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Using Expected Numbers to Determine the Best Guild


Guilds of Ravnica has 259 cards that appear in booster packs: 111 Commons, 80 Uncommons, 53 Rares, and 15 Mythics. Ten of the Commons are Guildgates that only appear in the "basic land" slot. (There are two alternate art versions for each of the five guilds in the set.) In addition to these 259 cards, there are another nine that don't appear in booster packs, so they don't affect Limited formats and we will ignore them for the purposes of this analysis. We'll also ignore foil cards since the chance of getting a specific foil is low enough that it has relatively little impact on Limited.

Each booster pack contains ten non-Guildgate Commons, three Uncommons, one Rare or Mythic, and a Guildgate. As usual, one out of every eight packs contains a Mythic instead of a Rare. Let's use this information to determine how likely we are to see a specific card at a given rarity when opening booster packs, bundles, and booster boxes.
 
  Contents Guildgate Non-Guildgate Common Uncommon Rare Mythic
Booster pack 1 Guildgate, 10 non-Guildgate Commons, 3 Uncommons, 7/8 Rares, 1/8 Mythics 0.20 0.10 0.04 0.017 0.008
Bundle 10 booster packs 2.00  0.99 0.38 0.17 0.08
Booster box 36 booster packs 7.20  3.56 1.35 0.59 0.30

You're twice as likely to see a given Guildgate as you are to see any other Common, which makes sense because each Guildgate appears twice. You're about 2.6 times as likely to see a copy of a given non-Guildgate Common as you are to see a copy of a given Uncommon, 2.3 times as likely to see a copy of a given Uncommon as you are to see a copy of a given Rare, and twice as likely to see a copy of a given Rare as you are to see a copy of a given Mythic.

Now let's apply this information, along with the numbers of packs used for each format, to determine how likely we are to encounter copies of specific cards at each rarity in various Limited environments. We will then apply this information to Luis-Scott Vargas's card rankings to determine the best guild in the set.

Draft

An eight-person Guilds of Ravnica draft uses a total of 24 packs and will, on average, contain 4.8 copies of a given Guildgate, 2.4 copies of a given non-Guildgate Common, 0.9 copies of a given Uncommon, 0.4 copies of a given Rare, and 0.2 copies of a given Mythic.

Sealed

Individual sealed uses six packs of Guilds of Ravnica, so each player has access to a quarter as many copies of any given card as in an eight-person draft. A sealed pool will, on average, contain 1.2 copies of a given Guildgate, 0.6 copies of a given non-Guildgate Common, 0.23 copies of a given Uncommon, 0.1 copies of a given Rare, and 0.05 copies of a given Mythic.

Team Sealed

Three-person team sealed uses twelve packs of Guilds of Ravnica, so each player has access to half as many copies of any given card as in an eight-person draft. A team sealed pool will, on average, contain 2.4 copies of a given Guildgate, 1.2 copies of a given non-Guildgate Common, 0.45 copies of a given Uncommon, 0.2 copies of a given Rare, and 0.1 copies of a given Mythic.

Two-Headed Giant

Two-Headed Giant sealed uses eight packs of Guilds of Ravnica, so each player has access to third as many copies of any given card as in an eight-person draft. A Two-Headed Giant sealed pool will, on average, contain 1.6 copies of a given Guildgate, 0.8 copies of a given non-Guildgate Common, 0.3 copies of a given Uncommon, 0.13 copies of a given Rare, and 0.07 copies of a given Mythic.

The Best Guild

Now we'll apply this information to Luis-Scott Vargas's card rankings for the set to determine the best guild. The Guildgates are not included in his rankings, so we'll just consider non-Guildgate Commons for the rest of this article, and will refer to them simply as "Commons".

I've summarized the results of the assessment in the two charts below. Here's how I got the data for the charts:
  • I kept LSV's assessments intact, even where I disagreed with them. He's the pro and has probably drafted the set a lot more than I have.
  • Nightveil Predator is listed under both Best of the Rest and Premium Cards. I've assumed that the one under Premium Cards was intended to be Nightveil Sprite.
  • Hybrid cards are counted under both their colors.
  • The ten split cards in the set have a hybrid half and a multicolor half. Unlike the non-split hybrid cards, I've only included these under their color pair. While many of them are playable even if you're in only one of the two colors, they all fall into a lower tier if you can only ever cast the hybrid half.
  • I kept the Signets under artifact instead of moving them into their respective color pairs because I haven't seen them played much, and it would penalize Boros disproportionately since its Signet understandably didn't make the list. I think the Signets aren't played because Izzet is usually aggro in this format, Selesnya's creatures serve as acceleration for Convoke fatties, and Dimir and Golgari need to have a better turn three play to survive the early game against aggro. Also, there are enough Guildgates to support three-color decks even without the Signets.

The first chart compares the number of cards in each tier for each of the colors and guilds in Guilds of Ravnica.  

The second chart compares the number of monocolor and multicolor cards that are in-color for someone playing one of the ten possible color pairs. (I was careful to avoid double count hybrid cards.) Note this doesn't include any kind of assessment about whether the card is actually good in that color pair. It also ignores the possibility of splashing cards.

Here are some observations from the charts. Keep in mind that all quantities discussed here are in terms of expected number of cards in Limited formats, not the raw number of cards in the set.

  • About 70% of the playable cards in the set are monocolor, but the most powerful cards tend to be multicolor. (Duh!) The top two tiers contain twice as many multicolor cards as they do monocolor cards, the third tier contains about equal numbers of both, and the bottom two tiers of playable cards contain way more monocolor cards than multicolor cards.
  • White and Blue have the most playables, followed by Black and Red, and Green is in last place as usual. White has the most cards in the top two tiers. When you add in the third tier, Blue and Black have the most cards, followed by White and Green, with Red having significantly fewer than the other colors.
  • Boros, Dimir, and Golgari have about 3.5 cards each in the top two tiers, followed by Selesnya with 2.5, and with Izzet in last place with 1.5. When you add in the third tier, Dimir and Izzet have the most with about 9.5 each, then Boros and Golgari with about 8.8 each, and Selesnya in last place with about 7.
  • Looking at the combined chart (guild cards plus monocolor cards in that color pair), we see that Boros, Golgari, and Selesnya have the most cards in the top two tiers with about 7 each, followed by Dimir with 5.8 and Izzet with just 3.5. When you add in the third tier, Dimir has almost 30, followed by Golgari and Izzet with about 25.5 each, and Boros and Selesnya with about 21.5 each.
  • The five guilds not represented in the set have even fewer cards in the top three tiers, but Azorius and, to a lesser extent, Orzhov have enough playables that it is possible to cobble together a deck in those colors if necessary. However, it is worth noting that the set has a number of cards that can make an Azorius player's life difficult. White/Blue is usually a Skies deck that uses defenders and other creatures with high toughness to hold the ground while it wins with flyers, so Demotion, Goblin Locksmith, Maniacal Rage, Undercity Uprising, Invert // Invent, and even Collar the Culprit are all excellent against them. Another issue for a White/Blue Skies deck is that creatures with Mentor can keep attacking into low-power creatures even if they're not getting any damage through because they're still making other creatures bigger.
Another way to look at the card rankings is to see which colors/guilds have the cards at the lowest rarity in each tier:
  • Best of the Best: White has one Rare in this tier, Green has two, and Dimir, Golgari, and Izzet have one each. Green has the most cards in this tier.
  • Best of the Rest: White has two Uncommons in this tier while the other colors have one each. Among the guilds, Boros has three (including the split card Integrity // Intervention), Dimir has two (including Discovery // Dispersal), Golgari has two (including Status // Statue), and Izzet and Selesnya have one each. White and Boros have the most in this tier.
  • Premium Cards: Blue and Black each have two Common in this tier while the other colors have one each, Among the guilds, Dimir has three (including the hybrid card Whisper Agent), Izzet has two, and the remaining guilds have one each. Blue, Black, and Dimir have the most cards in this tier.

Conclusion

Dimir, Blue, and Black have the most cards in the top three tiers, so if there are roughly equal numbers of players drafting each guild, Dimir players are the most likely to end up with enough playables. However, if you're being passed strong White cards or Boros cards, you should consider going into the archetype as it has the most number of cards in the top two tiers and probably has a higher ceiling.


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