Warframe - Math and statistics - Quantifying the Grind

[Lolacrayola]

I think what master_of_destiny said about psychology is really interesting. If you think of fast, clean eidolon hunting as a rewarding goal in itself with arcanes as an inevitable byproduct, the psychology is completely different to thinking of arcanes as the goal and eidolon hunting as the barrier to their acquisition.

Either way you define the goal, it is likely to be a long term endeavour. It took me roughly 200 tricaps to get to the point where I felt that a 5 cap was possible in a 4x3 recruitment pugs. I currently have 580 tricaps and hunt eidolons for fun. I treat it a bit like a Mario Kart time trial where you race against your own ghost and the goal is to achieve a personal best time. The arcanes just piled up in the background along with sentient cores and eidolon shards.

[Morthal]

On 2020-09-07 at 10:32 PM, master_of_destiny said:

Platinum is not the panacea for bad drop rates.  It's a placebo for bad economic models.  If you support that, fine.  It'll be the slow death of this game by bleeding players who constantly see no reward to the grind.

I already uninstalled Warframe. The point made here likely won't be understood by new players or those with a chronic lack of self worth. But whatever, a fool and his money are soon parted. 

[Morthal]

12 hours ago, Serafim_94 said:

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

Warframe 'mafia' brought to you by DE's piss poor management. Don't forget it.

[(PSN)Madurai-Prime]

15 minutes ago, Morthal said:

I already uninstalled Warframe. The point made here likely won't be understood by new players or those with a chronic lack of self worth. But whatever, a fool and his money are soon parted. 

Yea definitely, people should just only work and never spend money unless it's on investments and flipping houses. Only a fool would entertain themselves in the peace and privacy of their own home.

It's definitely not foolish to quit a game and hang around on the forums to preach to people how bad a game is that you probably played for years, either. 

[master_of_destiny]

5 hours ago, Buff00n said:

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

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

The setup:

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

The punchline:

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

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

It has four parameters:

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

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

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

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

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

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

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

Three interesting things about this result:

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

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

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

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

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

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

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

 

How did I come up with the 67 runs?  End goal, with most players not tolerating infinite grind.

 

Well, each instance is 0.05% drop chance.  That means it's really easy to calculate the individual likelihood of a drop, and how many chances are required.  Create a table on n values, calculate 1-(1-0.05)^n.  

Now, how many of these instances are required?  For a mod it's 1, but for an arcane it's 21.  p^21 represents a point where you have functionally calculated the probability that with a given number of total runs, repeated 21 times, you have a likelihood of assuring the 21 drops.  In this instance 1 run copied 21 times is a 0.05^21 chance.

 

Now, the assumption.  How much of the player base does DE want to have a full set of arcanes?  Is it 10%, 20%, 100%?  I'm setting my end goal as 50% of the entire player base, because we aren't really interested in having less.  This will force trading for virtually all of our players, but will still allow for us to reasonably suggest that everything in the game can be earned.  Working backwards:

0.5 = (1-(1-0.05)^n)^21 .....math later..... n ~ 67 runs, yielding a 97% success rate for each individual arcane drop. 

At 67 runs there are definitely people getting 3 or more drops, but I don't care about them.  I care about the point of frustration which will make players quit.  Inside that 3+ drop population I'll get people willing to get 21 and stop, willing to grind as long as there's platinum in it, and those who will only continue to grind as long as the drops seem like they are rewarding.

 

 

So this is the point where I ask again about assumptions.  You're 100% right that each individual player needs on average 420ish runs to get a full arcane.  Virtually nobody is doing that math.  They're looking at their rewards to runs, and making decisions based upon outcome.  I cannot really model the losses of players per drop, because I don't have data.  What I can do is aim for an end goal where a given percentage of the community is assured to have at least the 21 drops.  I can also calculate the average player bleed per arcane, knowing that it's likely not a linear 3% but actually a power function where the more you get the less likely that you are to quit (ie 20 arcanes in the bank will have 0.5% bleed, but 100 runs without only 1 arcane drop might have a 10% bleed).

The thing about this modelling is that presumably DE did all of it, and set the goals, when they started the whole arcane rework.  I'm assuming they have internal goals for players to reach the maximum potential power level, and arcanes were that.  50% is an estimation....but it makes economic sense because they want people to desire this power, they want enough people to have it to motivate others to get it, but they don't want everyone to be able to get it.

This is where the psychology breaks into the pure mathematics.  My assumption could be 100% wrong.  Maybe they planned for anyone who didn't get an arcane after 20 runs to quit.  That would mean an average of 36% player bleed per arcane, with 0.0089% of players assured to have the full arcane after 420 total drops.  

 

 

So I'm going back to the two questions that were answered and the assumptions.

1) How many runs does an individual player have to perform on average for them to get the 21 arcanes at 0.05% drop rates.  420 (rounded) per your binomial distribution.

2) How many runs are required by the player base to assure that 50% of the population will have the 21 arcanes at a 0.05% drop rate.  The population will on average run 1407 times.

 

Instance 1 assumes players grind infinitely and without stoppage.  It assumes the binomial distribution is fair.  It also assumes no other method for getting the arcanes are pursued.

Instance 2 assumes player bleed will occur, and there will be people with 0-20 arcanes who never get to 21.  It also assumes that some players exist who get far in excess of 21 arcanes, and if tradeable will generate an economy around trading other players these drops.  End goal is to have a pool of assured "winners" and a pool of people generating economic actions by trading.  This is utilizing the psychology of rewards to spur an economy, because people are functionally reward driven and do not frame things by calculating a total average and strapping themselves in.  They respond to the dopamine hits of getting rewards, and without that will quickly seek other means to satisfy their desires.

 

Why do I prefer instance 2 for warframe?  Well, let's look at the introduction.  You start with 50 platinum for "free" upon start.  A warframe slot is 20 platinum.  A pair of weapon slots is 12.  A pair of companion slots cost 12.  Etc...  My point is that DE has given you the poisoned apple here.  There's no way to spend exactly 50 platinum.  They are spurring people to buy more platinum, because using 40 or 44 platinum will leave you with a remainder.  Psychologically, that remainder is a lost opportunity, so most people will eventually see it as a challenge to buy platinum in order to use it.  It's a base level psychological driver, and it's been present in game since basically day one.

If that sort of tactic is so fundamentally baked into warframe, then it makes perfect sense that when DE creates an economy they start with the end goal in mind.  You assume that 100% of players are not going to get a thing.  You therefore aim for a percentage of players to get it, and not.  If it's a single instance the math is easy, but if it's multiple instances you factor in a desired bleed per instance to drive that economy.  I think DE is much smarter than people give them credit for.  Their economics team is 100% aware of this, and they're constantly pushing the bubble to see what they can get away with.

Case in point, arcanes at 10 per maxed value didn't match their economic desire.  Bump it to 21.  Have a single event to silence players, and wait for a new economic stability.  Seems to have worked.  Railjack...seems to have failed.  They waited long enough to demonstrate that, and decided to halve costs.  I think that DE's economics team is manipulating things well, as they should be.  I'm just depressed that each time they push the boundaries it seems to be in ways they then offer paid short cuts.  Case in point, avionics packs, the kuva lich pack, and the mod drop chance booster. 

[master_of_destiny]

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

Yea definitely, people should just only work and never spend money unless it's on investments and flipping houses. Only a fool would entertain themselves in the peace and privacy of their own home.

It's definitely not foolish to quit a game and hang around on the forums to preach to people how bad a game is that you probably played for years, either. 

Say it with me....dopamine.

 

Let's talk real rewards here.  Your first eidolon hydrolyst capture was a dopamine hit.  It was fantastic to finally slay the beast, demonstrate that you could do it, and show your power.  Borrowing from Daikatana advertising, you made it your bi***.  That's a rush and a reward.

Now, what about Eidolon 10....20....1260?  Well, by that time the rush of killing the thing is long gone.  Why do you still do it then?  For some the dopamine rush comes from pushing themselves to do it faster.  They pioneered the 3x3, then the 4x3, and now the 6x3 barrier is there.  Maybe they can find and be the first to a 7x3, ad this is their rush.

For most people, the reward is the arcanes at the end of the mission.  Did I get the one I wanted, so that in regular missions I can shred enemies faster, live longer, or be more durable?  If not...it's a failure.  Maybe not a huge one, but there will be enough failures in a row to get people to measure their time investment versus simply forking over cash.  That's the point you reach when the dopamine is gone, and you weigh your time in game against the money.

 

So we are clear, this is about rewards being rewarding.  Tell me, is killing Vor a reward?  Is it perhaps instead a reward to get what he drops?  Do you do daily sorties because of the higher levels, or do you do it because of the reward potential?  People may play this game for many reasons, but the root is 100% the same.  We want the dopamine.  If you can't get it you put the game down and seek it elsewhere.  Denying that is foolish, because it assumes we are simply robots.  Also foolish, assuming that our dopamine source is the same as everyone else's.  Respect that other people can't get that hit from warframe, and maybe consider why.  You might find something rewarding that was not before, and give yourself a new reason to enjoy things.  I know sped runs are a dopamine hit I never thought of years ago, but immensely enjoy now.

[(PSN)Madurai-Prime]

7 minutes ago, master_of_destiny said:

Say it with me....dopamine.

 

Let's talk real rewards here.  Your first eidolon hydrolyst capture was a dopamine hit.  It was fantastic to finally slay the beast, demonstrate that you could do it, and show your power.  Borrowing from Daikatana advertising, you made it your bi***.  That's a rush and a reward.

Now, what about Eidolon 10....20....1260?  Well, by that time the rush of killing the thing is long gone.  Why do you still do it then?  For some the dopamine rush comes from pushing themselves to do it faster.  They pioneered the 3x3, then the 4x3, and now the 6x3 barrier is there.  Maybe they can find and be the first to a 7x3, ad this is their rush.

For most people, the reward is the arcanes at the end of the mission.  Did I get the one I wanted, so that in regular missions I can shred enemies faster, live longer, or be more durable?  If not...it's a failure.  Maybe not a huge one, but there will be enough failures in a row to get people to measure their time investment versus simply forking over cash.  That's the point you reach when the dopamine is gone, and you weigh your time in game against the money.

 

So we are clear, this is about rewards being rewarding.  Tell me, is killing Vor a reward?  Is it perhaps instead a reward to get what he drops?  Do you do daily sorties because of the higher levels, or do you do it because of the reward potential?  People may play this game for many reasons, but the root is 100% the same.  We want the dopamine.  If you can't get it you put the game down and seek it elsewhere.  Denying that is foolish, because it assumes we are simply robots.  Also foolish, assuming that our dopamine source is the same as everyone else's.  Respect that other people can't get that hit from warframe, and maybe consider why.  You might find something rewarding that was not before, and give yourself a new reason to enjoy things.  I know sped runs are a dopamine hit I never thought of years ago, but immensely enjoy now.

Oh yea I agree. I left a game that wasn't satisfying me anymore and moved on to something else. Some people don't think speeding is fun, yet we have an entire sanctioned sport and subculture for racing.

I think some people either won't like the game when they start it, and they'll leave, and I think some people play a game too long and aren't satisfied anymore. 

I haven't been here since 2013 so I didn't get to watch the game change over time. I like warframe for what it is now, but I understand if someone looks at a new person and says "How the heck could you like this? All my friends have left and it's going down the drain." But fortunately life is varied enough that people can like many different things. I plan to play warframe for multiple years, and if I get tired of it I'll leave, but for now I'm having a lot of fun. 

 

[Felsagger]

On 2020-09-07 at 5:58 PM, master_of_destiny said:

Hello all,

 

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

 

Eidolons

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

 

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

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

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

 

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

 

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

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

-Edit-

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

-Edit end-

 

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

 

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

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

 

 

 

Necramechs

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

p₃= 1-(1-0.00201)^^(n*3)

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

p₂= 1-(1-0.00201)^^(n*2)

p₁= 1-(1-0.00201)^⁽ⁿ⁾

 

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

 

 

The Conclusion:

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

 

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

 

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

 

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

I always enjoyed binomial distributions. <3

Precise explanation. One of the best accurate academic argument I've seen in the forums. 

 

1. This is a business and business needs profits. At least this is not a Pachinko machine. There is a game involved with lore, weapons, upgrade systems and options for play styles. The player is not stranded or obligated on the possession of Rivens and Arcanes. These are power creep devices for people who seek endurance. Efficiency, efficacy and effectiveness are personal preferences. 

 

2. The player can moderate their progress. They are not forced to run the mill the first day. DE has moderate content for the fresh player but the veteran simply breeze if he/she is not capped. If there is no restriction people would be finishing Deimos in two days. The game has obligatory XP time gates, resource gates and gear check gates for a reason. If the game liberates those boundaries then players will consume content faster than the capacity of the developer of producing them. 

 

3. I do not disagree with your idea of disproportion of grind and reward. If grind is designed to be this punitive then at least the reward should be equally satisfying. But once 90 passes DE and TENCENT will expect gains. Eventually Trumna, Mauslon, the War Hammer 40k hand gun and the Dreadnought or Necramech will get the nerf since interest needs to be shifted in this GAAS F2P ARPG pseudo 'MOBA' game. 

If DE forces us mining and fishing at least make it be more appropiate to War Frame lore like the excavation game modes but with the option of calling more than three orbital drillers. The grinding must not become an ANTI FUN device. The probability drop rates are absurd for what the game rewards. If there are some sort of moderation, the majority of players will accept the moderate challenge. DE must learn from Railjack, Plains of Eidolons, Fortuna. Deimos was great but it's just to brief. It's understandable but we expect a bit more from it. With the experience gained up to this point, Railjack, PoE and Fortuna may get a well deserved update. These places can be great again other than being content islands, in my opinion. 

 

 

[(XBOX)ECCHO SIERRA]

On 2020-09-07 at 4:22 PM, DrivaMain said:

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

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

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

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

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

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

"Hurr durr its optional"

Sure. In the same way playing warframe at all is optional.

 

"HuRr DuRrRrRrR *slurping noises* but you dont have to do the thing* doesnt mean its designed well.

 

[xombob89]

55 minutes ago, (XB1)ECCHO SIERRA said:

"Hurr durr its optional"

Sure. In the same way playing warframe at all is optional.

 

"HuRr DuRrRrRrR *slurping noises* but you dont have to do the thing* doesnt mean its designed well.

 

Indeed, most things in the game are optional and not required for progression but warframe is all about customization. Arcanes change the way your warframes and weapons perform considerably, so it shouldn't be locked behind  1 gamemode with a ridiculously low droprate for something you want. I wouldnt mind the drop rate as much if you could get them from alternative sources, grinding same mission for thousands of times with no guarantee you'll ever get what you want is not fun. 

In fact they should rotate all rewards sometimes, like put those arcanes in ISO vaults for a limited time for example or arbitrations, then after a while move somewhere else for sake of variety at least. Maybe not in the way I proposed but you catch my meaning, variety! 

[abstractwhiz]

On 2020-09-07 at 4:36 PM, C-Core said:

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

The uncharitable interpretation is that those numbers are chosen for two reasons: 

1. They're low enough that people will engage with the system a lot to try and get those rare drops. This improves gameplay metrics, which looks good for the company.
2. The rarity will drive up demand, which will raise trading prices for the rare items, which ultimately means someone will buy plat with real money to bypass the insane grind. This makes DE money.

Of course there will be a lot of angry yelling and negative feedback. But none of that means anything if enough people still end up grinding and/or buying plat. From the company's perspective, it's a tradeoff: Does the expected value we gain from the low grinds outweigh the expected loss from the negative feedback? If yes, then ignoring the negative feedback and just continuing on your present course is the optimal move. And it looks like that's what we're seeing. 

There's also a potential hybrid strategy: Keep all the drop chances low for a few months. You'll make a bunch of money and see a lot of gameplay during these periods. Eventually you'll hit diminishing returns, because a general consensus has built up among those without the stuff that it's not worth engaging with. Then you boost the drop chances or make the items available for standing or something. That generates some positive publicity, you see some more gameplay from people grinding RNG or standing, and you make some more money when the people who get the mods sell them to people who are willing to pay for skipping the grind. 

It's not enough to complain about the grind. It's only when no one is engaging with it -- by grinding or trading -- that there is a real incentive to address the complaints. Right now this is not the case: People complain, but also grind and/or buy the stuff.

Also disengaging might not be enough if we're dealing with a disconnected content island with no downstream implications, such as the Steel Path. Then it's just a sunk cost that gets written off. 

[(XBOX)Tucker D Dawg]

23 minutes ago, abstractwhiz said:

There's also a potential hybrid strategy: Keep all the drop chances low for a few months. You'll make a bunch of money and see a lot of gameplay during these periods. Eventually you'll hit diminishing returns

This has been their implementation for years. Hard to acquire or massively resource intensive for months (or even years) then reduce it when something new and shiny comes out.

Mutagen Samples drop locations, mesa key requirements, kela/ambulas requirements, focus schools, cetus wisps, alcolyte mods, warframe blueprint costs from simaris....

it is no longer financially beneficial to have the cetus/PoE grind be excessive as that is not what is attracting new players -its the current world hype.  its not financially beneficial to have old content that is a requirement (or a big advantage in gameplay) to complete new content be gated for newer players - so they reduce the old content cost to allow new players to breeze through it to get to the latest shiny.  

They (DE) got their usage spike, doubler and plat sales from PoE already and now need to min/max effort/profit on Deimos.

 

 

[Morthal]

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

Yea definitely, people should just only work and never spend money unless it's on investments and flipping houses. Only a fool would entertain themselves in the peace and privacy of their own home.

It's definitely not foolish to quit a game and hang around on the forums to preach to people how bad a game is that you probably played for years, either. 

Go buy plat, Tencent needs your support.

[(PSN)Madurai-Prime]

27 minutes ago, Morthal said:

Go buy plat, Tencent needs your support.

Go buy....anything really. You're still supporting China yourself. The electronic device you used to type that response was made using materials mined by children or slaves. No one's "innocent" dude.

[master_of_destiny]

On 2020-09-07 at 6:22 PM, DrivaMain said:

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

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

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

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

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

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

So, let's circle back and explain exactly what was said one more time.  Let's also clarify.

 

Statement 1, DE has sold this as a free to play game, that is not pay to win.  This included the statement that power is not locked behind a pay wall.

Statement 2, DE is a western style developer, competing largely in western markets.  This is clarification of acceptable practices from a cultural standard.  I make it because "Korean grind MMO" is a short-hand for stating that grind is far in excess of reasonable without purchased items.  This is defined from the perspective of a western consumer.

Statement 3, "It's optional" as not a valid argument for anything that provides real power or utility.  This statement is bound by DE's mechanical choices.  This means anything influencing stats, offering mastery rank, or otherwise capable of modifying stats.

Statement 4, DE is not stupid.  While individually we may consider their actions as questionable, their goal is to actually develop a secondary market and spur the sale of platinum.  It's not a free game, and developers have to eat.  

 

 

Now, with all of that said, you're basically making my argument in a different way here.  Buf00n rightly pointed out that it really only takes about 420 runs for a single person to obtain the 21 required arcanes by modeling a binomial distribution of the drops.  They were even kind enough to provide the underlying mathematical construct, so it could be demonstrated and checked.  

Where then does my 1407 come from?  Well, per your above statement there's an economy.  Pointing to Statement 4 above, DE has designed the drop economy and chances in such a way as to have basically forced an economy.  50% are guaranteed to have at least the 21 arcanes at 1407 total runs within the player pool, but that player pool also includes people with a lot more than 21 and those who stopped the grind with a lot less than 21.

DE relies on that to drive platinum sales.  The simple logic is "screw this, my time is worth more so I'll just buy it from another player."  That's fine, it means somebody somewhere has to purchase platinum with real money.  This means that by installing such a grind DE will get paid, even if it's half a dozen player to player trades down the line.  Fantastic.  It also means that there's quite a lot of grind built into the system that will inevitably burn people out.  That's not so fine.

 

Put in short....I am accounting for the extra arcanes with my calculation.  A binomial distribution will give you a single player's requirement to get the 21 arcanes, and it's about 420 runs.  The crux of your argument is that arcanes can then be traded for platinum....so that you don't have to do the grind and can buy it from someone else....who had to do the grind.  This is how the 420 runs becomes 1407 with a different mathematical model (and why the two of us spent pages trying to come to an understanding).

As an aside, DE survived before arcanes.  They still sell all the things they used to, cosmetics and prime access.  This is how they survived for 4+ years before PoE dropped.  This is how the arcane market wasn't a thing when they only dropped once a day from the Raids.  You're welcome to use the backwards justification of "bad drop chances and grind are acceptable because developers have to eat," but if you do then you've got to justify how we got here.  I cannot.  I happily paid DE when the game was significantly less robust, but with all of the multi-layered and painful grinds they've installed I cannot justify giving them money any longer.

[master_of_destiny]

1 hour ago, Morthal said:

Go buy plat, Tencent needs your support.

 

1 hour ago, (PS4)Madurai-Prime said:

Go buy....anything really. You're still supporting China yourself. The electronic device you used to type that response was made using materials mined by children or slaves. No one's "innocent" dude.

 

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.

[Buff00n]

12 hours ago, master_of_destiny said:

 

How did I come up with the 67 runs?  End goal, with most players not tolerating infinite grind.

 

Well, each instance is 0.05% drop chance.  That means it's really easy to calculate the individual likelihood of a drop, and how many chances are required.  Create a table on n values, calculate 1-(1-0.05)^n.  

Now, how many of these instances are required?  For a mod it's 1, but for an arcane it's 21.  p^21 represents a point where you have functionally calculated the probability that with a given number of total runs, repeated 21 times, you have a likelihood of assuring the 21 drops.  In this instance 1 run copied 21 times is a 0.05^21 chance.

 

Now, the assumption.  How much of the player base does DE want to have a full set of arcanes?  Is it 10%, 20%, 100%?  I'm setting my end goal as 50% of the entire player base, because we aren't really interested in having less.  This will force trading for virtually all of our players, but will still allow for us to reasonably suggest that everything in the game can be earned.  Working backwards:

0.5 = (1-(1-0.05)^n)^21 .....math later..... n ~ 67 runs, yielding a 97% success rate for each individual arcane drop. 

At 67 runs there are definitely people getting 3 or more drops, but I don't care about them.  I care about the point of frustration which will make players quit.  Inside that 3+ drop population I'll get people willing to get 21 and stop, willing to grind as long as there's platinum in it, and those who will only continue to grind as long as the drops seem like they are rewarding.

 

 

So this is the point where I ask again about assumptions.  You're 100% right that each individual player needs on average 420ish runs to get a full arcane.  Virtually nobody is doing that math.  They're looking at their rewards to runs, and making decisions based upon outcome.  I cannot really model the losses of players per drop, because I don't have data.  What I can do is aim for an end goal where a given percentage of the community is assured to have at least the 21 drops.  I can also calculate the average player bleed per arcane, knowing that it's likely not a linear 3% but actually a power function where the more you get the less likely that you are to quit (ie 20 arcanes in the bank will have 0.5% bleed, but 100 runs without only 1 arcane drop might have a 10% bleed).

The thing about this modelling is that presumably DE did all of it, and set the goals, when they started the whole arcane rework.  I'm assuming they have internal goals for players to reach the maximum potential power level, and arcanes were that.  50% is an estimation....but it makes economic sense because they want people to desire this power, they want enough people to have it to motivate others to get it, but they don't want everyone to be able to get it.

This is where the psychology breaks into the pure mathematics.  My assumption could be 100% wrong.  Maybe they planned for anyone who didn't get an arcane after 20 runs to quit.  That would mean an average of 36% player bleed per arcane, with 0.0089% of players assured to have the full arcane after 420 total drops.  

 

 

So I'm going back to the two questions that were answered and the assumptions.

1) How many runs does an individual player have to perform on average for them to get the 21 arcanes at 0.05% drop rates.  420 (rounded) per your binomial distribution.

2) How many runs are required by the player base to assure that 50% of the population will have the 21 arcanes at a 0.05% drop rate.  The population will on average run 1407 times.

Thank you for explaining it again, I think I finally see what you're getting at, but there are still issues.

0.5 = (1-(1-0.05)^n)^21 => n = 66.82.  Fine, but what is that actually calculating?  Let me go from the inside out and interpret each stage.

(1-0.05)^n) = the probability of doing n runs and not seeing a single arcane.

(1-(1-0.05)^n) = the probability of doing n runs and not not seeing a single arcane = the probability of going n runs and seeing at least one arcane.

 (1-(1-0.05)^n)^21 = the probability of doing n runs and seeing at least one arcane, 21 times in a row.

0.5 = (1-(1-0.05)^n)^21 => solve for n such that the probability of doing n runs and seeing at least one arcane, 21 times in a row, is 50%.  

Okay, I think I understand why 67 works out perfectly in my simulation given that description.

However, the conclusion you draw, that every full arcane set requires 67*21 runs across the player population, does not follow.  Among other issues, you can't ignore the "at least" part of the interpretation.  If we allow for trading, and I believe that's your intention, then the extra arcanes that most players will get doing 67 runs can go towards completing other players' sets, even players that gave up or never farmed the arcane at all.  The expected average outcome from 1407 runs is 70 arcanes, enough for more than three complete sets. 

You can't say that 1407 runs are required to complete each set when there is so much surplus in this scenario.  If we want to know how many runs are required, then we should be looking for the minimum number of runs that must occur for half the player base to have a complete set. 

 

Let me try thinking about it differently.  

If the player base is N people, and you want to find out the minimum total runs it takes for 50% of those N players to have 21 arcanes, including trading, then isn't it sufficient to calculate how many runs across the entire population it takes to accumulate 0.5 * N * 21 arcanes in total? 

Before trading, some portion of the population has exactly 21, and the rest either have a surplus or a deficit.  After trading, 50% of the population has 21 and the other 50% have zero.  We don't have to care which players give up, and which players farm hundreds of runs.  It doesn't matter which players sell all their arcanes, which players sell their surplus, which players buy their way to 21, or which players never get any.  If the population has accrued 0.5 * N * 21 arcanes, distributed in any possible way, then there's enough for half of them to have a full set.

To make things more useful, it's probably better to calculate the expected average for the minimum total runs.  This is a very simple calculation.  A drop rate of 0.05, or a 1 in 20 chance means the expected average number of runs to get one drop is 20 (the one and only place in statistics where the obvious answer is the correct one).  So the expected average number of runs Rx needed to get X drops is X * 20, or X / 0.05. 

Rx = (0.5 * N * 21) / 0.05

If we have 0.5 * N complete sets, then to calculate the expected average number of runs per complete set, R1, we divide by 0.5 * N:

R1 = ((0.5 * N * 21) / 0.05) / (0.5 * N)

Simplify:

R1 = 21 / 0.05

Expected average runs for each full set = 420

Note that the both N and the 50% criteria cancel out of the equation.  It doesn't matter how big the population is, and it doesn't matter if our goal is for 10% of the population to have a complete set, or 99% of the population to have a complete set.  The expected average number of runs per complete set, across the entire population, assuming everyone trades, is always 420.

 

The only assumption here is that everyone trades until they either have a full set or nothing.  If we want to say that not everyone trades, or that some hoarders will keep a surplus stockpile, then those are things we would have to explicitly model to get any numbers out of.  That would be fun, but it would probably produce a model too complex to solve any way other than empirically.

We can also try taking about the median instead of the expected average, but unfortunately that also turns out to only be solvable empirically. 

 

420 runs is still an absolutely ridiculous number considering the average tryhard can do maybe a 10-20 runs in a day.  There's no need to invent ways get higher numbers when the obvious one is already outrageous.

[Buff00n]

5 minutes ago, master_of_destiny said:

50% are guaranteed to have at least the 21 arcanes at 1407 total runs within the player pool, but that player pool also includes people with a lot more than 21 and those who stopped the grind with a lot less than 21.

I hit submit before reading your latest response, and now I think I'm back to not understanding what you're trying to calculate at all.

How does the 67 * 21 run gauntlet you've constructed get spread out among more than one player? 

It's constructed in a way that ensures 50% of players will make it through, but the vast majority will hit 21 arcanes long before hitting 1407 runs.  Are you assuming that all those players just keep going after 21?  If not, where does it account for players bailing either because they went 67 without an arcane or hit 21? 

If trading is not included in the model, then why are runs a player makes past their 21 arcane goal relevant at all?  Those runs are purely voluntary and don't help the population reach 50%.

 

If you're not allowing for trading until after 50% of the player base completes a set, and you're trying to model discouraged players leaving after 67 failures, then I believe the python simulation I provided earlier produces the correct result.

[master_of_destiny]

5 minutes ago, Buff00n said:

Thank you for explaining it again, I think I finally see what you're getting at, but there are still issues.

0.5 = (1-(1-0.05)^n)^21 => n = 66.82.  Fine, but what is that actually calculating?  Let me go from the inside out and interpret each stage.

(1-0.05)^n) = the probability of doing n runs and not seeing a single arcane.

(1-(1-0.05)^n) = the probability of doing n runs and not not seeing a single arcane = the probability of going n runs and seeing at least one arcane.

 (1-(1-0.05)^n)^21 = the probability of doing n runs and seeing at least one arcane, 21 times in a row.

0.5 = (1-(1-0.05)^n)^21 => solve for n such that the probability of doing n runs and seeing at least one arcane, 21 times in a row, is 50%.  

Okay, I think I understand why 67 works out perfectly in my simulation given that description.

However, the conclusion you draw, that every full arcane set requires 67*21 runs across the player population, does not follow.  Among other issues, you can't ignore the "at least" part of the interpretation.  If we allow for trading, and I believe that's your intention, then the extra arcanes that most players will get doing 67 runs can go towards completing other players' sets, even players that gave up or never farmed the arcane at all.  The expected average outcome from 1407 runs is 70 arcanes, enough for more than three complete sets. 

You can't say that 1407 runs are required to complete each set when there is so much surplus in this scenario.  If we want to know how many runs are required, then we should be looking for the minimum number of runs that must occur for half the player base to have a complete set. 

 

Let me try thinking about it differently.  

If the player base is N people, and you want to find out the minimum total runs it takes for 50% of those N players to have 21 arcanes, including trading, then isn't it sufficient to calculate how many runs across the entire population it takes to accumulate 0.5 * N * 21 arcanes in total? 

Before trading, some portion of the population has exactly 21, and the rest either have a surplus or a deficit.  After trading, 50% of the population has 21 and the other 50% have zero.  We don't have to care which players give up, and which players farm hundreds of runs.  It doesn't matter which players sell all their arcanes, which players sell their surplus, which players buy their way to 21, or which players never get any.  If the population has accrued 0.5 * N * 21 arcanes, distributed in any possible way, then there's enough for half of them to have a full set.

To make things more useful, it's probably better to calculate the expected average for the minimum total runs.  This is a very simple calculation.  A drop rate of 0.05, or a 1 in 20 chance means the expected average number of runs to get one drop is 20 (the one and only place in statistics where the obvious answer is the correct one).  So the expected average number of runs Rx needed to get X drops is X * 20, or X / 0.05. 

Rx = (0.5 * N * 21) / 0.05

If we have 0.5 * N complete sets, then to calculate the expected average number of runs per complete set, R1, we divide by 0.5 * N:

R1 = ((0.5 * N * 21) / 0.05) / (0.5 * N)

Simplify:

R1 = 21 / 0.05

Expected average runs for each full set = 420

Note that the both N and the 50% criteria cancel out of the equation.  It doesn't matter how big the population is, and it doesn't matter if our goal is for 10% of the population to have a complete set, or 99% of the population to have a complete set.  The expected average number of runs per complete set, across the entire population, assuming everyone trades, is always 420.

 

The only assumption here is that everyone trades until they either have a full set or nothing.  If we want to say that not everyone trades, or that some hoarders will keep a surplus stockpile, then those are things we would have to explicitly model to get any numbers out of.  That would be fun, but it would probably produce a model too complex to solve any way other than empirically.

We can also try taking about the median instead of the expected average, but unfortunately that also turns out to only be solvable empirically. 

 

420 runs is still an absolutely ridiculous number considering the average tryhard can do maybe a 10-20 runs in a day.  There's no need to invent ways get higher numbers when the obvious one is already outrageous.

 

I'm going to simplify the entire argument from my side, and state that the calculations from DE's side are to begin with the end in mind.  To that end, their considerations are to have some number of players get the reward, a different number of grinders provide arcanes for trade, and most of the players stop short of that goal and engage with the grinders to spur a platinum market.

 

With the above assumptions, they can figure out what percentage of people they want to earn it and what percentage will be engaging in the market.  I suggested the 50% mark because it really boils down to the vast majority of people trading.  Is it fair....debatable.  Is it realistic, I'd suggest so given that there are players more than willing to grind these for months.  If I had data  I could justify myself, but I do not.  Since DE doesn't provide such the only "data" is the relative cost of an arcane in the trade market.  At one point this was over 100 platinum, pointing towards DE maybe actually getting 30% or less as their end figure and bleeding way more than 3%.

 

Why not just use the 420 like you're suggesting?  Same reason you gave, it's unrealistic.  4 runs a day would be 100 days of eidolon grind, and very few people are capable of that kind of grind.  It's even more unlikely given the bugs and visual/audio poison.  I do want to address the common retort of "just go buy it" at the same time though, because it's the response you always get when you comment on the grind.  To do that, I suggest the entire community's number of captures, and you get to defang the platinum argument in one shot.  It's really me fighting the platinum argument in the same breath as the grind, and in doing so I get to use an even more ridiculous number.  There's nothing quite like justifiably making the opposing argument even worse, by framing your argument in a way that people will have a visceral hateful reaction to.

 

 

Is the framing reasonable...It's not technically inaccurate.  Is it stretching the argument?  A little.  I have explained the way I constructed things, so anybody checking the math (like you) can call out whatever they want.  As such, I have a reasonable argument.  You're welcome to view it as unreasonable, but it isn't inaccurate.

[Chaemyerelis]

On 2020-09-07 at 3:22 PM, DrivaMain said:

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

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

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

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

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

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

Arcanes arent  needed if you like playing a gimp build.

[Chaemyerelis]

honestly for arcanes they should allow us to purchase which ever arcane we want from onnko using the shards or whatever they were called.

[(PSN)Madurai-Prime]

55 minutes 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.

Yea definitely. 

I don't really have a hand in this debate anymore so I'll head out lol. I hope DE does bring Scarlet spear back soon though.

 

[Buff00n]

11 minutes ago, master_of_destiny said:

I'm going to simplify the entire argument from my side, and state that the calculations from DE's side are to begin with the end in mind.  To that end, their considerations are to have some number of players get the reward, a different number of grinders provide arcanes for trade, and most of the players stop short of that goal and engage with the grinders to spur a platinum market.

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.

[master_of_destiny]

2 minutes ago, Buff00n said:

I hit submit before reading your latest response, and now I think I'm back to not understanding what you're trying to calculate at all.

How does the 67 * 21 run gauntlet you've constructed get spread out among more than one player? 

It's constructed in a way that ensures 50% of players will make it through, but the vast majority will hit 21 arcanes long before hitting 1407 runs.  Are you assuming that all those players just keep going after 21?  If not, where does it account for players bailing either because they went 67 without an arcane or hit 21? 

If trading is not included in the model, then why are runs a player makes past their 21 arcane goal relevant at all?  Those runs are purely voluntary and don't help the population reach 50%.

 

If you're not allowing for trading until after 50% of the player base completes a set, and you're trying to model discouraged players leaving after 67 failures, then I believe the python simulation I provided earlier produces the correct result.

 

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.

[Felsagger]

I think this thread requires careful reading. DE should look at this material. 

 

This is a high standard discussion that deserves a careful revision. I suggest that many of you report this thread on a positive side because the material discussed here is top quality. I enjoyed every inch of this thread. I'm going to keep reading without commenting in it. I don't want to deviate it. It's amazing that we have conversation like these in the forum.