Drop rates.

toastie

Volrak wrote:

andrewvanmarle wrote:

khurram wrote:

andrewvanmarle wrote:

The drop rates between mythics is separated into 4 groups, so there isnt an equal chance to get any mythic. This has bedn confirmed by a friend who's name i wont say who had a look at the code in the game.

So now we know why we get so m many dupes

So you are saying that there are 4 rarities among mythics?

Yes, exactly that....

And that's why some mythics are so elusive. And why we have skewed chances when buying an elite pack

It's an interesting idea, but so far it's in the category of "Obama wire-tapped me"... no proof offered, hard to disprove, and questions abound - such as what possible reason anything to do with drop rates would have to be present in client-side code, whether certain weights, which are indeed present in the code (according to my own friend who shall not be named), may actually be to do with the AI's hand sorting or spell targetting algorithms, and of course whether your friend who shall not be named was playing a practical joke on us all.

Also like "Obama wire-tapped me", the claim has spurred interest disproportionate to its veracity, including my own curiosity, which has prompted me to start working to gather evidence which can support or debunk it.. but don't hold your breath, as it will take some time.

If anyone feels like cutting to the chase, a concrete theory about which specific mythics are in what "group" and what the relative drop rates might be would bring results sooner, but that is something I will also not be holding my breath for.

That is going to be very, very hard to collect enough data for. I honestly don't see a way of proving that outside of the devs confirming it or looking into the code.

TibbyGenn

the problem with data projects like this is the variation of response between players.

Sure if we all opened a set amount of boosters over a set amount of time and measured we could do some meaningful analysis, but these guys are clearly hiding.

It's a lot of effort to confirm what we mostly intuitively know, that drop rates are terrible.

It would be simple enough and really awesome if we had a history screen, which displayed the amount of boosters opened which types etc. how many cards bought directly etc etc.

D3H, if you are listening, please do this.

Certainly Wizards do this for MTGO.

I consider that I've run pretty well opening some key cards fairly early each time, so I can't really complain when I open completely nothing. Just a little frustrating at times.

andrewvanmarle

@volrak,

I agree, i have no proof. Though i dont this a practical joke is the case.

I'll ask my friend to do some digging, maybe a list of which mythic goes to which tier...

toastie

TibbyGenn wrote:

It's a lot of effort to confirm what we mostly intuitively know, that drop rates are terrible.

Just want to take a moment to point something out related to this:

It doesn't actually matter what the drop rates are when it comes to making players happy, it matters how the drop rate feels. Currently, pretty much everyone agrees that the drop rate feels terrible, and I suspect duplicates being awful contributes significantly to this. What we want as players, especially if we are spending a good chunk of money, is to be excited about opening packs. This means getting new things to play with, either through opening them, or being able to work towards cards we want (like in Hearthstone).

aesith

20% mythical on a fancy top end pack of packs? Clearly I have the **** luck since the update going 0-4 or 5.

Amadeus

so i am not sure if it's luck or better drop rate, I have gotten 6 mythic's since the update 5 in the last 8 days.
3 from kld 5 card booster pack
1 from monthly super pack
1 SOI 5 card booster pack
1 Daily 3 card booster

and oddly enuf nothing from the 600 gold deal from last week

also none where dups

babar3355

Volrak wrote:

Astralwind wrote:

Without those drop rates, how can we tell between basic, super and premium?

The data collected so far (~6700 cards) has been analysed to see if drop rates per card differ depending on pack type, but that theory couldn't be supported from the data. So you can assume that opening a super pack is identical to opening three basic packs, and opening a premium pack is identical to opening five basic packs plus getting a bonus rare.

Astralwind wrote:

We need something like:
Basic - 10% chance of uncommon, 3% chance of rare, 1% chance of Mythic
Super - 15% chance of uncommon, 4% chance of rare, 1.5% chance of Mythic
Premium - 20% chance of uncommon, 5% chance of rare, 2% chance of Mythic

Here you go:


The odds above don't depend on pack type.
The total chance of certain rarities dropping does depend on pack type:


You can see from the 2nd table that the chance of rare from a Super pack (46.0%) is indeed "higher" than the chance of a rare from a normal booster (18.6%). But I think d3 advertising the chance as "high" is misleading. (It's likely wording left over from advertising the 20-card Fat Packs, which they forgot to check was still valid).

*All of these figures assume that drop rates haven't changed over the months the data was collected.

Is this from this website? https://docs.google.com/forms/d/e/1FAIpQLScQGVZ8yXANx45y73Il9HbsKvj89DLnvX_DRrqbE5iKNoKNcg/viewform

I wonder if you guys throw out outliers if it is? The first pack I loaded was a big box, and I realized I did it in reverse order... 32 mythics, 35 rares, etc lol

babar3355

Volrak wrote:

Astralwind wrote:

Without those drop rates, how can we tell between basic, super and premium?

The data collected so far (~6700 cards) has been analysed to see if drop rates per card differ depending on pack type, but that theory couldn't be supported from the data. So you can assume that opening a super pack is identical to opening three basic packs, and opening a premium pack is identical to opening five basic packs plus getting a bonus rare.

Astralwind wrote:

We need something like:
Basic - 10% chance of uncommon, 3% chance of rare, 1% chance of Mythic
Super - 15% chance of uncommon, 4% chance of rare, 1.5% chance of Mythic
Premium - 20% chance of uncommon, 5% chance of rare, 2% chance of Mythic

Here you go:


The odds above don't depend on pack type.
The total chance of certain rarities dropping does depend on pack type:


You can see from the 2nd table that the chance of rare from a Super pack (46.0%) is indeed "higher" than the chance of a rare from a normal booster (18.6%). But I think d3 advertising the chance as "high" is misleading. (It's likely wording left over from advertising the 20-card Fat Packs, which they forgot to check was still valid).

*All of these figures assume that drop rates haven't changed over the months the data was collected.

Is this from this website? https://docs.google.com/forms/d/e/1FAIpQLScQGVZ8yXANx45y73Il9HbsKvj89DLnvX_DRrqbE5iKNoKNcg/viewform

I wonder if you guys throw out outliers if it is? The first pack I loaded was a big box, and I realized I did it in reverse order... 32 mythics, 35 rares, etc lol

Volrak

babar3355 wrote:

Is this from this website? https://docs.google.com/forms/d/e/1FAIpQLScQGVZ8yXANx45y73Il9HbsKvj89DLnvX_DRrqbE5iKNoKNcg/viewform

I wonder if you guys throw out outliers if it is? The first pack I loaded was a big box, and I realized I did it in reverse order... 32 mythics, 35 rares, etc lol

The data is from Octal's spreadsheet (https://docs.google.com/spreadsheets/d/ ... edit#gid=0); the website you linked to is one source of its data. You can also add data directly to the end of the data table in the spreadsheet.

We eyeball all the data, and if anything looks odd we can reject it, or check with whoever provided the data and ask if there was an entry error. Your 32-mythic box, while not technically impossible, is so highly implausible that Google Sheets has a numerical overflow in trying to calculate the odds.

Volrak

andrewvanmarle wrote:

The drop rates between mythics is separated into 4 groups, so there isnt an equal chance to get any mythic. This has bedn confirmed by a friend who's name i wont say who had a look at the code in the game.

So now we know why we get so m many dupes

So I've tested this theory with some data, thanks to Octal.

Octal has kindly exported actual counts of each mythic owned in each saved collection on mtgpq.info. I've compared the actual counts from Origins (851 drops of 24 different mythics over 110 collections) to simulated counts for both uniform random and tiered drop rates. I chose Origins because it has the largest sample size and avoids skew from exclusives.

Each graph below shows the results of 10 runs of a simulation which pulls 851 total non-dupe drops in 110 collections in blue/purple/green, plus a red line which is the actual numbers dropped. In each case, the X axis (mythics) is sorted by the number of drops, to allow easy comparison.

• The first graph simulates a tiered drop rate with four tiers, the relative odds of each tier being 1x, 2x, 3x, and 4x.
• The second graph also simulates a tiered drop rate, but with less pronounced relative odds: 1x, 1.333x, 1.666x, and 2x.
• The third graph simulates uniform random drops (no tiers).

You can judge for yourself, but it seems the actual observed data (red line) fits well for the uniform simulation (3rd graph), and is a real outlier in both of the tiered simulations (1st and 2nd graphs).

andrewvanmarle

Volrak, you dont take duplicates into account here. If you open a 1000.000 packs which mythics will appear only once and which will appear multiple times.

Octals site only records if the mythic is owned or not.

Volrak

andrewvanmarle wrote:

Volrak, you dont take duplicates into account here. If you open a 1000.000 packs which mythics will appear only once and which will appear multiple times.

Octals site only records if the mythic is owned or not.

If I understand correctly, you're suggesting a methodology which measures dupe rates in order to determine whether drop rates are tiered. However, as you say, that methodology is impossible with the data we have, which is why I've used a different approach to test your theory.

The comparison of the shape of the observed drop rate curve with to the simulated curves is a valid way to check whether tiered drop rates are plausible, and the validity is not affected by the fact that dupe mythics have dropped for the players from whose data this is drawn. In the simulations, I tracked 110 distinct collections and allowed dupes to drop, so long as the total number of non-dupe drops matched the real data (851 drops). If I run the simulations without accounting for this, and just directly generate 851 mythic drops instead, the difference is small, and does not change the conclusion. However it was important to rule this out as a possible source of error.

andrewvanmarle

Volrak,

I may be missing the point, but how complete a collection is, isnt dats use can use to approximate drop rates?

For one you miss the amount of cards pulled per account, and two duplicates are an essential part of the calculation.

In other words, if you dont factor in duplicates, then the conclusion will of course be that all mythics have the same drop rate.

The dats is incomplete...

Volrak

andrewvanmarle wrote:

Volrak,

I may be missing the point, but how complete a collection is, isnt dats use can use to approximate drop rates?

Here's a simpler example. Imagine you have the data for 10 player's mythic collections, and there are 5 mythics in the game. Between the 10 players, they've obtained a total of 25 non-dupe mythics. This is analogous to the data we actually have.

Now think about those 25 mythics. If the drop rate is uniform, you would expect on average a fairly flat distribution amongst the 5 possible mythic cards. Maybe 5,5,5,5,5? But some variation from averages is expected, and so a uniform drop rate will tend to produce a slightly skewed distribution, e.g. 6,6,5,4,4. This corresponds to the gentle slope of the green lines in graph 3.

Now consider what we'd expect to see if there was a "tiered" drop rate. Imagine an extreme case, where each of the 5 mythics is in a different tier with highly skewed probabilities, such as 50%, 30%, 15%, 4%, and 1%. Do you still expect a 6,6,5,4,4 distribution? Of course not - most players will have managed to get the mythic which drops half of the time you open any mythic, while very few, if any players will have managed to open the one-percenter. You can therefore expect a much steeper curve, perhaps 9,7,5,3,1. This corresponds (in an exaggerated way) to the steeper slope of the blue and purple lines in graphs 1 and 2.

By comparing how similar the shape of the actual curve from real data is to the shape of the expected curve given some assumptions about the drop rate, you can see which assumptions are plausible and which are not. This is exactly what the graphs are doing.

andrewvanmarle wrote:

For one you miss the amount of cards pulled per account, and two duplicates are an essential part of the calculation.

You're absolutely right if you think that we would be able to get even more insight if we knew the total number of mythics opened in those collections, and how many duplicates of each card there were. But the above gives us a result with sufficient confidence without knowing about dupes, so it's evidently not an essential part of this particular calculation.

andrewvanmarle wrote:

In other words, if you dont factor in duplicates, then the conclusion will of course be that all mythics have the same drop rate.

Not so: the red curve (actual data) could well have turned out to be steeper, and aligned with one of the curve sets from the tiered simulations. If that had been the case, we could conclude that a tiered drop rates for mythics is a plausible theory. It isn't, so we don't.

It's also worth noting that the more samples we use, the less variation there will be in each simulation run, and for a fair comparison, we can only simulate as many drops as the actual data we have. With less data, each of the blue, purple, and green curves would have more variation and be more spread out; in this case, perhaps the red curve could be a plausible member of any of the curve sets. If that were so, we could not form any conclusion on whether tiered drop rates were plausible, and we would need to gather more data for the analysis to be useful. (To make this really clear, look at the drops of each mythic from elite packs in the forum surveys. Are they all over the place due to natural variation from a low sample count, or because each mythic really has different odds of dropping in an elite pack? We can't reach a conclusion there without more elite pack data.)

This turned into quite the wall of text, but if there's any part which still isn't clear, I'm happy to explain further.

andrewvanmarle

Ah i get what you mean.

But you are comparing samples without equal circumstances: how many cards has someone bought and which mythic was duped how many times.

Take this example ten players have a full vollection of mythics, and dont tell you how many dupes they had: you'd get a flat rate.

Or ten players each have 3 mythics, but dont tell you that 5 opened twice as many packs.

Both would change the numbers in a substantial amount.

Yawgmoths_Left_Ilium

Nice start with the graphs. I do have a few critiques, essentially revolving around the fact that while it's a good start, I don't think there's enough data to draw a concrete conclusion. Since we don't know which mythics you're polling from, it's possible that all mythics from the sample were from a single tier. Maybe there's only a select few mythics in the upper tiers (from Origins that might be Nyx, TSN, etc). Also, it's possible that different sets have different tiers. For example, SOI, with Olivia, Deploy, Gisela (basically all the sought after cards), might have tiers, but Origins might not.

Edited for clarification

Laeuftbeidir

Also mythics that have been available for direct purchase shouldn't be in the calculation, for obvious reasons

[Deleted User]

They know a lot of us are addicted

Volrak

andrewvanmarle wrote:

Ah i get what you mean.

But you are comparing samples without equal circumstances: how many cards has someone bought and which mythic was duped how many times.

The comparison is equal: non-dupes vs non-dupes. We both agree that if we had data on dupes we'd get even more insight. But we get a useful result anyway, without using that data.

andrewvanmarle wrote:

Take this example ten players have a full vollection of mythics, and dont tell you how many dupes they had: you'd get a flat rate.

Yep. And if all 110 collections from mtgpq.info had every mythic, this method would tell us zip. They don't, so it doesn't.

andrewvanmarle wrote:

Or ten players each have 3 mythics, but dont tell you that 5 opened twice as many packs.

This is exactly this kind of possibility that makes small data sets of limited use. As sample size increases, the problem of unrepresentative obscured data shrinks. We know if our actual sample size is ok by checking the spread of the simulation curves; our confidence is only as tight as the tightness of the set of blue/purple/green curves.

But you're touching on another way the experiment could be improved. I let each collection open a random number of cards to get the total amount of non-dupe mythics. If we had the actual distribution of mythics owned in each of those collections we could follow the same distribution in the simulations and rule out another possible source of bias. I expect it would not make a significant difference, but it's something we could try if Octal wanted to do more data exporting.

Volrak

Yawgmoths_Left_Ilium wrote:

Nice start with the graphs. I do have a few critiques, essentially revolving around the fact that while it's a good start, I don't think there's enough data to draw a concrete conclusion. Since we don't know which mythics you're polling from, it's possible that all mythics from the sample were from a single tier. Maybe there's only a select few mythics in the upper tiers (from Origins that might be Nyx, TSN, etc). Also, it's possible that different sets have different tiers. For example, SOI, with Olivia, Deploy, Gisela (basically all the sought after cards), might have tiers, but Origins might not.

Thanks for your comments. To clarify, I'm polling from the full set of 24 Origins mythics. We can test other sets too, but there are data difficulties from exclusives.

For sure, our conclusions are limited to what we've tested. In this case, stated precisely, we can conclude that the Origins mythics do not drop in four equally-sized rarity tiers, where the most common tier drops twice as often or more than the rarest tier. You can also eyeball the red curve in graph 3, comparing the lowest drops (on right-hand side) to the green curves. If anything, the drop-off in the tail of the green (uniform) simulated curves is even steeper. It will be hard to find support for any tiered system for Origins mythics.

Tierists, take heart: we can likely never have enough data to show that mythics don't drop in tiers of relative probability 0.97, 0.99, 1.01, and 1.03! (But of course, such tiers would make essentially zero practical difference compared to uniform drops.)