Brewing in Oathbreaker: Is Overlapping Design Space a Problem?

by SumNeuron // Sep 2, 2019

A gripe one will eventually encounter with discussing Oathbreaker is the pool of available generals, especially in comparison to the myriad of generals available to helm one's deck in Commander. So let's take a more nuanced look at just how limited one's Oathbreaker pool may or may not be.

Excluding the debatable quality of Planeswalker deck Planeswalkers, there are 18.042% as many generals for Oathbreaker than Commander, only 21 (65.6%) of the possible 32 color identities available, and text-based analysis suggests around 27 "redundant" Planeswalkers. While by shear number Oathbreaker currently has a smaller pool of generals than Commander, the Signature Spell mechanic can not be discounted for the expanse it contributes to the brewing landscape. Further, we know that new Planeswalkers are on the horizon. Yes Oathbreaker is more limited for brewing in regards to selecting a general than Commander, and Oathbreaker is not too limited a format as a result.

Overview How Many Oathbreakers Are There?

At the time of writing, there is currently one banned Planeswalker, Saheeli, the Gifted, and one illegal Planeswalker, Urza, Academy Headmaster. In addition, it is worth recalling Oathbreaker's format rule number 5: A Planeswalker card in your deck is considered your Oathbreaker. In other words, no transforming Planeswalkers. Using Scryfall we can determine how many Planeswalkers are available to be one's Oathbreaker:

-type:creature type:planeswalker -name="Saheeli, the Gifted" -name="Urza, Academy Headmaster"

and... 183 potential Oathbreakers. Now, some might have the opinion that 183 is an inflated number because these results include Planeswalkers from the Planeswalker decks, which are intentionally made worse. While not all cards can be good, I'll indulge this notion and remove the Planeswalker deck Planeswalkers from our results (even though Vraska, Scheming Gorgon is a spicy build around):

-type:creature type:planeswalker -is:planeswalkerdeck -name="Saheeli, the Gifted" -name="Urza, Academy Headmaster"

now there are only 153 putative Oathbreakers.

How Many Commanders Are There?

So how does this compare to Commander?

((type:creature type:legendary) or o:"can be your commander") legal:commander

and we find 848 results... which includes mostly ignored "gems" like Barktooth Warbeard, Gallowbraid, Jasmine Boreal, etc. Not really surprising since legendary creatures introduced in 1994 and Planeswalkers first made an appearance in 2010.

How Does Oathbreaker Compare To Commander?

Worst case scenario and from a pure numbers perspective, Oathbreaker has 18.042% the number of viable generals compared to Commander (excluding those from the Planeswalker decks). Tada! A nice, simple and clean answer: Oathbreaker is 18.042% as brew-able as Commander... or is it?

A More Surgical Perspective

Now I am sure some may also lament that even 18.042% is too generous of an estimate. After all, of these 153 Oathbreakers, there are only 53 unique subtypes (named characters, e.g. Jace, Ajani, The Wanderer, etc).

Why might that be generous? Well let us inspect Magic's poster boy, Jace.

-type:creature type:planeswalker -is:planeswalkerdeck -name="Saheeli, the Gifted" -name="Urza, Academy Headmaster" type:jace

There are 8 variants of Jace you can run in Oathbreaker which are not from Planeswalker decks:

Notice anything?

Across these 8 Jaces, 5 of them have a similar first ability including the text "draw a card" somewhere in that loyalty ability; 3 our of the 5 have a minus loyalty ability returning a target to hand; and several have some form of mill / mass draw effect. In other words, there may be 8 Jaces, but the design space across these 8 Oathbreakers is potentially more narrow than 8 generals from Commander that share the same color identity.

So how might we inspect the "narrowness" of the design space from Planeswalker variants (Planeswalkers with the same subtype)?

Data Analysis

Here we will try two approaches to get a feel for the overlapping design space of Planeswalker variants.

Human Curation

To address the putative overlapping design space, we could make a table for each Planeswalker subtype (named character) and see how many variants share similar features. For example, let us inspect Ajani:

The above Ajani table is useful. After all it is clear that if seven of the nine Ajani variants care about +1/+1 counters, then the design space is somewhat overlapping. However, just because many Ajanis share a core design mechanic, does not mean they are locked into a singular function. Only four Ajanis create tokens, and one (Ajani Vengeant) even destroys lands! After all, Planeswalkers often have more than a single ability.

Now I could do this by hand for all 53 unique Planeswalker subtypes (and I did for all Planeswalkers with three or more variants), but this handmade method has some pros and cons:

Pros flexible human curation can provide better data aggregation (e.g. "creatures you control gain vigilance", "target creature gets +2/+0", etc can be aggregated as "Creature Buffs")

Cons time-intensive human curation can be inconsistent human curation can be ambiguous / noisy e.g. "Life Matters" vs lifelink and does Ajani, Mentor of Heroes's ultimate ("You gain 100 life.") count as Life Matters?



So instead of this hand-curated approach, let us try something a bit more data driven.

Light Textual Analysis

For simplicity, I will not show any of the code directly here. The code I used to obtain these results can be reviewed at the linked code repository if you would like to follow along.

What kind of textual analysis are we going to employ? The "flow" of our data processing goes like this:

Obtain all the card data for a given Planeswalker's variants (e.g. all Oathbreaker legal Ajanis). Extract the oracle text for each of these cards. Parse the oracle text into words. Remove words that might get in our way. These words includes: the top 100 common words in the English language (e.g. "a", "the", etc)

words that occur on only one Planeswalker from the collection of all Oathbreaker legal cards. If these words appear only once, they are likely not contributing to overlapping design space.

other irrelevant words. These are words I personally hand curated from the collection of all Oathbreaker legal cards and introduce some bias into our results. A few examples of some of these words include (full list at the repository linked above): "commander" (from the Planeswalkers which reference that they can be your Commander), loyalty costs such as "+1", "-8", "-6", etc, miscellaneous words such as "able" and "onto", as well as the specific names of Planeswalkers ("Jace", "Chandra", etc)

Lemmatize each word. This helps reduce the complexity of the oracle text. In short, you can think of this as converting words to how they would appear in a dictionary. For example, lemmatization would do the following: player ---> player

players ---> player

discard ---> discard

discards ---> discard

discarded ---> discard Remove the duplicate words, so that we have the set of the words which occur in the oracle text. For each card's lemmatized, post-filtered words, take note of whether or not a word appears. Here I also introduce a form of bias that you may not like. I am only concerned if a word, such as "draw", occurs anywhere on a Planeswalker, not how many times. Since we are looking at the design space of all the variants, it doesn't matter if a given Jace can draw a card in three different ways, just that this Jace involves card draw. Tally how many times a word occurs across the variants we are looking at. Since a card will only contain a word if it occurs anywhere in its oracle text, the maximum number this tally could be, per word, is the number of variants. Perhaps a concrete example to solidify the meaning. There are eight variants of Jace. If the word "draw" has a tally of seven, then we know that seven of the eight Jaces somehow involve someone drawing a card. The higher the tally, the more overlapping the design space.

Now that we have gone and done all that, let us inspect a view of the marquee characters. If you want to look at all the matrix images, they can be found here.

Examples

Ajani

Below is the "same" Ajani matrix that I hand curated above, but now produced via this automated text analysis. Note, for legibility, I am only showing the words which occur in at least 1/3 of the Ajani variants.

Notice, that from this matrix we can see that Ajani cards a lot about +1/+1 counters, gaining life, and tokens.

Jace

What does Jace's matrix tell us? Surprise, surprise, card draw and mill.

Chandra

What does the explosive Chandra tend to do? Well, she tends to do damage, with a few variants caring about spell slinging (the bottom two rows for words "instant" and "sorcery").

Calculating The Adjusted Number of Planeswalkers

Continuing from how we made the heatmaps above, we can now figure out how many Planeswalkers are redundant in the design space by:

Using the tallies from above, calculate the density of the word occurrence, Planeswalker variant matrix. The density tells us what percent of the variants have overlapping design space. Calculate how many cards overlap. This is simply the number of variants times the density. Calculate the adjusted number of variants. This is the number of variants minus the number of cards overlapping plus 1. We add one because we are removing all of the overlapping design space. However, at least one card should count for this part of the design space. If you disagree you can subtract 53 (one for each of the 53 Planeswalker subtypes) from the following result.

Results

Drumroll... and 126.916! This analysis shaved off ~26.084 Planeswalkers from the 153 Planeswalkers we looked at (Oathbreaker legal and not from a Planeswalker deck).

Was this more or less than you were expecting? Recall only a few Planeswalkers (namely the Gatewatch) have many variants.

What is that? This isn't good enough? Ok, ok, maybe even removing the overlapping design space is too generous a metric. After all, the different color combinations of Magic allow one to express themselves. Perhaps Oathbreaker does not cover enough of the color pie.

Color Identity

So just how much of the color pie is represented in the current legal Oathbreakers? Currently there are 21 color identities represented in Oathbreaker out of the possible 32. Oathbreaker has colorless, all five mono colors, all ten guild combinations, five of the ten three-colored shards, and no four or five colored Planeswalkers (sorry Urza). So 65.6% of the color identities are currently possible in Oathbreaker. It is worth keeping in mind that legal four colored generals for Commander are relatively new and there is only one legal four colored general for each option; in other words, the four-colored generals are also limited in Commander, but existent.

The Facts

Are there less generals in Oathbreaker than Commander? Yes . There are less format legal generals for Oathbreakers than format legal generals for Commanders.

Are there less color combinations in Oathbreaker than Commander? Yes, but . There are less format legal generals in Oathbreaker across the possible 32 color identities spectrum than Commander... but, aside from the four-colored Commander pre-cons, Commander also lacks format legal four-colored generals. Regardless, as of writing, only 65.6% of the color identities are currently playable.

Is the play design more limited? Maybe . I only looked at redundancy across variants of Planeswalkers for Oathbreaker. I did not look for redundancy across generals in the same color identity in Commander.

Is the play design of Planeswalker variants limited? Perhaps . Using the light text-based analysis of Planeswalker oracle text we shaved off ~ 26 "redundant" Planeswalkers in regards to design space. That still leaves ~126 Planeswalkers to be your Oathbreaker (again, excluding Planeswalker deck Planeswalkers) The fact that a Planeswalker can have several variants implicitly limits play design to make these character centric cards around, well, the characters. Outside of major character arcs, personalities can stay the same leading to may similar expressions of that character's personality across their variants (e.g. +1/+1 counters for Ajani, dealing damage for Chandra, etc). However, with War of the Spark behind us and Wizards willing to introduce new characters like Huatli, Rowan and Will, we may see novel aspects of a color identity expressed through these new characters.



The Question At Hand

With 21 (65.6%) of the possible 32 color identities available, 153* (18.042%) compared to the 848 possible generals as Commander, only 53 marquee characters resulting in ~27 overlapping designs, is Oathbreaker too narrow a format? *using the non-Planeswalker deck Planeswalkers.

Not at all!

1. A key part of the Oathbreaker format is the Signature Spell mechanic, an instant or sorcery spell which accompanies your Oathbreaker in the Command Zone. While there are likely hundreds of instants and sorceries which will likely never be paired with an Oathbreaker, there are thousands more which can be for unique combinations. These pairing opens up the brewing possibilities, especially as having a tutor effect in the Command Zone can help one build their Rube Goldberg combo machine.

2. Planeswalkers are not going away any time soon. Even after the dust from War of the Spark has settled we are already anticipating a return of Rowan in the upcoming fall set Throne of Eldraine. More Planeswalkers are coming to help fill out the gaps in both the set and auxiliary Planeswalker decks.

3. With Throne of Eldraine we will also be receiving, for the first time, Brawl pre-cons as a push from Wizards of the Coast to rejuvenate the struggling format. Brawl the rotating, Commander / Oathbreaker hybrid also allows Planeswalkers as commanders. While we can not be certain that a Planeswalker will be a part of the Brawl pre-cons, the already spoiled Chulane, Teller of Tales suggests that these pre-cons generals are not to be trifled with. Further, the fact that Wizards of the Coast is making such a concentrated effort to support Brawl means that in addition to making legendary creatures to helm Brawl decks, they may also be thinking of unique Planeswalkers specifically for the format.

Even if you find the current Oathbreaker selection lackluster, for those with patience, having War of the Spark behind us means new planes of the multiverse to explore and with Wizards of the Coast more actively supporting Brawl, new Oathbreakers are on the Horizon (Wrenn and Six anyone?). As for those only concerned with the pool of Oathbreakers at hand, the Signature Spell mechanic opens up a new world of brewing possibilities in the majority of color identities.

These are just my opinions (and analysis), but I'd love to hear your thoughts. Do you find the number of Oathbreakers underwhelming? Have you personally evaluated every one of the 848 generals for Commander? Do you think the new wave of Brawl support will bring us more Planeswalkers to round out missing Planeswalker mechanics and color combinations? Want more data-driven articles? Let us know.