For a game that features quantitative thought, there are a lot of Magic concepts that rely on intuition or estimates of reality rather than measurement. For example, mana base construction is much more of an art than a science, even in decks with stringent and demanding color requirements—but, articles like this one from Frank Karsten, have done a lot of work laying out a mathematical approach. The construction of a mana curve is another area that is based much more on feel than calculation, and one that hasn’t been mathematically examined (to my knowledge).

Today, I want to focus on a third area that has traditionally relied more on general feeling than math: the pro-level metagame. There have been some attempts at understanding GP and PT results that come close to quantifying results—I grew up reading weekly “Five with Flores” articles, and those blue and white dots indicating wins or Top 8s for a given archetype have stayed with me since—but they mostly rely on subjective groupings of decks into archetypes.

flores

That can miss certain changes in deck composition, both major and minor, and makes it hard to evaluate exactly how much a format has shifted between two points in time. A good example of this is in the various flavors of Abzan decks over the last year: Aggro, Midrange, Control, Megamorph, Company, and probably some others I’m forgetting. They all share a lot of cards, and an argument could be made that they represent anywhere from one to five different archetypes. If a tournament had a Top 8 filled completely with different types of Abzan decks, is that more or less diverse than one split evenly between Mono-Red and Blue/Black Control?

In the past we haven’t had the tools to answer this. While “diversity” is a fluid enough concept that a single answer probably doesn’t exist, I though the information was there to at least have this discussion in a much more rigorous way.

So, I’ve created a card-level analysis of the past year or so of Standard, since the release of Khans of Tarkir in October of 2014. For each Standard PT or GP since then, I recorded the contents of each deck that a) made the Top 8 of a GP, b) had 37 points or more (12-2-1) at a GP but didn’t make the Top 8, or c) had 24 points or more (8-2) in the Standard portion of a PT.

This might not fit everyone’s definition of “the metagame,” so feel free to mentally replace that with “top-performing decks” or whatever you prefer. This also might over-represent decks from Pro Tours, as there’s a lower bar for their inclusion and more than from any given Grand Prix. These PTs are the first real impression of a new Standard format, so I think it’s acceptable to potentially overemphasize those results somewhat. In any case, I think this dataset conveys interesting information about a format. I’m going to break this article down by format, looking first at the tournaments that happened between each new set release and format change.

ktkchart colorsharesktk

In these tables, to generate the card rankings, I ignored basic lands, and divided the total number of times a given card was included by the number of decks. For the creature/noncreature and color proportions, cards with multiple types or colors are counted multiple times, once for each. The five new creatures from Origins that flip into planeswalkers were treated like any other card with two types.

The number of unique cards and what I called the “diversity coefficient” give two different measures of the diversity of a format. The first is fairly self-evident: the total number of unique cards (ignoring basic lands) that were in a high-performing Standard deck over the course of the format. Higher numbers presumably indicate more viable options for players looking for a top deck.

The diversity coefficient is a bit more nuanced. It’s the standard deviation of all the rates for the unique cards. More cards results in a lower figure, as does a more even distribution. This means that, for example, a format with two decks equally represented among top performing decks will have a lower score than a format heavily slanted toward one of the two, even if the two formats have the same number of unique cards. A lower score therefore fits my intuitive feeling for a more diverse format, but it’s definitely subjective, so make of it what you will.

This table showcases the first task this analysis is capable of, which is to confirm and quantify beliefs that had previously relied on intuition. Abzan decks dominated Standard over this period, and that shows up in the top performing cards: eight of the top ten are in almost every Abzan deck. Green also tops the color shares leaderboard, due in large part to its versatility, playing a key role in the aforementioned Abzan decks and the big-mana Nykthos decks.

Blue is emphatically in last on the color shares list, and it’s not any better when looking at individual cards, with the first blue card ranked at #40 (Mantis Rider) and the first mono-blue card ranked at #57 (Dig Through Time). Some of this is a function of the lack of blue cards played as 4-ofs—there were 32 unique blue cards making up their 5.5% of the format, versus 50 unique green cards (less than twice as many) making up their 30.4% of the format (more than five times as many), indicating the green cards were more likely to be played in multiples. But this was also simply not a good format for fans of blue.

fatechart colorsharesfrf

A lot of pros seemed to feel a bit shell-shocked by the brevity of this format, and the combination of a Pro Tour featuring Modern rather than Standard and the early release of Dragons of Tarkir means there aren’t many results to base this analysis off of. This is evident in the lack of turnover among the top cards in the format, and the relatively limited impact of Fate Reforged, with only two new cards making the top 20.

There were some new toys—Nykthos decks got a shot in the arm from the addition of Wild Slash and Whisperwood Elemental, and Valorous Stance gave the UW Heroic deck a versatile tool, but overall, there’s not too much to say about this pair of tournaments. Unsurprisingly, there weren’t many unique cards featured in these two weeks, and while the diversity coefficient is lower than in the previous Standard, I think that’s more the result of there being fewer tournaments and fewer extreme scores as a result. Goodbye, Fate Reforged Standard, we hardly knew ye.

dragonschart colorsharesdtk

Dragons of Tarkir had a much longer tenure as the newest set in Standard than Fate Reforged, and it also did much more to impact it. One of the biggest stories was the existence of a blue deck for virtually the life of the format, with Esper Dragons taking the color back up to a much more respectable 10.7%, and the highest monoblue card just outside the top 20 (Silumgar’s Scorn). There were impactful new cards for a variety of archetypes, and several older cards that saw their stock rise or fall in response. Rattleclaw Mystic pushed out Voyaging Satyr as the 2-drop green accelerator of choice, in large part because of the takeover of the format by Deathmist Raptor and Den Protector.

Still, despite those changes, Abzan remained at the top of the heap, with every single card in the top 10 fitting in at least one of the many versions of the deck. Green, already dominant in previous formats, finished as a whopping 38.7% of cards played. Despite more cards to choose from than after the release of Khans, fewer unique cards were played (146 vs. 161), though the diversity coefficients were practically equal.

One positive aspect of this Standard was the successful integration of some of the themes of Dragons. In addition to megamorph, a number of Dragons or “Dragons-matters” cards (like Silumgar’s Scorn) also played a role in the format, including Scorn, Ojutai, Haven of the Spirit Dragon (#29, 0.7), Dragonlord Atarka (#36, 0.6), Crux of Fate (#39, 0.5), Foul-Tongue Invocation (#42, 0.5), Thunderbreak Regent, and many other more marginal players. Often, a format has no relation to the flavor or overall feel of the most recent set, but that wasn’t the case with DTK-era Standard, which I enjoyed.

originschart colorsharesori

This format isn’t complete yet, so this is more meant for fun than as a rigorous analysis. I envision this work being much more useful retrospectively than as an evaluation of the current metagame, so don’t go preparing for your FNM with this. The relative youth of this Standard also means that decks that did well at the Pro Tour make up a large proportion of the whole set, and those decks (like UR Ensoul) might look more influential than they really are.

Despite that, Origins does appear to be extremely influential. I plan on adding old data as well as new tournaments, and I’ll be very curious to see how this format shift stacks up against those of older core sets, since my intuition is that ORI will blow most of them away. While the top cards still feature primarily Abzan staples, Hangarback Walker at #2 is a powerful and versatile card that fits into a number of archetypes. One of them, UR Ensoul, didn’t exist before the release of Origins, and has pulled two new cards into the top 10 (Shivan Reef and Temple of Epiphany).

The format also looks more diverse, and has been much more evenly balanced among the colors. The number of unique cards is already at its highest since KTK, at 177, and the diversity coefficient is at its lowest (most diverse), at .31. Green still leads the other colors, but with the much more reasonable rate of 29.5%, and blue has crept back up to 11.7%.

The bump in noncreatures is mostly due to the surge in artifacts (less than 1.5% before ORI, 11.7% since), another example of a set theme making an impact on Standard. The marquis cards of ORI, the planeswalkers, also have begun to show up, led by Nissa (#32, 0.5) and followed by Jace (#40, 0.4) and a single Chandra. Thus far, it seems like Origins has brought the format much more into balance, but it’ll take more GPs before I’m confident in that claim.

totalcardschart totalchart colorsharesall

The first chart shows the most played card of each color, from that set and of that type respectively. On the color shares chart, the dotted lines are the average for that color over the entire year.

This period of Standard has been a fairly lopsided one, in total. Green dominated the entire time, ending with more than a third of the format, while blue was consistently limited. The green column of the first chart is missing a number of cards that were prominent but were pushed out by other highly played green cards, while the blue column has to include all-stars like Torrent Elemental (two total copies, one at GP Providence and the other at GP Seville) and Interpret the Signs (a single copy at GP Denver).

The chart with the color distribution for each GP also showcases a somewhat worrisome trend. At the beginning of the various formats, the shares tended to be more evenly distributed, but as they went on, green quickly asserted its dominance. Origins-era Standard looked better above, but that might only be because green’s dominance has been recent. While blue and red were above their yearlong averages at the PT, they’ve since plummeted, and green has filled much of the gap left behind. This has been the year of Abzan, and it may be that Origins hasn’t really changed that.

I think the next big thing in macro-level Magic analysis will be using data to back up beliefs that previously had been based on intuition or gut feeling, and this is one example of that. I hope that in the future, a set’s impact on Standard, or a deck or card’s dominance of a format, can be estimated and compared to past sets or cards. As always, I’d love to hear any feedback or questions you have, so please feel free to reach out to me on Twitter @henrydruschel.