Tuesday, 9 October 2012

Cube Rarity

An important aspect of designing a cube of any kind is simply becoming familiar with a variety of draft environments. This allows you to compare and contrast various aspects of those environments - the things you liked and the things you didn't - with the draft environment that you're creating. Gaining this experience can be done in a number of ways. The first and most obvious is simply to draft a lot - whether in person or online, this is a great way to experience the nuances of an environment first-hand. However, if budget is an issue, there are other approaches. One simple one is to do mock drafts online. This website is one such place. Another good approach is to actually watch draft videos posted online by professional Magic players (at sites such as www.channelfireball.com, www.starcitygames.com and many others). This approach allows you to observe real-life drafts along with the commentary of the pros for little to no cost.

One of the ways that I use knowledge gained from such activities is to reference a draft environment as a basis of comparison for establishing card rarities. I started this approach with Magic 2011 which was a pretty good draft environment for a core set. However, one interesting thing to notice is that Magic 2010, Magic 2011, Magic 2012 and Magic 2013 are all exactly the same size in terms of the number of cards at each rarity. Because of this, and my experience with drafting these environments, I have a feel for how frequently a particular common or uncommon might appear in a draft. Extrapolating this into a cube environment allows me to tune numbers with relative rarity in mind.

In a singleton cube, of course, there will only be one copy of a particular card, but cube designers counteract this by including multiple cards with similar effects. For example, a cube might include both Wildfire and Burning of Xinye. These cards are functionally identical and effectively create 2 copies of the effect. But the cards don't need to be quite so close - a cube designer might simply decide that any card that deals damage to a creature or player is a "burn" spell, and consider the number of these as an entire group. Likewise, the same approach can be applied to the number of one-cost creatures in Black or the number of wrath effects in White.

The effective rarity, then, can be calculated as a number that compares to a known draft environment. There is no correct answer in terms of which environment is the best choice - anything that is familiar to the designer is fine. I think that no matter what you choose, the numbers should turn out pretty similar. Also, the reason that I choose a triple-set draft (e.g. three packs of M11) is because it's easier on the math and also easier for me to remember as opposed to the frequency with which a particular card appeared in Scars of Mirrodin-Mirrodin Besieged-New Phyrexia draft, for example.

So, what are the numbers? The first thing to identify is that a booster pack of M11 (my target set) contains 1 rare (which could be a mythic rare but doesn't matter for our purposes), 3 uncommon, and 10 common cards. The final card is a Basic Land which we won't be using. It doesn't matter if your cube pack fills this 15th slot with a real card because we're only looking at the effective rarity of any given effect.

So, M11 contains 101 commons, 60 uncommons, 53 rares and 15 mythic rares (as do M10, M12, M13, Avacyn Restored and a number of other large sets, incidentally). From these numbers, we can determine the average number of each card that will appear in an 8-person booster draft. Of course, the actual number in a given draft will vary, but over time it will tend toward the average.

Since there are 10 commons per pack and 24 packs then 240 commons will be opened. With 101 commons in the set, this means that each common will appear approximately 2.4 times (or 2.37 to be a bit more precise). Applying the same logic, we find that each uncommon will appear on average 1.2 times. Since 1 in 8 packs contains a mythic rare instead of a rare, 21 packs should contain rares, meaning that each rare appears approximately 0.4 times. Mythic rares appear approximately 0.2 times.

Right, so how does this help? Well, if you are building a 360 card cube then you have your numbers. Obviously, you can't include 2.4 copies of a particular card effect, but at least you know that if you have 2 copies it will appear a little less frequently than a common, and if you have 3 copies then it will appear a little more frequently than a common. Likewise, something that appears only once is roughly equivalent to an uncommon - just a little less frequent.

If you have a cube of a different size then you just have to adjust the ratios. For my 450 card cube I find the following ratios:

2.4/360 = x/450

Conveniently, a common equivalent appears exactly 3 times in my 450 card cube. An uncommon appears 1.5 times. From this point forward, I won't really bother with rares and mythic rares. The reason is that we only approach whole numbers (1) when cube size reaches 900 cards. Therefore, for any cube smaller than this, any card or effect that appears even once will be more frequent than a rare. Whatever your cube size, you simply need to convert these numbers to determine what your rarity equivalents will be.

I've been using these numbers (3 and 1.5) to assign values to a variety of effects within my cube for some time now. For example, if I have 6 1-drops in White, I know that that's equivalent to 2 different commons in a typical draft. This tells me that I have a good shot at finding a few copies during a typical draft. Also, if I have a single copy of an effect, I know it will turn up less frequently than an uncommon and I know that doubling it to 2 copies will result in it being more frequent than an uncommon. It is for this reason that I decided to spend the money to obtain a copy of Ravages of War - Armageddon provides an important effect for White-based aggressive decks and I wanted this effect to be more frequent. Ideally it would be about as frequent as an uncommon, but I'd rather err on the side of too frequent than not enough.

To take another example, I'm also designing a cube that is intended to feel very similar to a real Limited draft environment (though of course with my own favourite cards to make up the draft set). In doing so, I realized that removal is more restricted in a typical Limited environment than it tends to be in high-powered cubes. For example, in M11, White effectively has 2 common removal spells - Pacifism and Excommunicate - and one uncommon removal spell - Condemn (excluding the more situational Celestial Purge). Setting aside the quality of the spells mentioned here, this means that a typical 8-person booster draft should only have about 6 removal spells in White. Given this, I have been sure to design my draft set to have a similar ratio of removal. While it is not perfect, it does provide a nice guideline to work with. From there, playtest and season to taste.

Of course, all of this assumes that you're also doing an 8-person draft with your cube. But the whole purpose is to provide a rough tool for calculating how frequently an effect should appear, regardless of how you end up using it.

After playing with the ratios for awhile, I recently realized that there is another nice round level at 600. In a 600 card cube, a common appears exactly 4 times and an uncommon appears exactly twice. These are very nice round numbers to work with. Furthermore, while a rare would appear about 0.67 times, it is certainly possible to create a pseudo-rare slot - any effect that appears exactly once is a little more frequent than a rare.

In a previous post I discussed the most common cube sizes and indicated that cubes were often built in multiples of 90-cards as a means of supporting exactly 2 drafters per 90 cards. This approach is not required of course, and as I consider expanding my cube from 450 cards, I am very seriously considering 600 as my next jump.

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