Many weeks back, I wrote my yearly "State of Design" article, where I evaluated the previous year of design. The major topic of the article was the Theros block, which had been the majority of the design work done during that year. In response to that article, I got a lot of feedback from players, many of which expressed the same complaint: They had really wanted Theros block to be to enchantments what Mirrodin block had been to artifacts. This question kept coming up on my blog, but I felt it was too complex a topic to answer there.

I thought about writing an article on the topic, but I knew an open space where I wasn't going to tie into Khans of Tarkir was quite a ways off. So I chose to do a podcast explaining why Theros wasn't that and why such a future block would be a real design challenge. That podcast is one of the ones down below you can listen to today.

During the podcast, I talk a bit about an important design concept—something known as volume. Discussing it on my podcast made me realize that it was a meaty topic I hadn't yet covered in my column. And the topic would be appropriate for this week, as it ties into an important point about Khans of Tarkir. So if you're in the mood for a meaty design article talking about one aspect of how design works, you're in for a treat. Today, we talk volume.

Pump up the Volume

I guess I should begin by defining what I mean when I say volume. When you are designing a new mechanic for your set (or for your game in a general game-design sense), the first question you ask yourself is, "What is it?" You have to define the space it fills and figure out what role it plays in your design.

The second question is, "How much of it does my set/game need?" Knowing what the mechanic does is only the first step. The next step is understanding how much of your mechanic is needed for your design. That is volume. Volume is very important because it is one of the most key tools you have to control what kind of impact it will have on your overall design.

In trading card games, volume is extra vital because it is one of the most important tools in determining how your audience perceives your new set. Remember that each person will experience the set differently because he or she will get a unique mix of cards. It is only through volume that you have some control of what order, on average, players will experience the mechanics of your set.

In today's article, I'm going to walk you through the different decisions one has to make about volume, while also showing you the tools R&D uses to both determine its level and regulate its use. Also, I hope to get you to walk away from today's article with a little more appreciation for an aspect that you might have never given two thoughts toward before.

A quick aside before I begin. When I was in high school, I had a math teacher who told us to listen up, because no matter what we did in life, math was going to be important. I scoffed at the time because I had plans of being a writer. I was going to be working with words; I didn't need to know numbers. As long as I could order my pages and count my salary, I figured I was good. And then I became a game designer. I bring this up because today's article is math heavy. An important part of Making Magic is to give an insight into Magic design, and there's quite a bit of math involved. Normally, I shield you from a lot of it but today's topic doesn't allow me that luxury. So be warned—math ahead. By the way, many years later, I revisited my high school while back in good old Pepper Pike. I ran into my old math teacher and the first thing I said to her was, "You were right. I need math."

Now with Added Volume

So you have the mechanic or theme you like and it's time to figure out how much of it you need. Here are the questions you have to ask yourself.

#1—Does this mechanic or theme have a required limit?

What I mean by this is the following: is there a certain number of cards the set must have in order for this mechanic or theme to work? If you have a card with this mechanic on it, do you need to have any other cards in your deck? With something like a tribal theme, the answer is yes because you're going to need to have enough of that tribe. But with a mechanic like kicker, you don't. One kicker card can easily go into your deck without requiring any other specific card. For longtime readers, this is getting into the areas that I labeled linear and modular. (Read here if those terms don't mean anything to you.)

#2—If the answer is yes, how many cards does it need?

The key to answering this question is figuring out how many cards you need to draw to make the card usable. Does the mechanic or theme in question require having just one card on the battlefield? Does it require multiples? Does it require dedicating yourself to the mechanic or theme? How many cards do you need at any one time to make it work?

Once you have the answer (or at least a ballpark answer), you can do some math to figure out how many cards you need. This is what we in R&D call "as-fan." The idea behind as-fan is simple. It helps you figure out, in an average booster pack of your set, what percentage of cards will be part of your theme. To explain, I am going to use an aspect of Khans of Tarkir to illustrate. That aspect is multicolored cards. Note that, by multicolor cards, I'm talking about any card that has more than one color. This includes traditional "gold" cards (cards with more than one color of mana in their mana costs) as well as hybrid cards and split cards (assuming the two costs make use of more than one color of mana).

Khans of Tarkir and Return to Ravnica are both sets that make use of a multicolor theme. Khans of Tarkir is about three-color wedges while Return to Ravnica is about two-color guilds. On the surface, these two sets might seem very similar, but let's take this idea of as-fan and look at the sets a little more closely. Remember that as-fan is a number that states how many cards, on average, a booster pack of the set in question will have of the subset—in this case, multicolor cards.

Khans of Tarkir's as-fan is 1.85, while Return to Ravnica's as-fan is 3.58. Once again, that means if you open up a random Khans of Tarkir booster, you will on average have 1.85 multicolor cards. In general terms, this means that most of the time you will have two multicolor cards. Sometimes you will have one, and every once in a while you'll have three or more. Return to Ravnica's as-fan is 3.58. That means if you open a random Return to Ravnica booster, you'll most often get four multicolor cards, but you'll often get three, and every once in a while you'll get two or fewer or five or more. Both sets have the same theme, but in Return to Ravnica you're going to open almost twice as much of it. That's going to have a very different impact in how the sets play. This also, by the way, has a lot to do with why we were able to revisit a multicolor block so soon. While Khans of Tarkir is a multicolor block, it relies on the multicolor cards much less than Return to Ravnica did, and thus allowed us to return quicker than normal.

The reason as-fan is such an important tool is because you can use it to properly figure out what the right amount is for the subset you're mechanically caring about. Here's how you do this. Let's assume you're playing a Sealed Deck game. In it, you normally get six booster packs. Removing the basic land, that's 84 cards. Now, how many cards of the theme do you need in your deck to make it work? Let's say you figure out you need to have at least six. Well, let's look at the as-fan. What as-fan would you need to guarantee that you have six cards of the subset in question? The answer is an as-fan of 1. If each booster you opened had, on average, one card, then six packs would get you the six cards you need.

Except it's not quite that easy. Why? Two reasons. First, the game has five colors. If the six cards all make use of different colors in their mana cost, it might be impossible to play them all together. That means you have to start doing things like getting an as-fan of the subset in each color. Imagine we're looking for Human tribal. We might focus on things like how many Humans might you open in white? By crunching the numbers, we can figure out what will and won't be possible to play. The key is that part of setting the right volume involves understanding how much you need each player to have. To complicate things even further, be aware that what is needed for Sealed is different than what is needed for Draft.

I know I make it sound like the decision of what volume you need is a purely mathematical one that can be deduced by writing numbers on paper. The truth is that it's not that exact. It many ways, when you start, it's a guessing game. Yes, you can use some logic to increase the chances of your first guess being as accurate as possible, but in the end, you're going to need to playtest to figure out if your volume is correct or not. There's a lot of "getting the right feel" of your mechanic's volume.

Because there's math involved, it's important to track your results, as any one playtest can have skewed data. The card mix in any one sitting might not be representative and you can succumb to what we call "experience bias," where you overvalue your own experience over data. And yes, keeping track of what each of your playtesters' experiences during the playtest is important. Development usually tracks numbers on every Sealed pool build in every playtest so Erik can run numbers.

#3—How do you want to concentrate the subset?

The next important thing you need to consider is what part of your set/game wants to have the mechanic or theme in question. If it's the major component, maybe every color needs it, but often it's much better if you learn to concentrate. You'll notice that, often, when we do a mechanic, we don't do it in every color. Why is that?

First, it ensures that the colors play differently and increases the variance in play, meaning that over time players are less apt to get bored because the game play will be more varied. Second, it allows you to mess around a bit with the as-fan. Let me explain. Let's say you want to do a new mechanic. If that mechanic only shows up in red and green, then you are able to concentrate your as-fan within those colors. What this means is if the player isn't playing red or green, he or she won't play this mechanic. But if the player is playing red and/or green, the chances of being able to play it are much higher. By concentrating the mechanic to a few colors, you increase the chances that the players who are playing the chosen colors will play the mechanic.

This is important, because part of making a fun set is carving out different play styles for different color combinations. It also helps you make a mechanic viable without having to need quite as many cards. For example, if you want a player to get six cards of the mechanic and it's in all five colors, you're going to need a pretty high as-fan to ensure the player gets six cards in the colors he or she is playing. But if the mechanic is just in red and green, you no longer need every player to get an as-fan of 1. You just need the players who are going to choose red or green to get the as-fan of 1. It also means any player who opts into playing red or green has a heightened chance of having the needed as-fan to play.

#4—What rarity do you want your mechanic to be in?

A number of years back, I used to run a weekly Magic design seminar in R&D where I would talk about various topics. My first seminar was about looking at the nuts and bolts of how a trading card game is put together, where I examined the basic building blocks of a TCG. I later turned this talk into an article ("Magic Design Seminar: Looking Within"). In it, I explain some of the fundamental truths about TCG design. One of them is about the role of rarity in the game

Combining a game and trading cards has a lot of upside. It allows exploration, it creates metagames, it makes opening up each new component of the game more exciting. But this comes at a cost for the game designer, and that cost is control. Not being able to dictate in what order the audience sees the various game components is problematic. It takes away one of the most powerful tools a game designer has. Rarity is one of the few things that helps give a little of it back. You might not control the order in which your audience sees what, exactly, but through rarity you have some assurance that certain aspects will (on average) been seen ahead of other things.

If volume is about as-fan, then as-fan is about rarity. Remember that every booster pack, on average, has one slot for a land (most often a basic land), ten slots for common, three slots for uncommon, and one slot for a rare. One out of every eight packs, the rare slot is replaced by a mythic rare slot. Determining as-fan is simply a formula, where you look at how many cards from a rarity exist of the subset in question. For example, a large set has 101 commons. To simplify math, I'm going to pretend it's 100. Let's assume you have a mechanic that's on ten commons and no other cards. Well, if each booster pack has ten commons, then your as-fan is 1.0. Why? Because if 10 commons have the mechanic out of 100 then there is a 1 in 10 chance any common has the mechanic. As there are ten common card slots in a booster pack, that means it's 1 in 10 (or 1/10 or 0.1) times 10, which is 1.0.

If you then added ten uncommons with the mechanic to your set, your as-fan becomes 1.375. Here's why. There are 80 uncommons in a large set. If you have 10 cards with the mechanic, that means it appears 1 out of 8 times (or 1/8 or 0.125). When you multiply that by 3, because there are three uncommon slots in a pack, you get 0.375. When you add that to 1.0 (the as-fan you got for having 10 commons with your mechanic), you get 1.375.

Now let's say you add 10 rares. Your as-fan goes up to 1.540. Here's why. If you have 10 rares, that means you have a 10 in 53 (or 0.189) chance of getting one in your rare slot, as a large set has 53 rares. Here's where rares get tricky. Because you only get a rare in seven out of eight packs, on average, you count the rare slot as 7/8 (or 0.875) of a slot. This means you multiply 0.189 by 0.875 to get 0.165. When you add that to 1.375 (the as-fan with 10 commons and 10 uncommons) you get 1.540.

Math is hard.

Finally, let's say you decide to have one mythic rare with your mechanic. This would change the as-fan to 1.548. Here's why. There are 15 mythic rares in a large set, so you have a 1 in 15 (or 0.067) chance of getting one. The mythic rare slot is 1/8 (or 0.125) of a slot because rares are 7/8 (see above). When you multiply 0.067 times 0.125 you get 0.008. When you add that to 1.540 (the previous as-fan with 10 commons, 10 uncommons, and 10 rares) you get 1.548. I said, it was going to get math heavy.

Basically, rarity is key when setting as-fan, because the more of the subset of cards you have at common, the higher the as-fan. By carefully picking where you stick your mechanics, you can exactly adjust your as-fan. This is something R&D does with every set. We figure out the components that matter and then place them accordingly.

Now let's talk New World Order, as we've come to the part of the article where it becomes important. New World Order limits the amount of complexity at common, to help keep the game in check for new players learning how to play. (There's a lot more nuance to it than my quick explanation, so if you've never heard of New World Order before, you can read the full article I wrote about it here.)

New World Order is important as it dictates what kind of mechanics can be done at common. This becomes important for volume because if you need to get to a certain level, it's hard to do it without having some common cards. The end result is that sometimes you come up with a mechanic that requires a volume all but impossible to achieve without breaking New World Order.

I should note that there are mechanics not done at common that can reach certain as-fan levels, but it requires a heavy dedication at uncommon. In general, if your theme is happening mostly at rare (as the legendary creature theme was done in Champions of Kamigawa block, for instance), it ends up being almost invisible to the players, especially if they only purchase a handful of packs.

#5—Does a different mechanic hinge upon the volume of this mechanic?

Now we get to the part where we start to see the interrelation between your components. As I've been talking about Khans of Tarkir, I'll use it as my example. Once you figure out your volume of multicolor cards, you're not done yet. The next part is examining if the volume of multicolor impacts the volume of anything else. The answer is, "Absolutely." The biggest thing is mana. In order to be able to play your multicolor cards, you are going to have to have the colored-mana producers to support it, which mostly is talking about lands and artifacts. That means you then have to figure out the volume of your colored-mana producers.

Khans of Tarkir also has a factional component. This means you have to figure out not just how many multicolor cards there are, but how many cards exist in each faction. The factions are based on color, which means you are going to want them to be of equal size. But that isn't always the case with factions (Lorwyn, as an example, supported certain creature types more heavily than others). Then, within factions, you have to figure out the volume of not just multicolor cards but also monocolored cards. Each clan also has its own mechanic, and you'll need to figure out the volume of each of those. As you dig deeper into any design, what you'll find is that the volumes of your different mechanics do not live in a vacuum but are interdependent. This makes the math even trickier.

Volume of a Cube

My goal of today's article was to pick up a proverbial rock and show you all the little insects crawling around beneath it. I spend a lot of time in this column discussing big-picture vision, but it's important to understand that most of the work isn't coming up with the idea, but figuring out how to make the idea actually work. Volume is a very good example of something every designer (and developer) has to care about and spend a great deal of time on, but that most game players probably never think twice about. A mechanic has so many cards because, well, that's how many cards the designer made. As today's article tries to show you, it's much more complicated than it might appear at first blush. And it requires a lot of math, so pay attention to what your math teacher has to say, kids. It really is going to matter.

Today's article was much more nuts and bolts-y than normal (and way more math-y), so I'm very curious what you all thought of it. You can email me or talk to me through any of my social media (Twitter, Tumblr, Google+, Instagram).

Join me next week when I go mano a mano a mano.

Until then, give a math teacher a hug.

"Drive to Work #162—Enchantment World"

A number of players have communicated that they were upset that Theros block wasn't to enchantments what Mirrodin was to artifacts. In order to explain why Theros wasn't that, as well as to explain why a future block of that nature is a real design challenge, I made a podcast talking about it.

"Drive to Work #163—Onslaught, Part 1"

This is the first part of a multi-part series on the design of the set Onslaught.