M19 Premium Pack diminishing returns

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Larz70
Larz70 Posts: 132 Tile Toppler
in MtGPQ General Discussion
     This post was inspired by @freegenz 's post (https://forums.d3go.com/discussion/74520/the-cost-of-acquiring-all-mythics) and @Volrak 's previous analysis of fat packs even before the drop rates were known.  I can't trust myself with doing the math so I relied on a Monte Carlo simulation (10,000 random Premium Pack pulls using the rates posted on the booster pack).  I'm a statistics nut who also knows R programming so writing the simulator was not much of a problem.  Only risk was once I get into it, I have a tendency to forget to finish my ToTP (my 60 crystals, nooooooo).

     Based on some of the feedbacks I got from earlier work and the comments from @freegenz 's post, I made the simulation a bit more realistic.  Rather than running it until I got all the mythics, I ran it starting from zero, counting how many median pulls were needed before the first mythic was pulled.  And then I ran it again starting with the cards I already pulled until the second mythic was obtained, and so on and so forth.  By the way, I used the median instead of the average because bad RNG has a tendency to inflate the average.  If lucky, the sim can get the next mythic on the first pull, if extremely unlucky, it could take dozens of pulls before it sees the next mythic.  The minimum is obviously capped at one, but the maximum theoretically has no limit, so the average will get worse as the sim runs into more and more terrible RNG.  Also the median is very easy to interpret.  It splits the population exactly into the 50% of the lucky ones, and 50% of the unlucky ones.  For example, the median for the first mythic was 2 pulls.  I got my first mythic after 6 pulls so I know I definitely had a bad run.  The average was 3.35 but obviously, half the population got it in 1 or 2 tries so between a median of 2 and an average of 3.35, that's a significant difference that's only going to get larger as I run it for the rest of the mythics, so I picked median.  By the way, the worst run the sim encountered was 24 pulls before receiving the first mythic.  So if you think your luck was rotten, talk to the sim.

     My first version of the code did not consider MP as a mythic so it will continue pulling even though MP's are obviously a lot more valuable.  Maybe I will fix this in the next iteration but for now, MP's are rare enough that I don't think it would over-estimate the results.  However, I did run into some results were the sim pulled 3 MPs before finally receiving the first mythic :smiley: .  Come to think of it, it could be the same run that took 24 pulls!  As you might expect, the average will be affected by this, but certainly not the median.  Which reminds me of another median advantage, the median is always a whole number.  If I tell you 50% of the population only took 2 pulls, then you can expect to do the same half the time.  If I tell you it took 3.35 pulls, would you do 3 because it rounds down to 3 or would you do 4 pulls to make sure you get your first mythic.  You wouldn't just open a third of the pack and abandon the rest would you?  :smiley:

So here are the results:


     Starting from nothing, half the people will spend 640 crystals or an equivalent of $21.33 (based on price of $99.99 for 3,000 crystals) to get their first mythic.  Along with that are 25 common cards, 20 uncommon, 5 rares and 315 orbs for that one dupe.  Wait what?  315?  Since the results are the median of the 10,000 simulation runs, these numbers are the combination of the results of all people whose results are neither lucky nor unlucky.  The way to read the result is to take each number individually.  How many common cards can I expect after pulling my first mythic?  25.  How many uncommon? 20.  But don't expect to get exactly 25 common and 20 uncommon.

     From there, it will take another 3 pulls to get the second mythic along with 15 new commons, 13 new uncommons, 5 new rares and another 855 orbs.  The owned cards are cumulative, but crystals and orbs are not.  Here's what it looks like if we keep track of the running totals instead.



     As you can see, it could take 152 pulls, or 48,640 crystals, or $1,621.33 to get all the mythics (along with one MP) but you should not do that!  Not because it's a lot of money but because at the vault, for 25 bucks, you can buy a color bundle that comes with 50 jewels.  For 200 bucks, you can get yourself 400 jewels and get a guaranteed mythic or MP from the Elite Pack.  Why spend another $437.33 to pull that last mythic from a PP.  Boom, you just save $237.33.  No, I'm kidding, that's too much money people!  Seriously, at mythic #14, you would have accumulated 40k orbs (and possibly 400 jewels from playing AX and ToTP) to craft/pull Elite Pack the remaining 6 mythics.  The sad part though is you'd still have to pull 52 times or spend $554.67 to get to that point.  But it all depends on how much you're willing to spend or how much crystal you've hoarded.

     Another interesting point is that the lowest you can spend, if you're willing to spend is $21.33 (see mythic #1 cost).  If a mythic is on sale for under that amount, then you know that's a good deal, if you are going to spend money.  If you have a couple of mythics under your belt already, then pretty much all mythics for sale that you don't have yet and want are good deals.

     TLDR:  It's not the best looking chart, but I'm still figuring out google docs and it's the best I could do



Opening PPs are only cost effective at the beginning (hence diminishing returns).  Once you start crafting or pulling Elite Packs, you are reducing it's probability of getting your next new mythic.  But what I find surprising is that, it doesn't really get bad until you've pulled mythic #16.  It's a gentle rise as you can see on that green curve.  Sure, $40, $50 is a lot for some, and at mythic #16, the cost of $85.33 is definitely more than the cost of a new console game, but I know of a few people who have dropped hundreds in this game.  To those people, I hope this analysis helps you find your stopping point.

 
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Comments

  • NinjaE
    NinjaE Posts: 213 Tile Toppler
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    Thank you for all your hard work! It is appreciated.
  • babar3355
    babar3355 Posts: 1,128 Chairperson of the Boards
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    Interesting data Larz, thank you!  I would love to see the PP's with at least one decimal place to get a more accurate picture of the PPs needed for each new mythic.

    I would love to see an "optimal" model that suggests mythics hit before turning to orbs and jewels to finish the set.  I am not the math guy for that job =)
  • Tremayne
    Tremayne Posts: 1,612 Chairperson of the Boards
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    Nice data. Sadly it illustrates how bad my 11 PP used to get the first M19 Mythic really was.  :/

    So far my M19 PP have been insanely bad. Have lost count of how many PP opened, but I’m more or less inclined to just go for 400 pinkies and wait for the next set. 
  • Laeuftbeidir
    Laeuftbeidir Posts: 1,841 Chairperson of the Boards
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    I stopped at four because.. Yeah.. It doesn't feel rewarding.

  • Larz70
    Larz70 Posts: 132 Tile Toppler
    edited August 2018
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    babar3355 said:
    Interesting data Larz, thank you!  I would love to see the PP's with at least one decimal place to get a more accurate picture of the PPs needed for each new mythic.

    I would love to see an "optimal" model that suggests mythics hit before turning to orbs and jewels to finish the set.  I am not the math guy for that job =)
    I tried the Quote button and ended up inside the quote somehow and I have no clue how to get the cursor to go outside of the quote, so oh well, I'll just answer it here.  The PP's are median numbers not average so there are no decimal places.  Average does not work because the data will be skewed by people like me who has terrible luck (1 mythic pull in 6 tries)

    As for an "optimal" model, now that we no longer get duplicates from Mythic+ Elite Packs, it really all depends on how many jewels you can hoard.  You've had quite a streak lately and if you continue that, it's possible to receive 2400 jewels a month (1000 from AX and ToTP, 240 from JTH and 1200 +/- from coalition events).  As for orbs, I'm on pace to get 12,000 orbs for the month of August but 15,000 is probably doable.  2400 jewels and 15,000 orbs, that means you can get 8 guaranteed Mythic/MP cards a month once we are able to craft M19.  If you wait two months, it could be as much as 16 guaranteed.  So if you can hold off for the next two months and only open M19 PPs and hope to get at least 4 new mythics, then you'll get it for sure (along with 2 - 4 MPs perhaps).  The only problem is with all these other players showing off their Blue Sun Zenith and Plague Wind pulls, it's very hard to be disciplined and lay off from the elite packs.

    //Fixed quote bug :) -Brigby
  • freegenz
    freegenz Posts: 8 Just Dropped In
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    Fine work @Larz70! You make some very good points about the average skewing higher and the median being more representative of user experience as well.

    Numbers are still in the ball park of multiple hundreds dollars though. The more I think about it, the more I think it's not worth spending money on this game to acquire cards through packs.

    Also, I kinda feel stupid for saying this, but you just made me realize that I shouldn't use my gems until I've gotten a few m19 mythics...  
  • Spagooter
    Spagooter Posts: 2 Just Dropped In
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    Lucky to get a mythic? Hell, how about a rare?!? My last pp only had the guaranteed rare. Pretty disappointing when you grind away for crystals for what seems forever. They need to bump up the exchange rate. 100 for a rare is way too low. 500 for a mythic is pretty low too.
  • Mburn7
    Mburn7 Posts: 3,427 Chairperson of the Boards
    edited August 2018
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    Spagooter said:
    Lucky to get a mythic? Hell, how about a rare?!? My last pp only had the guaranteed rare. Pretty disappointing when you grind away for crystals for what seems forever. They need to bump up the exchange rate. 100 for a rare is way too low. 500 for a mythic is pretty low too.
    I dunno.  10 mythics per crafted mythic seems pretty reasonable, and consistent with other games I've played.
    The rest could stand to be a bit more, though.  Maybe just bump everything up by 50%?
  • IM_CARLOS
    IM_CARLOS Posts: 640 Critical Contributor
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    Larz70 said:
    babar3355 said:
    Interesting data Larz, thank you!  I would love to see the PP's with at least one decimal place to get a more accurate picture of the PPs needed for each new mythic.

    I would love to see an "optimal" model that suggests mythics hit before turning to orbs and jewels to finish the set.  I am not the math guy for that job =)
    I tried the Quote button and ended up inside the quote somehow and I have no clue how to get the cursor to go outside of the quote, so oh well, I'll just answer it here.  The PP's are median numbers not average so there are no decimal places.  Average does not work because the data will be skewed by people like me who has terrible luck (1 mythic pull in 6 tries)

    As for an "optimal" model, now that we no longer get duplicates from Mythic+ Elite Packs, it really all depends on how many jewels you can hoard.  You've had quite a streak lately and if you continue that, it's possible to receive 2400 jewels a month (1000 from AX and ToTP, 240 from JTH and 1200 +/- from coalition events).  As for orbs, I'm on pace to get 12,000 orbs for the month of August but 15,000 is probably doable.  2400 jewels and 15,000 orbs, that means you can get 8 guaranteed Mythic/MP cards a month once we are able to craft M19.  If you wait two months, it could be as much as 16 guaranteed.  So if you can hold off for the next two months and only open M19 PPs and hope to get at least 4 new mythics, then you'll get it for sure (along with 2 - 4 MPs perhaps).  The only problem is with all these other players showing off their Blue Sun Zenith and Plague Wind pulls, it's very hard to be disciplined and lay off from the elite packs.

    //Fixed quote bug :) -Brigby
    What is JTH? I would like to receive 240 more jewels.

    1200+ jewels on coalition events per month only happen, when older, high bracket PvP events (300 jewels Top5) are played. Newer event have less rewards (but more progression rewards).

    Maybe I count by myself for a month. 2400+ jewels sounds a lot like little bit too much if you're are not going in top10 coalition.

    1600 sounds doable to me. Depends what JTH is.... 

  • Larz70
    Larz70 Posts: 132 Tile Toppler
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    JTH is the non-coalition PvE event A Journey Through History.  For Platinum players, the reward is 30 jewels plus crystals, runes and booster packs.  We got two of these events each week for the last two weeks so that's 120 jewels in the last two weeks.  I thought if they kept running it for the next two weeks, then @babar3355  can get 240 this month alone from JTH.  But it looks like we're going to get NoP next week which only gives out a max of 20 jewels, so unfortunately, JTH will probably max at 120 this month instead of 240.  Still, given that babar plays for a top coalition and he's consistently hitting max scores, 2000+ jewels for the month of August is reachable.

    You're right though, if you're not playing for a top coalition and not getting perfect scores, 2400+ is very high.  But if you keep playing Trials of the Planes (ToTP) and Across Ixalan (AX), and if Journey Through History is available twice a week every week, that would be at least 1240 jewels a month.  But now I know that it's probably only two weeks of JTH a month (hopefully) which is still 1120 jewels a month.  So 1200 jewels a month I think would be a reasonable minimum, and for the top coalition players, 2400 is the max.

      
  • IM_CARLOS
    IM_CARLOS Posts: 640 Critical Contributor
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    I think 600 per month on top of AI and TotP is doable, even for minor coalitions. 

    I calc. with 1500 jewels and around 10k Orbs per month, aside from PP.

    So I need a while to catch my "last" missing 54 MP. At least I can go for it straight with new EP-policy. 
  • Bil
    Bil Posts: 831 Critical Contributor
    edited August 2018
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       First of all, that's an impressive and enlightening work about numbers and its is really interesting in order to measure our luck when opening pp's. Thanks for the hard piece of work.

        When it comes to the pinks count, the numbers look a bit optimistic though.
       We generally alternate beetween events with high jewel rewards (pvp) and events with lower jewel rewards (pve) and we seem to get only 4 AJTH per month.
       1000 from daily grind, 120 from JTH, 500-600 from pvp events (depending on which ones are scheduled) and about 100 for coalition pve. Also 320/month for top coalitions.  The total score being about 2100 jewels a month for the ultimate player, which is very good actually.

       The only problem here, is that very few players seem concerned by those numbers. Even for platiners that score in top 100 (personal and coalition), you can already reduce the total to 1400 jewels. If you're still in gold tier, it will start much lower and decrease even faster.
     
      My point is that when we drop that kind of numbers (even if they are accurate for a few of us), they can give the impression that the game is highly rewarding, but the reality is a bit diferent and most players still struggle to get enough pinks for an EP.
       Thats just a personal feeling though and i might be underestimating the proportion of wealthy players around here.
  • Kinesia
    Kinesia Posts: 1,621 Chairperson of the Boards
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    @Bil You're totally right about the multi layers of awards, it's can be really complex!

    The things affecting stuff:
    Mastery Level
    Personal ranking in events (Increasing Mastery when not ready can tank this badly)
    Understanding of what to play and to avoid
    Coalition ranking in events


    So a complete newbie in Bronze can be an excellent player with a good coalition and get great coalition rewards but very poor personal ones.

    A platinum player who does perfectly but is in a mostly dead coalition possibly winds up with similar rewards but the parts they are getting them from are different. And if they have always mostly been alone they might not completely realise what is and isn't worth their time to play.


    A "lot" (definitely not all) of the people in this forum have been here a long time and have coalition support networks and the extra information posted here as well, but there are a lot of different ways people can fall through the cracks, who never ever know anything that isn't posted in game, who never have any chat or contact with other players outside game (and possibly INSIDE it). 
    There's a missing bridge to get people to these forums easily and ALLOW THEM TO POST without the current badly designed barriers. The best way to get to beginners so they can fill in some of these gap is have in game announcements that lead to this forum multiple times a week. And then _remove_ the need to post in the intro channel, that's an obsolete requirement now you are forcing to people to enter settings and fix their birthdate. The birthdate thing is enough of an obstacle to block bots for now, the other ways aren't needed anymore and are hurting the beginners.



  • Sarahschmara
    Sarahschmara Posts: 554 Critical Contributor
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    To expand on @Kinesia ‘s post; there really ought to be a direct link to the forums from inside the game. Perhaps near the “submit a ticket” button? 

    This might deserve its own topic though... @Brigby
  • Tyrannicide
    Tyrannicide Posts: 9 Just Dropped In
    edited August 2018
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    Oh, so 3 mythics in 20 pp wasn't bad? This is honestly disgusting.
  • Volrak
    Volrak Posts: 732 Critical Contributor
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    Tyrannicide said:
    Oh, so 3 mythics in 20 pp wasn't bad? This is honestly disgusting.
    No, it was bad.
    (Using published drop rates) For an average group of 100 players who each opened 20 M19 PPs, you will find that 15 of them got 6 mythics from those packs, and another 15 got 7 mythics.  These are the most common outcomes; for other numbers of mythics, both higher and lower, you will find fewer people in the group who opened that number.  You could say hello to 5 of them who got only 3 mythics, the same as you (or just 4 others, if you are one of them), and commiserate with a further 3 despondent souls who got even fewer.
  • bk1234
    bk1234 Posts: 2,924 Chairperson of the Boards
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    Volrak said:
    Tyrannicide said:
    Oh, so 3 mythics in 20 pp wasn't bad? This is honestly disgusting.
    No, it was bad.
    (Using published drop rates) For an average group of 100 players who each opened 20 M19 PPs, you will find that 15 of them got 6 mythics from those packs, and another 15 got 7 mythics.  These are the most common outcomes; for other numbers of mythics, both higher and lower, you will find fewer people in the group who opened that number.  You could say hello to 5 of them who got only 3 mythics, the same as you (or just 4 others, if you are one of them), and commiserate with a further 3 despondent souls who got even fewer.
    I know at least 2 people who have opened 20-ish M19 PP without a single mythic. 
  • Gunmix25
    Gunmix25 Posts: 1,434 Chairperson of the Boards
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    M19 drop rates for mythics is abysmal for half and super gracious for the other half; very few in the gray zone.
  • Thésée
    Thésée Posts: 238 Tile Toppler
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    Tyrannicide said:
    Oh, so 3 mythics in 20 pp wasn't bad? This is honestly disgusting.


    I am at 19 premium packs in a row without mythics. 12 DOM and 7 M19.

    Last Mythic I got in a premium pack was on DOM release day the 23rd of May. 3 months ago.............

    :-(

  • DumasAG
    DumasAG Posts: 719 Critical Contributor
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    Thésée said:
    Tyrannicide said:
    Oh, so 3 mythics in 20 pp wasn't bad? This is honestly disgusting.


    I am at 19 premium packs in a row without mythics. 12 DOM and 7 M19.

    Last Mythic I got in a premium pack was on DOM release day the 23rd of May. 3 months ago.............

    :-(

    holy cow...

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