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Store Mechanics, Pack Drop Rates & probabilities of UR/R/UC (weapons,gear,mods,char)


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#1
Fuenf789

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Provides a weapon/ +character/+mod/+gear Pack droprate-lookup.
For those averse to reading,--> p36 (&34) of the attached document -summarizes it all.

Why this docu? The UR weapons slot droprate tallied with SP packs (one slot), but for AP,PSP, RP the raw pack data submitted by members could did not match with the 7.5% assumptions from the earlier paper and were thus experienced as random. It means there were some other factors at play beyond the flat 7.5% parameter, that were not accounted for.
This report aims to explain droprates where multiple probabilities are involved.
Spoiler

Attached :
STORE_MECHANICS_PACK_DROP_RATE

Simply put - choosing the wrong pack ie SP or AP (where both has 7.5% UR slot rates) can mean 2H:30s more playtime (wasted) to drop 5 UR weapons. For a whole manifest that can mean a lot of unnecessary time waste.

detail - The document:
Spoiler

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#2
Jeremiah12LGeek

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I was under the impression that there was a comprehensive thread that did an excellent job of compiling statistics around the drop rate. I'm quite sure it didn't contain "wild guesses" - the research was done very well, and several forumites dedicated an impressive amount of work to it.

 

I will see if I can track it down.


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#3
Jeremiah12LGeek

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It didn't take long, Dragonracer had it linked:

 

Updated Drop Rate Data Thread

 

It has been a while since it was updated, but it is regarded as being very accurate.



#4
Fuenf789

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It didn't take long, Dragonracer had it linked:

Updated Drop Rate Data Thread

It has been a while since it was updated, but it is regarded as being very accurate.

:) if u open the document u will notice that I'm using the same raw data as comradeshepard7. Difference is that I talk about Packs and not Slots. We buy packs, not slots. Hence the probabilities change when slots are viewed together. I've even referenced those links u tried 2 find... In there

#5
Salarian Master Race

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#6
Jeremiah12LGeek

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:) if u open the document u will notice that I'm using the same raw data as comradeshepard7. If even referenced those links u tried 2 find...

 

I did open it.

 

Since some earlier threads contained a number of wild guesses on how the probability theory actually works, I'm attaching a quick snippet to bring raw data and theory together.

 

The original thread's data was ultimately reinforced by confirmation in the game's code. I think it's great if you want to add to that data or expand on it, but you seem to be suggesting that the thread failed to work out how the theory actually works.

 

Some info/data has been gathered already before, so it was simply a matter of slapping it together tonight.

 

The thread by ComradeShephard was not just raw data, it was already assembled and researched thoroughly.

 

I encourage you to expand on information as much as you like, but I'm having a hard time seeing how re-presenting the same information with a different author is going to expand on what was already established - a 7.5% UR drop rate, with each potential UR slot calculated individually.

 

Maybe if you clarified what it is you hope your document will show?



#7
BurningBlood

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The only part of this that hasn't already been exhaustively covered in ComradeShepard7's thread is E) time required for maxed manifest.  It's simple enough to calculate that the average cost to unlock and fully level every UR weapon is 138,600,000 credits if one buys Arsenal Packs exclusively.  However RNG will play a huge role, any purchases other than Arsenal Packs will slow your progress, and of course how long it takes you to earn those credits depends on a number of variables.

 

I'm glad some people are still sufficiently invested in the this game to take the time and effort required to put this kind of thing together, but there's no need to re-invent the wheel.


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#8
Jeremiah12LGeek

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The only part of this that hasn't already been exhaustively covered in ComradeShepard7's thread is E) time required for maxed manifest.

 

As someone with three ME 3 MP accounts and nearly 1200 hours on my main account that will, realistically, never have a maxed manifest,* I honestly don't believe that it would be possible to calculate that information in any practical way.

 

The sheer number of variables involved precludes it, at least from our perspective. One could argue that BioWare might be able to put together a number, but you have to consider that their data would contain everyone from those with maxed manifests to those who literally played one game and then quit. There would never really be such thing as "average time to max manifest" unless one eliminated a massive portion of the total data and focused only on people with maxed manifests who could somehow accurately report the exact number of credits they spent before maxing it, as well as accurate data on the total time played to acquire those credits.

 

Unless I've misunderstood the mathematical definition of "average," if you have to eliminate the vast majority of the data to calculate it, then "average" tends to lose its practical meaning.

 

 

 

*Edited footnote: I have since changed my mind, and think I could max it within the next year.



#9
Fuenf789

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I did open it.

Thx - at least you opened something before forming an opinion. This is a topic close to heart of any player and often argued, in the past, without scientfiic basis, so I can understand the initial animocity.


... The original thread's data was ultimately reinforced by confirmation in the game's code...

Someone else also remarked on this before.
It is one thing to take a single variable from the code. It is another to explain why we are getting Pack (note - I am not saying "slot") drop rates like we do.
It's like saying - Black magic happens on a Pack Level, but at least we know that 7.5% have something to do with it on Slot level.

but you seem to be suggesting that the thread failed to work out how the theory actually works.

No. I used the word "threads". It's all other "threads" that refers to the work of ComradeShepard7 without understanding the science behind it. The latest example of such threads is the discussion crusader thread. Some people made valid statements, others just made popular assumptions.

ComradeShephard7's thread successfully uses statistical measures to prove that a specific variable (7.5%) plays a role (on slot level). That paper is, however, not sufficicient in itself to predict Pack drop rates, especially when multiple slots have different probabilities to drop the same rarity item/equipment.

There is no theory derived in the paper from Comradeshephard7. We don't buy Packs on slot level. Hence it doesn't show the droprate of a AP.

I encourage you to expand on information as much as you like, but I'm having a hard time seeing how re-presenting the same information with a different author is going to expand on what was already established - a 7.5% UR drop rate, with each potential UR slot calculated individually.
Maybe if you clarified what it is you hope your document will show?

Consider reading it now, after opening it.
  • It introduces a generic formula to predict the PACK drop rate(without using the 7.5% variable or the raw data), by simply using store mechanics (2 slots per UR, mutually exclusive) as basis. That formula holds true for any probability setting. We didn't use such formula in ComradeShepard7's paper.
  • thereafter we can use the 7.5% in that formula and calculate the predicted drops on pack level.
  • It goes on to show that the predicted PACK drop rate matches very well for large samples. ComradeShepard7 document doesn't predict based on Combinational theory. It predicts based on overall samples. Some samples were very dirty.
  • The new document that was submitted, now provides a way to verify the accuracy of some samples and to cross verify the accuracy of the comradeShephards' findings. So it provides the ability to say whether a submitted sample is "dirty" (not matching the theory) and should be ignored in the statistical data. The findings of ComradeShepard's paper were skewed slightly because of dirty samples. Up until now we had no measure to see how far it was skewed compared to most likely outcomes.
  • It shows why samples < 30 is not useful
  • why 2 simultaneuous UR's in AP happens very seldom and what that probability is.
  • ... (and more)

The only part of this that hasn't already been exhaustively covered in ComradeShepard7's thread is E) time required for maxed manifest. It's simple enough to calculate that the average cost to unlock and fully level every UR weapon is 138,600,000 credits if one buys Arsenal Packs exclusively. However RNG will play a huge role, any purchases other than Arsenal Packs will slow your progress, and of course how long it takes you to earn those credits depends on a number of variables.

I'm glad some people are still sufficiently invested in the this game to take the time and effort required to put this kind of thing together, but there's no need to re-invent the wheel.

Thx. Kindly show me in that paper where I can find the UR Pack Drop rate for an Arsenal Pack?
U used 15% to calculate those 138,600,000 and assumed that one can simply add 7.5% with 7.5%. That is an incorrect assumption for many reasons. These values becomes crititical when 3 mutually exclusive slots drops the same type of inventory. Probability Theory predicts 14.4375% and that matches to 0.0415% with specific (large) samples in the raw data. The more likely expenditure is 124m, and means a different average AP drop rate.

As someone with three ME 3 MP accounts and nearly 1200 hours on my main account that will, realistically, never have a maxed manifest, I honestly don't believe that it would be possible to calculate that information in any practical way.

I fail to see, how the fact that you have 3 accounts, or played a certain amount of hours, serves as a scientific way to calculate probabilities better than the binomial distribution.

The sheer number of variables involved precludes it, at least from our perspective. ...

Surprise. There is just 1 variable for UR weapon slots, and combinational theory explains how to combine that for multiple slots.
If within 0.04% margin of accurate prediction over 903 Purchases is not accurate enough...
-->The Store is much less chaotic than some think. One just have to know the rules and boundaries. The submitted document explains those boundaries.
Nature does the rest to always ensure that probabilities are met towards infinity.

Hence, with a certain probability, we can now show when you can expect another UR drop over a longer row of Credits (based on a ceiling certainty).There's now even a lookup table for that.

...rudimentary understanding of math is enough to know that there would never really be such thing as "average time to max manifest" unless one eliminated a massive portion of the total data and focused only on people with maxed manifests who could somehow accurately report the exact number of credits they spent before maxing it.

Unless I've misunderstood the mathematical definition of "average," if you have to eliminate the vast majority of the data to calculate it, then "average" tends to lose its practical meaning.

You misunderstood the mathematical definition of "average".
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#10
7twozero

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As someone with three ME 3 MP accounts and nearly 1200 hours on my main account that will, realistically, never have a maxed manifest, I honestly don't believe that it would be possible to calculate that information in any practical way.

The sheer number of variables involved precludes it, at least from our perspective. One could argue that BioWare might be able to put together a number, but when you consider that their data would contain everyone from those with maxed manifests to those who literally played one game and then quit, even a rudimentary understanding of math is enough to know that there would never really be such thing as "average time to max manifest" unless one eliminated a massive portion of the total data and focused only on people with maxed manifests who could somehow accurately report the exact number of credits they spent before maxing it.

Unless I've misunderstood the mathematical definition of "average," if you have to eliminate the vast majority of the data to calculate it, then "average" tends to lose its practical meaning.


Really? Because this seems to sum it up pretty nicely.

I also believe that the store is pretty messed up, especially with the UR drop rate compared to the number of UR cards (if memory serves correctly, that's 210 UR cards, at roughly 650k/UR, or 136m credits, or 1820 Gold matches, ignoring cost of consumables to complete those matches, or 758hrs at 25mins a match, and lets be honest, no PUG match is that quick, a private match can easily be sub-20, but a sub-30 pug match is pretty much a unicorn).


Edit: ninjad like a boss by someone un lazy enough to put in the effort.
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#11
Alfonsedode

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Good idea to put that properly :) fuenf, i ll read it a bit, at least the combined slot prob part


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#12
Alfonsedode

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and btw, even if it was the same study as comradeshep one, it wld still be intersting.

There, its going a bit further and it s shorter IIRC Comshep one, and i had forgotten how combining probs work :D



#13
Jeremiah12LGeek

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I fail to see, how the fact that you have 3 accounts, or played a certain amount of hours, serves as a scientific way to calculate probabilities better than the binomial distribution.

 

I didn't say that my accounts or hours represented anything scientific or represented a way to calculate probabilities.

 

 

Surprise. There is just 1 variable, and combinational theory explains how to combine that for multiple slots.

 

I honestly don't see how it is possible that the average time to max manifest could contain only one variable. But, I'm not a mathematician.

 

 

  • The new document that was submitted, now provides a way to verify the accuracy of some samples and to cross verify the accuracy of the comradeShephards' findings. So it provides the ability to say whether a submitted sample is "dirty" (not matching the theory) and should be ignored in the statistical data. The findings of ComradeShepard's paper were skewed slightly because of dirty samples. Up until now we had no measure to see how far it was skewed compared to most likely outcomes.
  • It shows why samples < 30 is not useful
  • why 2 simultaneuous UR's in AP happens very seldom and what that probability is.

 

I can certainly see the value in these. I would have assumed that 2 Ultra Rares in one pack would have been rare because each slot only has a 7.5% chance of producing one, meaning that the odds of getting both at once are .05625%.

 

You misunderstood the mathematical definition of "average".

 

I said that was a possibility. I understand average to be adding a sum total of a list of numbers, then dividing by the number of numbers.

 

I am not a mathematician. My point was that it is hard to see how "average time to max manifest" would be possible to calculate given that the variables include a huge set of numbers that do not represent maxed manifests. Or that the data doesn't include the credits spent buying packs that do not contain a possibility of ultra rares that is higher than 0% (Vet packs, JEPs etc.)



#14
Jeremiah12LGeek

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Really? Because this seems to sum it up pretty nicely.

 

I'm not disputing Arkhne's point.

 

This is a topic close to heart of any player and often argued, in the past, without scientfiic basis, so I can understand the initial animocity.

 

I just noticed this. What animosity?  :huh:



#15
Arkhne

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I didn't say that my accounts or hours represented anything scientific or represented a way to calculate probabilities.

 

 

I said that was a possibility. I understand average to be adding a sum total of a list of numbers, then dividing by the number of numbers.

 

I am not a mathematician. My point was that it is hard to see how "average time to max manifest" would be a possible to calculate given that the variables include a huge set of numbers that do not represent maxed manifests. Or that the data doesn't include the credits spent buying packs that do not contain a possibility of ultra rares that is higher than 0% (Vet packs, JEPs etc.)

 

Iirc, you are correct in your understanding of "average", what the people in this topic seem to be searching for, however, is the "mean", or "median".

 

And you might not be disputing my point, but I am. That is a "perfect world" situation where PUGs don't suck, and game-wipes never happen. So perhaps that number should be taken as the "minimum", sure, it's faster if the AHF curries you on Plat all day, but that is not indicitive of the general experience of even the "average" BSNer. Let alone those PUGs who wipe on Bronze.


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#16
Olivia Wilde

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TL, DR

Pe2X0uWm.gif

so I assume this means I should expect to buy 70 Spectre Packs to get my last 5 Ultra Rares?


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#17
JRandall0308

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TL;DR: once you have everything maxed out except URs, just keep buying packs.


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#18
Jeremiah12LGeek

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I do want to point out that I would be one of the people for whom further data would actually be useful and interesting from my position.

 

I fall into that broad group (probably a fairly significant percentage of those who post on BSN) that does not have a maxed manifest, but on my main account has only Ultra Rares remaining to be unlocked. In that situation, I think the variables narrow to a point where, as long as I could calculate a reasonably accurate "average time per game," I could come up with a loose idea of approximately what the average time to finish my remaining manifest would be for someone in my position.

 

But I guess the part the gives me the most trouble is "average time per game." That seems to contain the most variables that would be difficult to isolate for. There are games that I fail to finish, and where that failure occurs would be difficult to isolate for. If we fail on Wave 3 mid-objective, then that maximizes the time spent for no credits. If we fail on Wave 11, that has no impact on the credits, and actually speeds up the average time, as opposed to slowing it down.

 

But to calculate the average time from scratch would have to include the time taken to fill out the Common, Uncommon, and Rare manifests, which probably varies a lot based on what difficulty one spends most of their time playing during that phase.

 

If I gave the impression that I think more data is bad, then I misspoke (I tried to emphasize repeatedly that I think more information is good.)



#19
JRandall0308

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I think you could use a rough average of 30 minutes per game (conservative estimate). Most of your games will take between 20-25 minutes, but the extra 5-10 minutes accounts for failed games, time waiting in lobbies, and so forth.

 

Then multiply 30 minutes per game by the credits per game for whatever you play, Gold or Platinum. (ProTip: play Platinum.) If you want to be extra conservative, trim about 10%-15% off the Gold/Platinum credits per game to further account for failed games, or failure to extract. (Another ProTip: especially on Platinum, spending Medi-Gel or Ops Packs to guarantee you extract is *well* worth it, considering how cheaply you can refill consumables.)

 

Now you know your credits-per-30-minute-game, which you can convert to hour by multiplying by two. ;) Use that number in your time to maxed manifest calculation.

 

Et voila, the number of hours it 'should' take you to max your manifest.

 

= = =

 

Another way to look at this. Back when I was grinding Platinum for credits, I had a rough sense of how many I would earn in one evening's play. Take that number and use it in your calculations -- it will give you the number of playing evenings until maxed manifest, which might actually be a more relevant number. You'd know whether it's going to be something like 50 playing evenings, which is a long grind but the end is in sight; or 500, in which case you might want to find another way to waste your life.


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#20
Jeremiah12LGeek

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I think you could use a rough average of 30 minutes per game (conservative estimate). Most of your games will take between 20-25 minutes, but the extra 5-10 minutes accounts for failed games, time waiting in lobbies, and so forth.

 

Then multiply 30 minutes per game by the credits per game for whatever you play, Gold or Platinum. (ProTip: play Platinum.) If you want to be extra conservative, trim about 10%-15% off the Gold/Platinum credits per game to further account for failed games, or failure to extract. (Another ProTip: especiallyon Platinum, spending Medi-Gel or Ops packs to guarantee you extract is *well* worth it, considering how cheaply you can refill consumables.)

 

There's also the Pug/Friend Differential (totes scientific math thing that I didn't make up.)

 

The more time you play planned games with friends, the less lobby time and failure rate (in general - obviously your friends could suck.) The more time you play with PuGs, the more lobby time, and the higher the failure rate (in general - I doubt Grim_AoD fails very often regardless of how many PuGs are in the match.)



#21
JRandall0308

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Well, sure, make whatever 'PUGs suck' adjustments you want to your estimates.


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#22
Catastrophy

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In terms of maxing the manifest I recommend: "Just play the ****** game!", which totally did for me, beyond detailed droprates. I didn't really care if it's 7.6% or 9.1% but I like how people try to figure it out by trying *science*.



#23
Jeremiah12LGeek

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In terms of maxing the manifest I recommend: "Just play the ****** game!", which totally did for me, beyond detailed droprates. I didn't really care if it's 7.6% or 9.1% but I like how people try to figure it out by trying *science*.

 

bb-yeah-science.gif

 

Tangential: If I ever did max my manifest (I suppose if I keep playing another year or two at my current pace, it may happen) I would actually be kind of sad. I hate admitting that the carrot plays a role in my motivation, but if I'm being honest with myself, it does.



#24
Alfonsedode

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I do want to point out that I would be one of the people for whom further data would actually be useful and interesting from my position.

 

I fall into that broad group (probably a fairly significant percentage of those who post on BSN) that does not have a maxed manifest, but on my main account has only Ultra Rares remaining to be unlocked. In that situation, I think the variables narrow to a point where, as long as I could calculate a reasonably accurate "average time per game," I could come up with a loose idea of approximately what the average time to finish my remaining manifest would be for someone in my position.

 

But I guess the part the gives me the most trouble is "average time per game." That seems to contain the most variables that would be difficult to isolate for. There are games that I fail to finish, and where that failure occurs would be difficult to isolate for. If we fail on Wave 3 mid-objective, then that maximizes the time spent for no credits. If we fail on Wave 11, that has no impact on the credits, and actually speeds up the average time, as opposed to slowing it down.

 

But to calculate the average time from scratch would have to include the time taken to fill out the Common, Uncommon, and Rare manifests, which probably varies a lot based on what difficulty one spends most of their time playing during that phase.

 

If I gave the impression that I think more data is bad, then I misspoke (I tried to emphasize repeatedly that I think more information is good.)

U could just divide your total credit earned by the number of game played. Wait, maybe it s not a challenge...



#25
JRandall0308

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But once you max your manifest you get to...

... look down on unmaxed manifest problems

... drop into Silver lobbies and cycle through every character each with two UR level X guns, yell 'BOOYAH!' on the microphone, then leave (OK, maybe that's just me)

... do silly challenges because you can

... get more excited about seeing a Cyclonic IV *and* a Warp Ammo IV in the same pack than you ever were about another UR

... only play with Uncommon guns because URs are for chumps


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