by OtakuMZ - 7 years ago     show comments

Introduction

A few days ago in our BlizzPro slack chat, Kevin ‘Odinn’ Hovdestad was talking about the idea of an article that is doing the math on how much money one would have to spend to get the full set of the upcoming set Mean Streets of Gadgetzan (MSG). To be honest, I was already asking myself the question of how much I would invest when a few months back there was a discount of 20% on iTunes cards. I bought myself 100€ worth of vouchers for 80€. I also did the pre-order of the 50 packs right away and saved up 4.5k of Gold and 4k arcane dust. I will obtain 80 boosters through the gift cards, 50 from the pre-order and 45 from Gold, leaving me with a total of 175 packages at an investment of 130€ (approx. $138). Did I get the best deal available and will it be enough to get me a competitive collection with some fun cards as well? Before I answer these questions, there are some basics I want to highlight first.

Basics

Discounts on Packs

You can buy packs either directly from Blizzard via the game on PC and Mac or on iOS and Android devices which have their distinct stores in place. Discounts can be obtained via the exclusive 60 packs bundle on the PC/Mac client only. On Android devices, you have the option to by Amazon Coins at a reduced cost. On iOS (iPhone/iPad), you can sometimes grab reduced iTunes gift cards with a saving of up to 25%. Apple sells packs generally with a 10% increase in prices which should be included in the calculation when buying via iOS devices. A detailed guide to why buying with Amazon Coins is best value can be read here.

I made the math myself for individual pack prices which can be found below in the ‘How Much Is A Pack Worth – Money’ paragraph. So much is said, buying with Amazon Coins seems the best deal at the moment.

Figure 1: Amazon Coins savings, US store.

Rarity Distribution

Legendaries render acquiring a complete collection expensive and Epics do this to a smaller extent. If we compare Arcane Dust (AC) cost for each rarity slots, the difference becomes apparent. On the one hand, AC cost of all Legendaries is as high as for all other cards in the set. If we sum up the dust value for Epics and Legendaries, the amount needed is almost 5-fold compared to all Rares and Commons. On the other side, Commons and Rares account for more than two-thirds of the whole set (compare Table 1), not taking into account that Legendaries are non-duplicates.

Table 1: Card count in MSG vs. dust cost.

Figure 2: Comparison of relative rarities in all Hearthstone expansions. The distribution in between the sets is almost identical. TGT and MSG share the same numbers.

Figures 3: comparison of relative absolute rarities in all Hearthstone expansions. Legendaries amount for 20 in all expansions while there are only minor variances in Commons, Epics, and Rares.

Most importantly, if you are not a completionist, you do not need each and every Legendary. There were a lot of crappy Legendaries released in the past three expansions as well as a comparable number of “fun tech” Legendaries that would not see tournament play. The first category is 5-9 per set; the latter are 3-8 more. These counts signify that 8-16 of the 20 Legendaries per expansion already released are not needed to build the majority of ladder decks. This number significantly dropped with every expansion. Whispers of the Old Gods had the least amount of fringe playable or bad Legendaries.
The same holds true for Epics. Unplayable Epics accounted for 5-6 so far and fun/fringe playable ones for 10-13, totaling up to 15-18 of non-necessary Epics on the ladder. Atop, some Epics are only played as a ‘one of.’
For MSG, IMHO, 4/9 Legendaries, and 8/12 Epics fall in the ‘unplayable/fringe playable’ categories.

To conclude, for serious decks, we only needed approx. 45% of the Epics and about 40% (25-60%) of the Legendaries so far with the number being expected 10% higher in MSG due to better card design. Not needing to craft the useless cards cuts cost by a huge margin if you just want to obtain meta-viable cards.

Chances to Draw Cards of A Certain Rarity

We know from this article what the chances are to draw the different rarities from a pack (compare screenshot 1-3). I will quote most what you see below regarding draw probabilities from this article. Although the chances for Legendaries are at a mere 5.37% per pack and a 1.10% chance total, there is a pity timer that guarantees to draw one Legendary in every 40 packs. The remaining probabilities are displayed in Table 2. For more information on the topic, please take the time and jump to the source article over at the Gamepedia Hearthstone Wiki.

Table 2: Probabilities to draw cards of different rarities out of a Hearthstone pack. Included studies: Steve Marinconz (June 2014), E. R. Kjellgren (August 2014), Amaz (February 2015), HearthSim (August 2015). Total sample size of 27,868 card packs with 139,340 cards in total.

Table 3: Probabilities to draw golden and regular cards. Note: data for golden cards gathered before TGT showed significant differences from later expansions. For this reason, the information is from the HearthSim study only: HearthSim (August 2015) which included 15,109 packs.

How Much Is A Pack Worth

Arcane Dust (AD)

There is a very thorough study on that topic. TLDR: A single card has a mean value of 19.65 arcane dust and a pack 98.25 AD respectively; taken into account, that you do not disenchant every single card. If you d so, the value rises to 108 AD/pack.

Gold

100 Gold per pack, no discounts, no nothing.

Money

A pack costs in between $1.495 and $1.167 if bought on the desktop client (PC or MAC) depending on the bundle you choose. The 60 pack offer is for PC/MAC only and not available on any other platform.

If you buy the biggest bundle of 40 packs with Amazon Coins (AC) at a 21% discount (10000 AC; $79), the price per pack drops to $0.988. It is worthy to note that this is without counting for coin rewards, which sadly are not available in the EU region. If you are insane enough to invest for the full 25% cost reduction (50,000 AC; $375) costs are down to $0.938/pack. If you compare that to the 50 packs of the pre-purchase these, cost $0.999 each.

Buying packs on iOS are the most expensive option even if you can grab a 20% discount on iTunes gift cards because all bundle prices are 10% higher on iPad or iPhone.

Therefore we can conclude that buying packs with Amazon Coins on Android devices or an emulator is the cheapest way to obtain them. It is even 1% to 6% cheaper than buying the pre-purchase bundle which nevertheless is a good option if you do not want to buy more than 50 packs. It is also reasonable if you have not Android device or are not willing to go through the process of installing an emulator.

Ok, with all that out of the way, let’s get back to the initial question.

How Many Packs Do I Have To Buy?

To answer this question, you have to know first what you want to get as a result. Do you want a full collection with all cards, only cards that you need for being competitive on the ladder or something in between? Therefore I constructed four scenarios. All these assume that you have no Gold and dust left.

Scenario 1: competitive only
You only want to play ladder/tournament viable decks – not just a single one but all tier 1 and 2 decks to be able to participate in tournaments. Therefore you need about 60% of all Epics and 50% of the Legendaries*. For Epics the number is kept that low as you will play some Epics only as single copies in a deck. You will obtain all Commons and Rares, though. You have no interest in golden cards. Because of the studies mentioned above, dusting crap Legendaries, etc. is not accounted for. I assume that you get some you some you want and some you don’t. Therefore I apply a penalty of 5% to the “needed” cards accounting for additional crafting atop of dusting the worthless cards. Packs are bought the cheapest way possible (see above paragraph) by spending pre-purchased Amazon Coins in the appropriate chunks.

*Clarification: This number seems high at first glance but I think the new set has a lot of potential and even more playable cards than WotOG. For just one or two tier one decks this number is lower by a huge margin. You can check out figures 4-6 to determine your sweet spot.

Scenario 2: competitive and fun, no crap
All the above mentioned but you also want the playable, fun Legendaries and Epics resulting in 75% Epics/Legendaries needed.

Scenario 3: completionist (non-golden)
You want it all. Every single card matters and is worth trying out. These cards can be either golden or non-golden.

Scenario 4: completionist (golden)
You want every single card all in shiny gold disregarding that you may spend a fortune obtaining them. Probably, if you are even considering this path, money isn’t an issue for you.

Crafting Strategy

According to an article of PCGamer, the average result from the pre-order will give you 91 Commons (93% of all MSG Commons),46 Rares (64% of Rares), 11 Epics (20% of Epics) and 3 Legendaries (15% of Legs). This amount is not enough for all the scenarios we painted. There are two studies that try to answer the exact question the article poses. One for Whisper of the Old Gods (Old Gods study) and the other for The Grand Tournament (TGT study). The upside of the TGT related study is that the sets are identical regarding card distribution. For this reason why I will quote more from that study despite the fact that both are well done.

The Old Gods study gives an exact value of a mean of 380.453 packs for 100% completion of your collection with a minimum of 258 packs and a maximum of 507 in 10,000 runs performed in the simulation. There are some nuances though in how to obtain cards. Will you complete your Collection by investing the dust in missing Commons or  Rares first or do you start at the top end with Legendaries? In the case you plan to get >100 packs, the recommendation is to start with the precious orange crystals first to get the most value out of every single booster opened. The argument for this strategies is displayed in the three figures below (figures 4-6).

Figure 4: Completion by starting with Commons

Figure 5: Completion by starting with Rares and skipping Commons

Figure 6: Completion by starting with Legendaries.

Percentage-wise, you will complete your collection faster up to a certain point by starting with Commons because the Legendaries account for very few cards. By doing so, you will have to dust more cards reducing the overall value. Figure 7 shows an accumulated graph of completion for all rarities combined depending on crafting strategies. In the end, the difference will be just a few packs, but why waste any value if you are aiming for a ≥ 70% collection.

Figure 7: Completion strategy comparison Commons vs Legendaries first.

Brute forcing the completion of the set is not a good idea, meaning not dusting any card and just waiting until you get all cards. Completing the set will take >1000 packs in comparison to approx. 380 boosters when dusting unnecessary copies (compare Figure 8).

Figure 8: Comparison of completing the set with and without the use of arcane dust.

Conclusion

Finally, we come to the answer of the question how much you and I should invest for each stereotype proposed. I mainly base the statements on Figure 6 out of the TGT study.

Scenario 1: competitive only: Average 175 Packs, $180 investment (500 coins left)

Scenario 2: competitive and fun, no crap: Average 240 Packs, $237 investment

Scenario 3: completionist (non golden): Average 380 Packs, $375 investment (2,500 coins left)

Scenario 4: completionist (golden): approx. 1,000 Packs, $930 investment
Note: Brute forcing 155,600 dust for all golden cards would cost you 1,440.74 packs. Nevertheless, in 1,000 packs you get an average of 35 golden Legendaries and 95 Golden Epics which should be fine taking into account duplicates and dusting

In 1,000 packs you can only expect 3.5 golden Legendaries and 9.5 Epics, therefore crafting most of it seems the only validstrategy of obtaining a full golden set – which very few will ever do (compare Tab.4).

Table 4: Chances to get at least one golden card off a pack. Percentages sorted by rarity and total.

Finally, are you interested in a mere “I will get x% of my collection done by y number of packs? Below, you can find the average number of packs you have to invest for the given percentage of the set (according to the TGT study; also compare fig.7+8):

• 50 packs ≈   50% complete
• 100 packs ≈ 75%
• 150 packs ≈ 85%
• 200 packs ≈ 90%
• 380 packs ≈ 100%

Update (thanks for the huge number of comments on Reddit): These numbers show that for starting off playing the ladder, less than the above mentioned 175 packs are needed. 50-100 packs is a perfect start for everyone not playing tournaments regulary. In most cases this means buying the 50 pre-purchase boosters and dumping the Gold amassed over the last weeks in additional packs. This way, investment decreases significantly from the “shocking” prices mentioned above.

This concludes my article. I hope I saved you some money. If so, I would be happy if you could spread the word to other players of our community. As always,  please comment below or tweet me @OtakuMZ1978 Bling, bling!

Yours,

OtakuMZ