Statistics for card packs are a means of observing the rarity drop rates for cards from card packs, determining the opportunity cost of whether a player should continue to buy or not buy packs. Show
NB: For inclusion into this article, studies recording the rarity drops of card packs should have a reasonably large sample size and should have a citable reference from a reputable source. Notes[]
Duplicate protection now extends across all rarities, before Ashes of Outland (2020-03-17).
Pity Timer[]"Pity Timers" exist,[17] which define the maximum number of packs that a player opens before guaranteeing the next Rare/Epic/Legendary card.[18][19] Pity Timer counters are tracked individually for each store-bought expansion set, including the Classic set. However, no Pity Timers are applied to Golden Classic packs.[20][17] A translation of the announcement Blizzard made in complying with China's "disclose odds" law stated:
The statement that the probability increases as more packs are opened may be a reference to the (otherwise-unannounced) pity timer. Actually statistical studies have shown the following:
Pitytracker.com has also compiled their own card pack opening statistics for each expansion: pitytracker.com/insights. In addition, Blizzard announced that beginning with Knights of the Frozen Throne, players are guaranteed at least one legendary card in their first 10 packs from any given expansion.[21] This, however, does not apply to Golden Classic packs.[20][17] Combined with the usual 40-pack pity timer, this implies that if a player buys a 50-pack bundle (of packs of a never-before-opened type), they're guaranteed at least 2 legendaries, and can reasonably expect 3 or more. Expected dust value[]According to the below meta-study's data tabulated under the "Golden cards" section, the average card pack has a disenchanting value of 102.71 Arcane Dust.[22] Each card has an average disenchanting value of 20.54 Arcane Dust. Meta-study[]The following numbers combine data from several other studies on this page. Since it has at times been suggested that the distribution of cards has changed over time or is different for different expansions, the numbers are shown per expansion. Note that all data collection has been done for each expansion when it was the most recent expansion, so there is for example no data available for card distribution in Classic packs that were opened after the release of Goblins vs Gnomes. Currently included studies:
This produces a total sample size of 32,697 card packs, describing 163,485 cards in total.
Rarity distribution[]This table shows the likelihood of any single card being of a given rarity. The differences in the percentages appear to be all within the boundaries of statistical variance. This suggests that, at least up to and including the Un'Goro expansion, there have been no changes in the distribution of cards per rarity.
* Note that the sample size for Goblins vs Gnomes & Knights of the Frozen Throne are probably too small to be statistically relevant. Due to how cards are generated (with the guarantee of at least one Rare or better in any pack, plus the existence of a "Pity timer" for Epic and Legendary cards), the chance of finding at least one card of any given rarity cannot be simply mathematically computed from the numbers above. However, for all pack openings since the TGT expansion the card rarities in any individual pack have been recorded. With these data, it is possible to determine the chances for these events:
Golden cards[]The data from Marinconz does not include details of regular vs. golden opened in the packs. However, all other studies did include this data. After excluding the 5,000 cards from Marinconz' study, this results in the following probabilities of finding regular or golden cards of any rarity when opening packs. (For readability, the totals and the percentages are split over two separate tables):
Disregarding the data from GvG (which is statistically irrelevant because of the small sample size), it appears that the chance of receiving a golden common card has been slightly increased as of the Old Gods expansion, while simultaneously lowering the chance of a regular common card. In other words, the chance of a common is unchanged, but any common card generated has an increased chance to be golden.
This data again shows the increased chance of a Common card being golden since the Old Gods expansion. The seemingly erratic changes in the chance of a Legendary card being golden are probably a result of the relatively low amount of legendaries in the data, making the data statistically less trustworthy. However, it cannot be ruled out that the rules for generating a Legendary as golden or regular have been changed by Blizzard. Class distribution[]Only a single data set (the HearthSim data) tracked the class of the cards opened in addition to their rarity. Fortunately, this data set by itself is large enough for statistical relevant. However, this obviously means that there is no way to verify whether there have been changes in distribution across the classes over time, and whether the same pattern applies for expansions other than TGT. The table below shows, per rarity and by class, the average number of times each card was opened. (Example: A total of 3,227 Common Mage cards were opened; since the TGT expansion includes 3 Common Mage cards the average number per card is 1,075.67).
The variations in the numbers are all within the boundaries of expected statistical variance. This suggests that the pack opening algorithm does not favor any specific class, nor neutral cards over class-speecific cards. However, that does not mean that there is an equal chance of finding any class or neutral; it means that any card of a given rarity is equally likely to be found. Since TGT (like all other expansions) has more neutral cards than it has class-specific cards, the chance of getting a neutral card is still higher. Data[]June 5, 2014: Steve Marinconz[]On June 5th 2014 Steve Marinconz published the following results in an article on Kotaku.com.[23] The data was collected by aggregating the results of numerous card pack opening videos found online, with a total of 1,000 packs. The study used only videos filmed in the last two months.
* NOTE: The data in this row is as published in the article, but appears to be incorrect. According to these numbers, the chance of finding at least one Rare or better card in a pack is (73.11 + 19.73 + 6.33) = 99.17%, which is inconsistent with the guarantee of at least one Rare or better card. Apparently Marinconz computed these figures from the "Percentage of total" chances, based on the assumption of a flat distribution; however the "at least 1 Rare or better" guarantee invalidates this assumption and hence these numbers. Based upon this data, Marinconz provided some interesting 'fun facts'. While these are based on the results of this single, relatively small study, the closeness of the study's results to those of other and larger studies suggests that the below information should still be relatively accurate, at least for the lower rarities.
Unfortunately, Marinconz only posted aggregated data. Without data about individual packs, it is not possible to use this data for the "Probability of at least 1 per pack" table in the Meta-study. Also, since Steve didn't publish the exact number of golden cards, this study has also been excluded from any of the tables representing the chance of golden cards. August 2014: E. R. Kjellgren[]In August 2014 E. R. Kjellgren published an investigation into the rarities of cards found in card packs.[24] This was achieved by collecting user data from forums regarding the contents of 11,359 different card packs. The author notes that the investigation suffered from two main problems: the information collected was anonymous and its accuracy cannot be guaranteed; and the sample size, while adequate for the lower rarities, is still smaller than might be desired for the higher rarities. Kjellgren also divided rarities into golden and regular versions. Based on the data below, the average card's dust value is 21.51 dust. The average pack's dust value is 107.54. Percentage of total
The data showed golden cards to be on average around 30 times less common than regular cards. However, the proportion of golden and regular versions varied substantially by rarity. The author also notes that the sample sizes for the higher golden rarities are too small to be considered conclusive.
Unfortunately, Kjellgren only posted aggregated data. Without data about individual packs, it is not possible to use this data for the "Probability of at least 1 per pack" table in the Meta-study. February 12, 2015: Amaz opens 400 GVG Packs[]Sources: YouTube - Reddit
Percentage of cards of each rarity that are golden:
Unfortunately, the sources for this pack opening only include aggregated data. Without data about individual packs, it is not possible to use this data for the "Probability of at least 1 per pack" table in the Meta-study. August 29, 2015: HearthSim compiles 15,109 TGT Packs[]Sources: Reddit (initial post) - Reddit (update) - HearthSim - Raw CSV data
Percentage of cards of each rarity that are golden:
April 28, 2016: Kripparian opens 713 Old Gods Packs[]Sources: Youtube - Raw data
Percentage of cards of each rarity that are golden:
April 28, 2016: Amaz opens 413 Old Gods Packs[]Sources: Youtube - Raw data
Percentage of cards of each rarity that are golden:
December 1, 2016: Kripparian opens 896 Gadgetzan Packs (Before Tri-Class Bug Hotfix)[]Sources: YouTube - Raw data
Percentage of cards of each rarity that are golden:
December 1-2, 2016: Kripparian opens 450 Gadgetzan Packs (After Tri-Class Bug Hotfix)[]Sources: YouTube (end of video, first 300 packs) - Raw data
Percentage of cards of each rarity that are golden:
April 6, 2017: Kripparian opens 1101 Journey to Un'Goro Packs[]Sources: Twitch VOD (will eventually be deleted) - Raw data
Percentage of cards of each rarity that are golden:
April 8, 2017: N. Millar opens 1256 Journey to Un'Goro Packs[]Sources: YouTube - Raw data
Percentage of cards of each rarity that are golden:
Analysis from past data[]Prior to Patch 17.0.0.44222 (2020-03-26)[]Prior to Patch 17.0.0.44222 implemented on March 26th 2020, the duplicate protection rule only applied to legendaries when opening card packs. The following are some statistics from that period: Pack opening
References[]
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