from table B, then strikes it from the list for the next run for that player and now only has 18 items in the loot pool, and that loot pool should be refreshed for that mission once all 20 items have been collected from it's pool. That way RNG still is a factor, you might get Item c from table b on your first try, you may get it on your 20th try, BUT YOU WILL ALWAYS get it within 20 tries. Otherwise you are simply gambling.

Fortuna Atmos systems is a perfect example of this. 10% drop rate (my left foot) is what it is listed as on the Wiki. So you run mission 2 of profit taker, and 10% of the time you should recieve this item meaning 1 in 10 runs will have it in theory. In practice it's RNG inside of RNG and I have ran that same mission over 700 times and I have been stuck at rank 2 with Vox Solaris for over 1.5 years because I gave up because the item i needed to progress refuses to drop for me but I have 492 radiant relics to show for that instead of being able to rank up because I need 2 more of a item that in 700 missions on the same exact mission dropped a 10% item exactly once. You see how this RNG inside of RNG is not rewarding in the least. 

 

I appreciate that you've got this understanding.  

 

Allow me to suggest that this would require a lot of back end crazy on the server.  For instance, imagine a random group of 4 people.  I have had a bad time, and this is my 96th run.  I define this as getting none.  My compatriot, Xxdooky_masterxX, has had a good time and is currently sitting pretty at 5 arcanes and 60 runs.  The server queries both of our accounts, and discovers that it cannot do both.  Does it err on my side, and give out an arcane?  Does it err on the side of my compatriot and give out another garbage one?  More importantly, the other arcanes also have percentage drops so it's going to be an absolute nightmare of rules and counter rules to calculate something.  Worse yet, does the server simply decide to reward everyone differently?  There's nothing quite like seeing two people get something awesome and knowing that you got hot garbage....like how the Void used to reward rare mods.

 

No, DE errs on the side of pure numbers.  Pure in the sense that if their system produces a random enough number, and we ask for enough rewards, then our results will match the provided percentages.  As such, sometimes RNGesus is capricious and cruel.   Other times you've got a full release of prime parts on day one.  

 

 

This is why sometimes you get people rolling around in Legendary cores (a 0.18% chance drop) and other times you have someone complaining that they had a single rare arcane drop after 200 runs.  I'm picking on these numbers not as an example, but because it's an anecdotal truth.  At 1050 days I should have about 1.89 legendary cores.  I have 4.  At 200+ runs of the Eidolon capture I had 1 arcane barrier.  This is what statisticians like to call a sample size too small to be significant (1), so my results are not worth consideration on their own.  It's largely why I take stock of my results as a bell weather for the human side of the equation, but not for calling shenanigans or truth for any numerically significant trends.

I do though bend that rule for DE when it feels dishonest.  DE has a long history of stupid errors.  This history started all the way back with forma drop rates, and has continued through to Scintillant.  As such, if it feels really impossible (like outlying 10% of supposed numbers) it deserves to be reviewed.

[Buff00n]

5 hours ago, master_of_destiny said:

Terminology

420 - the average you've calculated.  This is a no brainer, as a 5% chance means with infinite runs you get 1 every 20.  21*20=420.  You'll note a discrepancy in your value and the simple calculation because of the very nature of calculating your way.  Want to demonstrate?  Well, run multiple instances of your calculator and note that the returned values vary....this is kind of the issue with this methodology.

413 - your median value.  As the expected with this calculation, the value is shifted to a lower value than the mean.  Why?  Well, the thing isn't a normal distribution, so has a much longer tail to one side.  Basically you need 21 at a minimum so cannot have a value less than that, creating compaction between 21 and 420 which moves the median lower.  This is why a binomial distribution rather than a normal one is accurate....but when you're looking at (420-413)/420 = 1.67% of an error I really don't have an issue with this being modeled as a normal distribution.  Especially not when the standard deviation it more than 10x the shift between the average and median values.

Standard deviation - 89.  You're already calculating it....and never applied it.  I believe this is a function of the function you used.  I hate to point this out, but did you include it intentionally?  If so you've provided the whole statistical argument for using 68% instead of 50%.  If it was accidental, then you've now got a justification for why it's there.  

Expected Value (statistical) - 68%.  Long bit of story, but when you're looking at a controlled system the 50% average isn't statistically useful.  What you need is the standard deviation, which is 1 sigma.  This will show you what is expected for you population.  In this instance your one sigma is between (420-89) and (420+89).  My expectation therefore is that players will run between 331 and 509 eidolons.  Please note that this is assuming they earn the thing....and the 352 value includes a bleed.

Guaranteed Value (statistical) - 99.7% coverage or 3 sigma.  The range here is 420-89*3 and 420+89*3.  This means 99.7% of the population runs between 153 and 687 runs to get 21 arcanes.

 

Note all of the above is exceptionally hard to express to someone not versed in statistics.  It is how I can come to any number between 331 and 509 and technically be correct expressing a single value....despite the fact that no single value is actually the full picture.  Try explaining to people that they will have to run a 5% drop rate between 153 and 687 times for a relatively guaranteed drop though and they'll simply glaze over.

 

 

Inadequacies of a purely mathematical model

OK, show me your mathematical model accounting for:

Player burn-out

A market to allow people to purchase the rewards rather than get them in a random drop

Any indication of what population will quit without getting the full 21 arcanes, and what that quantity is

 

I am unaware of any purely mathematical model accounting for the above.  

 

The end game 

So, I could spend a huge amount of time explaining the history.  Perhaps covering the decrease of 4 sources to 3, perhaps covering the motivations of DE to create platinum sales.  Perhaps even touching on what they seem to find as acceptable burn varying wildly between game modes.  It almost seems like each new piece of content is bolted on without regards for any other, and they have not a single person responsible for economics.

 

The problem is that if nobody drives the economic ship it will crash.  This was demonstrated with the Riven black market.  It was demonstrated with the insane price for primed chamber mod.  It was demonstrated with the maiming strike insanity.  If DE wants a player economy it has to be balanced, controlled, and not based upon value which can disappear in an instant.  With variation between 18 hours (153 captures at 7 minutes each) and 80 hours (687 captures at 7 minutes each) how can you have a reasonable value on an arcane?   When you grind out a string of functionally worthless arcanes, that you cannot even use because there's a limit of 1 per type how can you feel anything but cheated of your time?

My net point is garbage drop rates are not acceptable for valuation of anyone's time.  We can argue how to express whatever you'd like.  If a thing is valued such that it could either be 58 platinum an hour or 13 platinum an hour (assuming a 50 plat per arcane price) the game doesn't want grinding for platinum.  It wants whales to buy the items with real money.  That points towards wanting to be a mobile game, and I cannot abide it.

Okay, here are my definitions:

By "expected average" what I mean is Expected Value or mean, the weighted average of all possible outcomes multiplied by how likely each outcome is.  This is 420 for a single player with no bail out.  I use with the term "expected average" because I feel it's the most understandable way to succinctly express that it's the expected value, and the mean, but not a guarantee.  The discrepancy you see in this calculation between different runs in my simulation is simply because it's not running an infinite number of trials, but the more you run the closer it will get to 420. 

By "standard deviation", I'm talking about the square root of the variance, where variance is the mean of the squared distance from the population mean.  This is a measure of how spread from the mean the data is, regardless of where the mean actually is.

This is why I don't understand statements like: "the expected value is one standard deviation".  This is nonsense according to those words as I understand them.

"Guaranteed Value" is not something I know a standard definition for.  I see this pop up on the wiki and the forums a lot, and it's annoying because it's arbitrary.  Setting it to three-sigma is just as arbitrary as picking any other number, it's not guaranteed for about 1 in 370 players.  Specifying your confidence explicitly, like 90% or 99%, is more useful and informative.

Avoiding glazed eyes is why I bring an actual picture of the distribution to conversations like these.  It allows me to express things like expected value, variance, confidence intervals, and outliers in an easy to digest way.

Your 352 number was obtained by taking the worst possible case of the bleed scenario and dividing by 4.  I've tried very hard to understand, but I can't find a purely statistical justification for this.

 

All we need for a mathematical model are rules with numbers.  

• Player burn-out = 67 run failure tolerance
• A market to allow people to purchase the rewards rather than get them in a random drop = Let's say 75% of the population wants a full set, this population is the demand.  The percentage of the population that does Eidolon runs, say 40% are the supply.  We run the model until the supply population's stockpile of arcanes equals the demand. 
  • The only real difference between this and the models I've been using up until now is we have to let the supply population that makes it to the 21 arcane goal without burning out continue past that.
  • If we want to model pricing then we have to get into supply and demand curves and economy modeling, which is possible and plenty of people do that sort of thing for a living but I am not one of them.
• What population will quit without getting the full 21 arcanes = can be derived from the player burn-out rate.  For a 67 run failure tolerance this is near 50%.
  • We can assume the percentage of those players that are also in the demand category will buy their way to 21, and the rest will sell off their partial sets.

We can assign numbers to anything a build as complicated a model as we like.  But I feel like that's unnecessary in this case.  The simple statistical models already make the case pretty strongly.

 

I get what you and @Felsagger are saying.  But if we want to make a case for a change in the grind then we can make two kinds of arguments: One based on numbers or one based on feelings.  My whole point is this:

It is possible, not that hard even, to make strong, rigorous arguments based purely on numbers and the laws of probability and statistics.  And I think such arguments are more convincing than ones based on feelings.  That's the kind of thing I was expecting when I clicked on a thread titled "Math and statistics - Quantifying the Grind", and my responses up to this point were to help us get there.

RNG is not going away.  It's by far the simplest, easiest, and most effective way to extend gameplay while providing a roughly equitable experience for players.  Yes, it is technically gambling.  We are all in a slot machine, where instead of pulling a lever we shoot things in the face.  Our wager is paid with time.  We can argue that certain slot machines are not fairly respecting our time, and I think we've done that multiple times in this thread.

I'm pretty sure the official answer for the case of arcanes is Scarlet Spear, and we need to make the case that they should be more forthcoming with exactly when Scarlet Spear will return.

The official answer so far for the Necramech situation is unsatisfying, and we should continue to make our case for change there.

There are plenty of other grinds that I think we can make the case for relief as well, check out the tail end of the Misc section in my RNG app's help file.  Shadow Stalker weapons, Broken War parts, Xiphos, there are broken slot machines all over this game.  If we understand the numbers then it's on us to make the case they should be changed by showing, with mathematical rigor, where those numbers lead.

[herflik]

On 2020-09-10 at 9:08 AM, master_of_destiny said:

 

I'm going to refrain from calling this stupid.  It's taking all of my will power, but I will call this completely inappropriate instead.

 

Being real here, your argument is that as long as there is any chance to drop it's acceptable.  Please, don't ever gamble.  This is the entire argument behind Vader/Luke in Battlefront 2 being a pain to earn.  The fact that people still use this argument is really baffling, as it is the admission that your time is not valuable.  If you aren't valuable, that's fine.  I think my time is valuable.  Please find some other argument that isn't devaluation of yourself, and come back to the table.

Online games have totally different drop table design and chances comparing to offline/single player games. Especialy games where you can trade stuff with other people. In them the drop rates are much, much lower to make the grind more rewarding and the economy not broken. If everything is easy to drop then everything is devaluted to nothing.  If everything is of no value, there is no point in trading, there is no purpose of replaying stuff, there is no challange in obtaing anything, there is no satisfaction of finding anything.

Actually you have no proper argument here, because you dont understand the simplest concept of what is "valuable". Value is equal to the effort, time and hardships invested into given activity in order to earn something. By going with your idea, you want everything to be easy, thus have no value, thus your playtime here is worthless too.

So come back to the discussion with some argument, because for now you are nothing more than socialist screaming around that you are alive, thus you deserve everything and your only accomplishment in life is being born.

If you want to discuss something  where this game have problem, then start with the lack of end-game content that would be fun enough to make you want to play it over and over and thus the grind wouldnt be so bothersom to start with.

 

[Felsagger]

3 hours ago, Buff00n said:

I get what you and @Felsagger are saying.  But if we want to make a case for a change in the grind then we can make two kinds of arguments: One based on numbers or one based on feelings.  My whole point is this:

Empiricism counts as experience. People where here seven years experimenting the probability and statistics of the Random number generator and the machine entropy. Yes, this is a case of mathematical rigor but here is the main problem. 

1. We don't have the excel pages of the official numbers generated by the users. 

2. We don't know the probability density function that Digital Extreme is using. 

3. We are trying to do reverse engineering the best way we can reconstructing an algorithm in our heads by a survey of limited information. 

4. We are gravitating on theories that helps us explain the situation but we can't measure the error percentage in our takes. 

5. We are selecting formulas without the certainty of having corroboration on the given data. We are gravitating on mere conjectures. 

 

This is my field of study. I'm simply reading what you two guys are going to bruise out of this conversation. Remember this is an exercise for us not a word written in stone or the amalgamation of information capable of making DE change their habits under TENCENT's direction. 

Quote

It is possible, not that hard even, to make strong, rigorous arguments based purely on numbers and the laws of probability and statistics.  And I think such arguments are more convincing than ones based on feelings.  That's the kind of thing I was expecting when I clicked on a thread titled "Math and statistics - Quantifying the Grind", and my responses up to this point were to help us get there.

 

Issue with this statement. Do we have the data for the quantification of the grind? The only thing that we have are the drop chance tables that DE disclose. We don't know if THAT is the truth. How we validate the truth on this information? 

 

Quote

RNG is not going away.  It's by far the simplest, easiest, and most effective way to extend gameplay while providing a roughly equitable experience for players. 

 

That's the cheapest way extending the game play when the things that should extend the game play must be replay value, enemy A.I., level design, lore and character development. However somehow we all accepted by consensus that RNG should be the way. 

 

Quote

Yes, it is technically gambling. 

Correct, there is nothing more to it. 

Quote

We are all in a slot machine, where instead of pulling a lever we shoot things in the face.  Our wager is paid with time.  We can argue that certain slot machines are not fairly respecting our time, and I think we've done that multiple times in this thread.

Then where we value skill, quick thinking, decision making, ability consistency, pedagogy of problem solving, memory learning? All of these should be considered too in a video game. 

Why should we accept simplification of immersion as the norm? 

Quote

I'm pretty sure the official answer for the case of arcanes is Scarlet Spear, and we need to make the case that they should be more forthcoming with exactly when Scarlet Spear will return.

I agree with this. DE established a quick remedy instead of a formal solution. They became victims of improvisation. 

Quote

The official answer so far for the Necramech situation is unsatisfying, and we should continue to make our case for change there.

There are plenty of other grinds that I think we can make the case for relief as well, check out the tail end of the Misc section in my RNG app's help file.  Shadow Stalker weapons, Broken War parts, Xiphos, there are broken slot machines all over this game.  If we understand the numbers then it's on us to make the case they should be changed by showing, with mathematical rigor, where those numbers lead.

 

I can't agree more with this. 

[master_of_destiny]

8 hours ago, herflik said:

Online games have totally different drop table design and chances comparing to offline/single player games. Especialy games where you can trade stuff with other people. In them the drop rates are much, much lower to make the grind more rewarding and the economy not broken. If everything is easy to drop then everything is devaluted to nothing.  If everything is of no value, there is no point in trading, there is no purpose of replaying stuff, there is no challange in obtaing anything, there is no satisfaction of finding anything.

Actually you have no proper argument here, because you dont understand the simplest concept of what is "valuable". Value is equal to the effort, time and hardships invested into given activity in order to earn something. By going with your idea, you want everything to be easy, thus have no value, thus your playtime here is worthless too.

So come back to the discussion with some argument, because for now you are nothing more than socialist screaming around that you are alive, thus you deserve everything and your only accomplishment in life is being born.

If you want to discuss something  where this game have problem, then start with the lack of end-game content that would be fun enough to make you want to play it over and over and thus the grind wouldnt be so bothersom to start with.

 

 

Wrong.  Let's break this down.

 

"Online games" include things like Unreal Tournament, Minecraft, and anything with a multiplayer aspect.  You actually mean games which are centered around a player driven economy, which the developers utilize as a means to pay for ongoing development and resources.  Let's really break this down, and look at what you are trying to come at backwards.

 

In Minecraft you purchase the game.  There is no in-game currency.  If you want, there's literally no additional payments required to the developers.  How then does Minecraft continue to work?  Well, option 1 is to sell server time.  They host a continuing world, players pay to connect and spend time there.  They can then plow server money back into development, and sell additional content or expand the offerings on their official servers.

 

How does warframe support itself?  Well, they've decided on a player driven economy.  They get money by maintaining a player economy with an intermediary currency, prime access, and cosmetics.  The important bit there, for your point, is the intermediary currency.  Yes, that's platinum.  DE can drive the sale of platinum by creating a resource in-game with some artificial scarcity.  That scarcity will amount to a developed price which people are willing to pay one another in order to avoid trying to grind the resource, and if you use the common intermediary currency in the transaction the developers will be able to have an influx of real money to pay for it.

Now, with that intermediary currency you also need continuous outlets, otherwise you'll experience devaluation by the sheer volume of it in circulation.  This is economics 101.  There's no natural decay due to usage with digital currency...so DE introduced the outlet valve of having to purchase slots.  Now there's input for purchasing, motivation for artificial scarcity of resources, and an outlet to purchase any basic resources from DE.  They control balance by offering things to grind for and things to pay for, stimulating players to continuously spend real money in order to support them.

 

Now, let's talk about the actual point you are missing.  Artificial scarcity of a digital resource.  Technically, I can infinitely reproduce a digital resource.  If DE wanted, they could send every player registered a cache of 1000 Scintillant.  This of course would crash its value.  It's almost like exactly what happened when DE decided to rebalance rivens, and the riven marketplace suddenly could no longer have insane rivens on day one costing thousands of platinum.  Why is this artificial scarcity, cited by you as a literal less than 1 in a billion chance, unreasonable?  Well, if something cannot be obtained in a reasonable amount of time people don't engage with it.  In this case, people meaning the population which plays the game.  There are outliers who will, and there are even outliers that will pay the other outliers insane amounts of the intermediary currency to do it.  The problem is that if the bulk of your community sees no value then the content dies.

Now let me simplify this for you, so your argument can be laid bare.  You suggest that if a thing drops at all there will be a trade market for it.  This is fair, as arcanes did get traded before PoE.  The catch here is that that market was functionally a joke.  The prices were nuts, the people willing to pay them were few, so you were looking at negligible volumes.  DE doesn't see a lot of profit from that.  What they can see a profit in is thousands of players wanting the arcanes, and thus large volumes of players trading with others.  This spurs people to spend real money to purchase platinum, as it's infinitely simpler than hobo farming to trade for the platinum already in-game.  The thought process is "If I spend $10 and get a thousand platinum it's infinitely easier than doing 100 trades at 10 platinum each, I don't have to grind, and the cost is small enough to not be a concern."  The question from DE's side is how to balance the drops against the grinders and payers.  

 

Now we're back to my point, and why yours is just wrong.  People will not support infinite grind.  If you look at my modelling, I even factored in a bleed factor which assumes that there will be people who find this unrewarding, and simply pay someone to grind it for them.  If I didn't this wouldn't be 1407 runs for the average (352 per player), it would be 1680 runs (420 per player).  If you read the discussion between Buf00n and I this will be a bit clearer.

I am already developing a model reliant on a market, and coming to the conclusion that the grind is too high.  You somehow missed that, and are apparently assuming I want everything accessible to all.  That's a big nope.  1407 runs for 4 people is 70 arcanes....when if everyone got the arcane it would require 84.  Those 14 represent a completely unbalanced economy that will always have less supply than demand.  That's a problem.  DE should be aiming to have the supply roughly match the demand to prevent wild fluctuations.  The total supply being dramatically under the demand leads to situations where players simply don't engage, not to an economic crash that prevents DE from getting money.

 

 

TL;DR;

Making excuses for poor drop rates, then claiming it's a way to support a virtual economy is stupid.  Really, really stupid.  In a balanced economy there will be imbalance, but because all actors understand this a relatively balanced situation will form where goods have a sustained relative value.  If you far under serve demand with a supply that is insanely low people simply will not engage in a market.  There will be outliers willing to pay a lot for things with negligible drop chances, but this forces an economy of whales.  Whales are great, but they herald pay to win.  If your game states that it is not pay to win, then develops an economy around it, you are a failure.

Please, stop devaluing your time.  I want a balanced economy, and that requires reasonable drop rates.  5% for a minimum of 10 minutes invested, with a 21 drop requirement is not a balanced economy.  The precipitous crash of value post Scarlet Spear proved this.  If you want to argue otherwise that's fine...just make a better argument than "they've got to."  If DE had better drop rates, or a smaller requirement than 21, Scarlet Spear wouldn't have been needed because the market would have priced the arcanes fairly.  It didn't, it crashed when the supply was dramatically increased because the RNG sucked, and demonstrated that DE was not running an economy that could sustain itself.

 

Alternatively, it's time to stop defending DE.  They can make money through prime access, cosmetics, and they even sell physical goods.  The development of a platinum market is the least direct route to support the game.  It's also the one most prone to manipulation of odds and subsequent claims of gambling mechanics.  Why, because EA.  Don't make this argument please.  It always ends badly, because EA.  Because FIFA.  Because once you start to gamble and get money by manipulation of odds it's really difficult to accept bad odds not being a transparent cash grab.

 

 

-Edit-

Let's talk the unbalance in a balanced economy.  I'm going to steal Buf00n's work, so credit goes to them.  The binomial distribution shows that no single number represents a "do this many runs and you get the reward," only that x amounts of the population require y runs.

 

As we have no assured drops, there will be people who require 21 runs to get the reward, and those that require 800.  In a binomial distribution you assume that each individual is ok with that, and will do the 800 runs to grind it out.  That's great in the sense that you can figure out the likelihood they have of requiring that many runs...but it's not really modelling a human system.  In the human system you're going to have some people willing to bang out 800 runs to get arcanes to sell, and those that aren't willing to run more than 20 without getting at least one arcane.  This means if there are a total of 1680 runs between 4 people, they will on average have 84 total arcanes.  The catch is the distribution of them will not be even.

This imbalance can be dealt with in two ways.  My preference is that you assume the player economy will deal with the imbalance, such that the non-grinder will purchase excess arcanes from the grinder, and the monetary costs will be balanced such that the grinder's time is valued.  In a system with enough people that will be balanced amongst the grinders, and develop a relatively stable price assuming that the influx of players stays relatively consistent with the current player population make-up.  Less obtusely, you don't suddenly get a bunch of grinders in the game tanking the market or the converse.

The less interesting way to go about this is the Baro trap.  This trap is taking a resource which is artificially scarce, and allowing for it to be turned into something else.  If that something else can buy other arcanes then the system becomes non-viable as a player driven economy of scarcity.  You just need to grind, and can earn anything, so no need to trade.  If that something else buys other things it means the supply far outstrips the demand and trade is fundamentally not viable.  Either way the Baro economy is a trap that removes common content, but devalues either trade or that content in the process.

 

For the record, arcanes are setup as a player balanced economy.  Prime parts are the Baro economy.  DE hasn't really figured out what they want, and as long as they make money I don't think they will care.  That's a bad attitude for them, but it's likely simply a case of not fixing what isn't broken.

-Edit end-

[ApocNizmith]

18 hours ago, master_of_destiny said:

 

I appreciate that you've got this understanding.  

 

Allow me to suggest that this would require a lot of back end crazy on the server.  For instance, imagine a random group of 4 people.  I have had a bad time, and this is my 96th run.  I define this as getting none.  My compatriot, Xxdooky_masterxX, has had a good time and is currently sitting pretty at 5 arcanes and 60 runs.  The server queries both of our accounts, and discovers that it cannot do both.  Does it err on my side, and give out an arcane?  Does it err on the side of my compatriot and give out another garbage one?  More importantly, the other arcanes also have percentage drops so it's going to be an absolute nightmare of rules and counter rules to calculate something.  Worse yet, does the server simply decide to reward everyone differently?  There's nothing quite like seeing two people get something awesome and knowing that you got hot garbage....like how the Void used to reward rare mods.

 

No, DE errs on the side of pure numbers.  Pure in the sense that if their system produces a random enough number, and we ask for enough rewards, then our results will match the provided percentages.  As such, sometimes RNGesus is capricious and cruel.   Other times you've got a full release of prime parts on day one.  

 

 

This is why sometimes you get people rolling around in Legendary cores (a 0.18% chance drop) and other times you have someone complaining that they had a single rare arcane drop after 200 runs.  I'm picking on these numbers not as an example, but because it's an anecdotal truth.  At 1050 days I should have about 1.89 legendary cores.  I have 4.  At 200+ runs of the Eidolon capture I had 1 arcane barrier.  This is what statisticians like to call a sample size too small to be significant (1), so my results are not worth consideration on their own.  It's largely why I take stock of my results as a bell weather for the human side of the equation, but not for calling shenanigans or truth for any numerically significant trends.

I do though bend that rule for DE when it feels dishonest.  DE has a long history of stupid errors.  This history started all the way back with forma drop rates, and has continued through to Scintillant.  As such, if it feels really impossible (like outlying 10% of supposed numbers) it deserves to be reviewed.

Simple you store it client side for each individual. So no server work needed, a addendum to the coding that tells it to remove the reward for that individual and send a packet to the pc and each person in party now has their own loot pool same as energy orb and health orb drops. As for the one dookie drop you got, doesn't matter it's now removed from the loot pool so next time that wont be an issue.

[Lutesque]

On 2020-09-07 at 11:58 PM, master_of_destiny said:

So, when people complain about the grind in this game it's time to listen and measure. 

No it's not ....

Fact is people are doing these grinds or paying to skip them...

Sure they are complaining but as long as they keep Paying that means DE has no reason to change anything.

On 2020-09-07 at 11:58 PM, master_of_destiny said:

Please, do the math for yourself, as it isn't hard. 

But it is hard 😱

On 2020-09-08 at 12:22 AM, DrivaMain said:

The thing you are forgetting is they are currently optional. Arcanes and necramech (currently) are not necessary for the main progression, 

That's fine if you are an emotionless Robot incapable of Experience Tedium and Frustration...

 

Of course you don't need Arcanes and Fancy Pants Mods to play Warframe.... Grendel Proves that you don't need those things.... But Grendel also proves that not playing without those things Sucks Donkey Balls....

Whether they are necessary or not just for the sake of getting things done is not the point....

They are necessary for most players to either Have fun...or to minimise Frustration.

I suggest you factor in Enjoyment when someone says something is needed before you disagree with them.

On 2020-09-08 at 12:22 AM, DrivaMain said:

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.

The fact that finding Groups became harder after Scarlet Speak kinda makes that Argument moot. Clearly the number of players who do Eidolon Hunts just for Funsies were eclipsed by the number of players who just wanted to get the shiny and go on about their Business somewhere else.

On 2020-09-08 at 12:22 AM, DrivaMain said:

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.

The Truth Hurts 😰. 

On 2020-09-08 at 12:39 AM, o0Despair0o said:

 

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

You're not bad at Math... You simply forgot the Probability Formula. It happens all the time... Because unlike the Formula for calculating Interesting or Area... It's not something you are likely to use often at work or at home.... You know... Doing Taxes and Fixing the Book Shelf and stuff like that.

On 2020-09-08 at 1:24 AM, C-Core said:

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.

I think you give Human Beans (no... That's not a Typo) too much credit. They are weak and Pathetic... If this Strategy didn't Work they obviously wouldn't be doing it... I don't think it's just a small group of players who are paying either ..... I think Alot of people forked over money to skip this bull S#&amp;&#036;... Myself included.

Just look at the recent update... One of the resources players had to grind was so bad that players were begging for the option to pay for it... 

On 2020-09-08 at 1:24 AM, C-Core said:

What did I do? Stop doing eidolon runs.

You would be surprised how many people lack the will power to say:. "This is Unreasonable, my time is better spent else where.".

On 2020-09-08 at 1:24 AM, C-Core said:

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..

I'm still shocked by People who don't understand this... Hell the very people who make that Argument also use Arcanes.... I guess they never bothered to check if they would keep playing if they didn't have them anymore.

 

[o0Despair0o]

11 minutes ago, Lutesque said:

You're not bad at Math... You simply forgot the Probability Formula.

I wish. I always had horrible grades in math.

 

I mean, we use numbers for grades here in germany. 1 being the best, and 6 the worst.

I got a 5 in math.

 

I don't even remember ever using that formula in math. The last formula is remember using were formulas like a² x b² = c². Geometry and stuff, and even at those I was horrible.

 

English always has been the only thing in school I was good at.