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Wurtil Wednesday: Quadrant Theory

What is the measure of a card’s effectiveness?

We play a game in which we are required to provide constant yet changing evaluations at every moment. We strive to win the game, but must be ever-vigilant in how exactly we plan on accomplishing this goal and what our cards can do to result in this end-state. Terms and theories such as Card Advantage, Tempo, and Cost Efficiency are all used in some way to try and quantify our efforts, but in the end we still will continue to argue even amongst our peers which values are most important and even what those values may be.

So to “Review” a set of cards for limited play is folly from the outset. No review will ever be perfect, because the definition of what is perfect is not even fully comprehended by those who have lived with card games their entire adult lives. And yet, here we are again grading and judging cards against one another because what matters to us who seek the competitive fuel that fires CCGs like HEX is not perfection in itself, but rather the pursuit of perfection in ourselves and our thought processes. Knowing that Extinction is an A+ card helps me for brief period of time, but knowing why Extinction is graded as such can benefit me for a lifetime. While you are reading the review series for Shattered Destiny Limited—while I will be happy if you take away some unique perspectives on the individual cards—what I hope to give you is a different way of thinking about those cards that you can apply in your own way to make better decisions for as long as you play.

Three paragraphs in, and we finally get to the words in the title: so what exactly is Quadrant Theory?

It would be poor form not to pay homage to the history of the theory in TCGs, and as such you can find a detailed article on Quadrant Theory in Magic The Gathering terms HERE. However, we can use some basic descriptions here for those that don’t want to click through. Essentially, Quadrant Theory is a tool to help frame card evaluations for Limited players.  Constructed gets extremely complicated for framing like this as there are so many different ways to exploit your advantages, while in Limited we very often end in the same manner of swinging through with more or better troops than the opponent. Like Curve Analysis and other tools we have used in some of my other articles, it is intended to be used by players to get different perspectives on how a card will actually perform in a real game of HEX without having to actually play hundreds of games first. Quadrant Theory differentiates from other tools by trying to boil down what stages of the game a card is good in.

That raises the question: what exactly are the stages of a game of HEX? At first glance it is tempting to boil things down into timestamps based upon when something is played with monikers such as “Early Game”, “Mid Game”, and “Late Game”. The problem is that those definitions not only leave some some grey area for evaluation but also don’t encompass the entirety of the situations we will see. First, the transition between those stages are difficult to properly define; using numbers of turns doesn’t properly account for games that get lopsided quickly and defining by board position gives us a great deal of confusion for what exactly constitutes a mid-game position versus a late-game position. Instead, we turn towards the following four stage definitions:

Development – This is the stage of the game in which you are planning for how you are going to build up your board position or start executing your strategy. As an example, a 1-drop or a 2-drop might be particularly effective during development since you can plan on how you are going to play them early if they are in your hand. Cards like Extinction and Onslaught can also be effective during Development as you can “develop” your game plan based around the fact that you know something about how the game can go that your Opponent does not.

Parity – This is the stage in the game in which the board is fairly even and it looks like either player could still win the game. Most often, this stage of the game manifests as a stalled board where neither player has many or good attack options available. As an example, troops with evasion or troops that generate card advantage can both be strong during Parity, either by increasing the number of good attacks you can have or by starting to create an overwhelming card advantage over your opponent.

Ahead – This is the stage in the game in which you are clearly ahead of your opponent in executing your intended strategy. Normally, this is a board position where you have many good attacks and the opponent has few good ones available and must devote their resources towards defending against you. As an example, cards like Countermagic or Burn to the Ground are very good when Ahead, as they will either prevent your opponent from coming back or kill them before they have a chance to come back in the game.

Behind – Intuitively, this is the reverse of Ahead; this is the stage in the game in which you are clearly behind your opponent in executing your intended strategy. Normally, this is a board position where you have few good attacks and must devote resources towards defending and your opponent has many good attacks. As an example, cards like Extinction or Heat Wave as great when you are behind, as they can create a more even board state. Cheap, efficient cards can also be considered good when you are behind—as you might be resource constrained which led to you being behind—and playing multiple cards in a single turn can help bring you back to parity.

All that being said, as a quantitative guy I like to be able to assign numbers to things. It is a bad habit I have been trying to kick since childhood but hey, might as well embrace it for an experimental review format, right? Numbers are not perfect, and as mentioned above you have to be aware that once a draft actually starts all the numbers will constantly shift as you build your card pool up and other players reduce the potential card pool available to you. Still, we would like to have some starting point for framing these cards so that when we see two cards we like we can begin to understand quickly which one will likely be better for us. Given an arbitrary 1 through 10 scale, with 1 being the lowest and 10 being the highest, I have used the following metrics for evaluating the cards in Shattered Destiny in each of the 4 quadrants:

10 – This is the best possible card for this situation I could imagine

9 – Having this card in this situation will make me very likely to win the game by itself

8 – Having this card in this situation will definitely help me win the game

7 – This card will almost always be good in this situation (>90% of the time)

6 – This card will be good in this situation most of the time (>50% of the time)

5 – This card will be okay in this situation on average, but rarely will it be very good or very bad

4 – This card will be poor in this situation most of the time (>50% of the time)

3 – This card will almost always be poor in this situation (>90% of the time)

2 – This card is equivalent to a blank card in this situation

1 – Playing this card in this situation will actively cause me to lose the game

So what would a well known Shards of Fate card look like in here? Let’s put Extinction to the test:

Extinction
DevelopmentParity
87
AheadBehind
210

In Development, we normally are looking for cards that help us curve out perfectly and create a strong board presence. In some respects, Extinction fails in that regard as you don’t want a line of play that goes 2-drop, 3-drop, Extinction. On the other hand, the key thing about having an Extinction in your opening hand is that only you likely know about its existence. Your opponent very rarely will play around an unseen Extinction, so letting your opponent drop troop into troop before creating a gigantic card advantage sweep is a huge deal. Development isn’t entirely about board presence, but also it takes into account a little bit of gameflow – if you know something about how the game is going to go and can play accordingly while your opponent gets trapped then that is a positive card for your Development.

In Parity, normally we can craft a positive situation with Extinction. Most often we stop playing troops for a few turns while the opponent continues to try and push their board presence before we blow up the board and recover faster. Other times, we push a slight edge we might have with the knowledge that we have a backup plan to reset everything. The big point is that very rarely are you sitting in a Parity situation where you aren’t able to create some advantage for yourself with Extinction.

When you are Ahead, Extinction is actually pretty bad. You aren’t going to want to help your opponent by blowing up your superior board, and while it is true that if your opponent gets back in the game then Extinction gets good again the entire point of having cards that are good when you are ahead is to slam the door shut before the opponent can mount those comebacks.

Finally, Extinction might be the ultimate “Behind” card. It is cheap enough that if you are down because you missed Shard drops then you can probably still get enough to cast it before the game is over. It is powerful enough that if you are behind because the opponent drew gas while you drew Shards then you can bring things back to at least Parity. The phrase “I lost because I drew Extinction instead of ______” just doesn’t exist except in the most mindboggling of pocket universes.

Back to our tool: if things go right, we will likely see something close to a Bell Curve in the population of these ratings, depending upon how the designers of HEX want to make each individual set. It is no guarantee that we will see even a single 1 or a 10 in any given set, and most of the cards we will be dealing with should fall in the 3-7 range for most of the ratings as we expect that cards should gravitate towards being average rather than being nothing but amazing bombs.

Since we are applying our ratings to each quadrant, we will be able to use the data to create an Average Rating. In Extinction’s example, that number would have been a solid “7”. It is certainly tempting to float this number out as a true rating, but is that actually going to help us evaluate cards? The problem is that not every Quadrant is equally helpful. For example, if I am already in an Ahead scenario, I might be fine drawing average cards for the remainder of the game while if I am in a Behind situation I likely need to find something strong in that quadrant soon or else I will outright lose that game. To illustrate this issue, I have applied Weightings to each quadrant to help give us a weighted average that should be better at framing how important each card is to us. Personally, I have found the Behind quadrant to be the most important of them all as it is frequently the hardest to fill when building your deck, with expectedly the Ahead quadrant being the easiest to take care of. Development and Parity are interesting, and their importance will likely shift depending upon what CZE wants the format to look like.

In Shards of Fate limited, board stalls were frequently common and it was only really some fringe decks that could run people over in the development stage of the game; in a case like that, the Parity quadrant will be slightly more important than the Development quadrant. For Shattered Destiny, I am going to go in with the assumption that it will not stray too far from the principles of Shards of Fate limited and that board stalls will continue to be quite common. Thus, as a starting point for these ratings I am going to use the following weightings for this series of reviews: 

DevelopmentParity
0.250.3
AheadBehind
0.10.35

 

Returning one last time to our Extinction example, this raises its rating up to a huge 8.05 thanks to being so very good in the quadrants that frequently matter the most. Each format can likely have a different weighting as some formats will emphasize having strong Development cards while others will lean more towards cards that can break Parity. We can look at a general spoiler and have a somewhat decent understanding on if a format will lean one way or another, but until we actually play it we will need to likely stick to some established numbers for a baseline.

I will try to release a copy of the spreadsheet used for these reviews once they are all posted so that you can play with ratings to see how your own personal opinions and priorities might change things. Hopefully some interesting information will emerge from the data we create, but at the same time if the numbers look totally different from every practical application then things should be re-evaluated.

2 Comments on Wurtil Wednesday: Quadrant Theory

  1. “Wurtil – Teaching players how to think since Alpha”. Great breakdown of the thinking process and thanks for sharing.

  2. You should really directly credit Brian Wong for this – the credit above makes it sounds like WotC came up with this idea when in fact Marshall’s LR Podcast ex-cohost Brian did.

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