Modelling

In a previous post I discussed examining existing draft environments as a way to help you build your own custom draft environments. The example application of this principle which I discussed was mapping the concept of card rarity to your cube. There are many other things to learn from looking at these draft environments as well, such as how many draft archetypes you can support, what are the pieces you need to build a viable ramp strategy or what makes a "fast" draft environment. However, at its core, these things are all examples of a more general concept: modelling.

A model is an example that you use as a study reference which forms a basis of comparison; what you learn from studying the model can then be applied to your "actual" design - the real thing. Often models are created specifically as new things to be studied because they don't already exist. For example, an architect might build a scale model of a building in order to get a better feel for proportion and the overall impression of a design. With cube design, though, we have existing draft environments that we can study. However, existing draft environments aren't the only models that we have available to us. One of the goals of cube design - particularly for "best of" cubes - is to mimic Constructed playable decks and strategies within a Limited environment. It would make sense, then, to use Constructed decks as models for the type of decks we're trying to support in our cubes.

As an example, let's answer this question: How many aggro 1-drops do you need in your cube?

2-drops and a number of other factors are also important and might be worth running the numbers on, but 1-drops are the thing that allows aggro decks to start applying pressure straight away. Every turn you wait, that's an opportunity for your opponent to get their slower strategy online and functioning. Based on experience thus far, aggro 1-drops also seem to be the limiting factor in terms of how many aggressive decks can be supported in a cube. Interestingly, this line of analysis could potentially provide an indication of the maximum cube size that can adequately support this definition of aggro (which will increase over time as more aggressively costed 1-drops become available).

Ok, so how do you do this? I use the method below to build up my understanding of the problem domain and ultimately produce a number that answers the question.

Aside: When doing analysis like this I rely heavily on probability as it applies to Magic. While I won't go into the detail here, there are some good articles available on the Internet which explain how this works. I've provided some references at the bottom. I've also distilled this into a basic spreadsheet which I add to from time to time. I've transferred some of this information into this spreadsheet online. While I definitely recommend learning the maths behind this, the spreadsheet is a handy quick reference.

Assumptions

a) Aggressively costed (i.e. power > CMC) 1-drops are a critical factor in defining an aggro deck. The primary purpose of this is to apply pressure to the opponent from the opening turn.

b) Since this is the resource that appears to be in shortest supply, it will be the limiting factor.

c) While Cube is a Limited format, from a design perspective the goal is to allow players to draft and build Constructed-style decks (but only if they want to ). This means that we can look to successful Constructed decks of a similar archetype as a basis for comparison.

Analysis

Step 1: Identify the model

In this case, our model is really a collection of successful aggressive decks from across the history of the game. Some examples include Zoo, Zombies and Boros. (Many Green-based decks will consider themselves aggro but open with a turn one mana-producer to accelerate into powerful 3- and 4-drops ahead of schedule. I personally classify this as mid-range though you may classify it differently. Here I'm discussing the decks that want to be attacking for two on turn two.)

Depending on the format, a typical Constructed aggressive deck will run anywhere from 8-16 aggressive 1-drops in a 60-card deck. The level of aggression is roughly correlated to this number. Eight provides a 65.4% probability of having a 1-drop in your opening hand, while 16 provides a 90.1% of the same. From personal experience, I think that eight is too few, and that a successful number tends to be 10-12.

10 provides a 74.1% probability of having a 1-drop in your opening hand while 11 provides a 77.8% chance (from the spreadsheet).

Step 2: Convert the model to your situation

To find the equivalent number in a 40-card deck, we simply find the number that provides the closest probability to the target range (~74%-78%). In a 40-card deck, six 1-drops provides a 71.1% chance of having one in your opening hand, while seven provides a 77.1% chance. For the purposes of this analysis, I'll say therefore that the prototype aggro deck in cube wants seven 1-drops.

Step 3: Decide how to apply the findings to your environment

So, for every aggro deck that could be drafted, you'll need about seven 1-drops in the draft. Ignoring variance for a minute (see step 4), if you have eight drafters and a 360-card Cube (meaning all cards are available in the draft), then you need to determine how many aggro decks you want available in a given draft. Of course, this doesn't mean that this many decks will be drafted, but does indicate the number of 1-drops you would ideally need. Let's say you want n aggro decks available in the draft. This means that you need n * 7 aggressive 1-drops. I'll say that I want three aggro decks in my 8-person draft, so I need at least 21 1-drops in the draft.

Step 4: Scale the model to your cube size

What happens if the entire cube is not drafted? I'll take the example of a 450-card cube with eight people drafting. This means that 360/450 cards are available in the draft. If you still want n aggro decks, then you still need n * 7 1-drops in the draft as above. So then how many do I need in my 450-card Cube?

360/450 = 21/x

Solve for x...x=26.25

I need 26-27 aggro 1-drops in my 450-card cube to support three aggressive decks in an 8-person draft. Of course, the split won't always be exactly this ratio. Sometimes there will be more or less available. You have two options: You can add more 1-drops than the calculated minimum to try to ensure that there are at least enough available most of the time, or you can accept that sometimes there will be 2 aggro decks available and sometimes there will be 3 (or whatever you calculated for). That's the variance.

Step 5: Make decisions about how to apply the numbers

It's all well and fine to know that you need X 1-drops, but how should these be divided by colour? It's probably not viable to expect the lone aggro drafter to put together a 4-colour deck to make it happen.

My own principle is to assume that the mana is good enough to run 2-colour decks fairly easily. I also don't personally plan to guarantee to my players that mono-X aggro will be supported. On the flipside, if a player wants to run Naya Zoo, that's fine but I don't think you necessarily need to do anything to support that other than make the mana available.

This means that the number of aggro decks that you want to support should be divided across the colours in which you want to support aggro. For the purposes of this calculation, I think that you need to include the Blue-based tempo decks, because if they're paired with an aggro colour for efficient 1-drops, then they'll be pulling from your the same pool. In fact, since Blue doesn't really have any aggro 1-drops (or maybe just Phantasmal Bear), you might need the second colour to provide the full complement.

So, then, for every 3.5 1-drops you have in a given colour which are available in a given draft, you can support half of a deck. So if a 360-card cube with eight drafters has seven White 1-drops, four Black 1-drops and three Red 1-drops, then your Cube can roughly support 2 aggro decks. Further, you can expect that either one will be mono-White and the other will be Black/Red, or both will be White/X.

I suppose in an ideal world I'd see something like 2 aggro decks, 2 aggro control decks, 2 midrange decks and 2 control decks in an 8-person draft. These numbers are very rough and I wouldn't want it to always be exactly the same every time, but this kind of tells me that I'd really need about 28 1-drops in an ideal draft!

Adjustments

There are other factors that can affect the numbers. For example, some players might draft 1 or 2 1-drops but not see anything else to support aggro (cut-off) so they might abandon that plan. That means that those picks are stranded in a non-aggro deck or sideboard, and are not available to the other players drafting aggro. It might be worthwhile erring on the side of greater than the minimum calculated.

On the other hand, you might not want it to be too easy, either. Part of drafting is knowing that resources are limited and that you need to know what to prioritise. If 1-drops are abundant, then drafters will not need to prioritise them as much. Mark Rosewater, the Lead Designer of Magic: the Gathering, addressed this point in a recent article entitled When Cards Go Bad Revisited. In it, he identified improvisation as a key element of game design:

Design Principle #4: Force Players to Improvise

Another truism of game design is that you can't give the players everything they need. Games at their core are about allowing players to challenge themselves. A good game designer gives the players some tools but not enough to easily complete the task. Why? Because the goal of game design is to force the players to seek out their own solutions.

Another similar consideration is that you need to leave players wanting more. When drafting, you can build a great deck - say, a UW control deck - but even if you win with it, you can often look at it and think "this deck could have used one more removal spell" or "it was lacking a bit of card draw". It's not often that you build the perfect Limited deck, and that's what helps to keep an environment from getting stale. Over the weekend I drafted Return to Ravnica five times on Magic Online. In one draft, I had a really good Golgari beatdown deck. I had wanted to try out the Golgari scavenge strategy, but my deck only ended up with about 3 cards in it with scavenge. Fortunately, I realised pretty early that I might not get the pieces I needed for the scavenge deck and prioritised making a viable beatdown deck if there was nothing with scavenge available. It worked out reasonably well for me, but I still wanted to go back and try again. It happened in the very next draft - I ended up with a deck with about 8 or 9 scavenge cards, some black fliers, etc. The deck ended up not being that powerful, but I think I didn't quite have it right...I'd want to try it again. And that's the point - if you have too much of what the players need, then they'll get it and they might not even have to fight for it.

Reverse Analysis

So, how am I actually doing? I'll look at my cube to figure out what I can support. From my current list:

White: 5
Blue: 0
Black: 5
Red: 3
Green: 1
Multi-Colour: 5

Total: 19

Based on these numbers, I'm likely to only get about two aggro decks in a given draft. It is possible to get a third, but I'd like to see a few more cube-quality aggro 1-drops printed before I try to increase the size of my cube. The recent additions of the incredibly flexible Rakdos Cackler and Dryad Militant have been a real boon to aggressive strategies in cube. Keep in mind that just throwing in bad 1-drops doesn't solve the problem. The cards being considered must be of cube quality. In addition, an aggro deck can also look to other plays that progress their strategy on turn one, such as AEther Vial, Black Vise or Bonesplitter. That's where improvisation comes into play.

Wrap-Up

This method can be applied to any number of card classifications to help you make appropriate design decisions and card selections for your cube. The final step, of course, is to play your cube and get a feel for whether there are too many or not enough cards of a particular type.

And if you're cubing, it can't be that bad.


Reference Material

http://www.kibble.net/magic/magic10.php
http://www.starcitygames.com/magic/generallimited/24900-Limiting-Chance-The-Opening-Hand.html
http://www.starcitygames.com/magic/generallimited/24978-Limiting-Chance-An-Explanation-Of-Methods.html