5000 Words for Snow

Posted by Sierkovitz, 2021-02-18

When Paul Jaccard published his seminal work: "Étude comparative de la distribution florale dans une portion des Alpes et des Jura" in 1901 he definitely did not expect that his work on comparison of alpine meadow flowers' biodiversity would be applied in the future to look at the successful builds of draft decks. But his methods of converting ecosystems to numbers are too useful to pass over. And surely it can't be a coincidence that Alpine Meadow is in the set we are analysing today, can it?

Let's start from the beginning. I am both a Magic player and a microbial ecologist. While playing cards has given me a surprisingly potent skillset in my non-Magic life, my professional training is also helpful in how I think about limited and cards in general. One concept I always wanted to apply to Magic is the comparison of similar ecosystems we often use in ecology. A limited metagame is like a planet. Each archetype is an ecosystem consisting of decks. Decks are samples of this larger ecosystem, like the sites on different alpine meadows prof. Jaccard was comparing in the early 20th century. Cards in those decks are like the meadow flower species - there is an overarching degree of similarity but each site (deck) has a slightly different species (card) composition. If that is the case, why can't we use the same tools he did to compare decks within an archetype?

This idea was bubbling in my head for some time, but with the arrival of Kaldheim I finally found inspiration. Snow is significantly different from the ZNR archetypes, which were very well defined and stuck rigidly to their 2-colour combinations. Snow is wild. You can find almost anything, from streamlined mono green to a luxurious 5-colour extravaganza through all the combinations of (mostly) G, U, R and B. This makes it easy to compare decks within the mega-archetype and lets us try and figure out what makes particular snow decks more successful than others.

How should we compare those decks? Here is where the ideas of Jaccard and later ecologists come in handy. They designed a toolkit of comparing sampling sites to one another. Briefly, you convert the combinations of species from each site to numbers and plot them on a graph. The sites most similar to each other are closer on the graph, and based on that you can cluster sites that are very similar and look at the features that make them so. This is exactly what I've done with the snow decks from KHM.

I've defined a snow deck as one that has at least 5 snow lands and at least 5 snow permanents. This gave me over 4300 snow decks from the 17Lands database to compare. I plotted these in a two dimensional space for our human brains to understand (the solution of such analyses is normally multi-dimensional and impossible to grasp). The closer two decks are on such a graph, the more similar they are. The axes of the graph have no unit nor dimension, so I've omitted them to avoid confusion. For boring details of the analysis, read the methods note at the end. As you can see, the plotting of thousands of decks yields an incomprehensible blob of points. But what do they mean?

Fig. 1: Raw plot of the snow deck diversity

My first idea was to mark the win rates of the decks plotted. The idea was that there might be some visible clusters of decks that win more, and there were. On the graph below, you can see the results with some potential clusters marked. This gave me hope that I could identify some high win-rate pockets and look at the compositions of decks within those pockets to identify their defining features.

Fig. 2: Snow deck diversity plot with win rates of decks and promising clusters of decks more likely to win marked in red circles.

This was an encouraging result. I could see that the high win rate decks seem to cluster together to some extent. If they were all over the place, it would suggest that trophying is a very random result. Instead, there seems to be a method in drafting a winning deck. Now all I needed to find is a method of my own to be able to identify those pockets of high performers. The idea I had was to look at a heat map of win rates. I calculated the average win rate of a deck and its 10 closest neighbours for each of the 4300 decks.

Fig. 3: A deck with its 10 closest neighbours. In this case the deck tested is medium (3-4 wins) and is neighbouring with 4 poor decks (0-2 wins), 4 medium (3-4 wins), and 2 decent (5-6 wins) decks.

With the data of all decks with their closest neighbours calculated, I started to look at best and worst performers. I plotted all 4300 decks, but highlighted the points with 100 highest average win rates and 100 lowest win rates. The 100 winningest areas on the plot were surprisingly close to the areas I selected by eye but some additional areas popped out as well.

Fig. 4: Win heatmap of snow decks. The 100 winningest areas based on average win rate of a deck and its 10 closest neighbours are in red circles, 100 most losing decks based on the same criteria in blue diamonds. The remaining decks are the small grey spots. The shading indicates the area where most successful decks reside.

Here we get to some interesting results. The first thing that strikes me are clear clusters of winning decks, which is the basis of further analyses. If decks are similar and have high win rates, you can look at compositions of those and find key features that can give you hints on why those decks are successful. The second thing that strikes me is the lack of such clear clustering in the losing decks. This is important as it suggests that there is no real recipe for disaster. Losing decks are peppered all over the plot. Some are even nested in clusters of winning decks, showing how razor thin a margin between a trophy and a failure can be. Even a good looking deck is a couple of bad draws, a couple of small misplays or a couple of unlucky pairings away from going 0-3.

Another look at the graph can show a careful observer that the pockets of winning decks are not necessarily located in most densely populated areas of the plot, which points towards the idea that the decks in question are not random piles but more coherent decks drafted with a plan and not created simply by what snow payoffs were floating across the table. Or that there are some defining features of good snow decks that are not universally shared by all of them - quite the opposite.

What are the compositions of these decks? How similar are the decks within each winning cluster? The good news is, they are quite similar. Each small cluster roughly represents a colour combination. By comparing the composition, we can convert meaningless blobs (Fig. 5 left) into something telling to Magic players (Fig. 5 right):

Fig. 5: Winning clusters (left panel), selected winning clusters based on their colour identity (right). The area of the plot is zoomed into the shaded area from Fig. 4.

As you can see, the winning decks divide into roughly 7 clusters, and these represent colour combinations of green, blue, red, and black. 5-colour decks occupy the space in the middle, 2-colour combinations are located on the peripheries of the graph with 3-colour decks in between. It looks that the snow decks, even though combining characteristics of multiple colours, come in several varieties and have accordingly adjusted plans. With that background, we can now dive into each cluster and briefly see what is going on in each of them. I will give you several statistics of each archetype and the most dominant cards in each cluster.



Most common cards

Cards present in 50% or more decks from the cluster in order from most to least popular; cards on the same line are equally popular

This archetype looks like a down-to-the-ground aggro deck with a slight twist. Instead of clunky 4 drops like the Craven Hulk, Spirit of the Aldergard lets you play Lindwurms and Hagi Mobs on curve. The 3-drop slot looks much better with a reliably activated Icehide Troll, mid game threat in Boreal Outrider, and a late game winner in Svella. Arni Slays the Troll is another key card. Again, a pattern of attacking with Icehide, pumping it and reusing its indestructability later to (oh the irony) slay the troll looks really strong. Concerning the Troll: RG doesn't ensure it will have enough mana to activate Icehide. If it happens, great if not, that's ok. The Troll is sort of a reward for putting this extra effort to get snow, not the reason in itself.

Unlike other snow decks, this one really wants to be 2-coloured. Only 18% of the decks had any splashes, choosing a streamlined RG plan over more durdly multicolour games. It also relied on many RG staples from the non-snow decks. Axgard Cavalry and Tuskeri Firewalker feel at home here, as are Sarulf's Packmates. Packmates are less abundant in the analysed decks, but that may be related to the need of picking snow lands and payoffs early.

This is also a great home for snow spells. Average of 1.5 snow spells per deck was achieved mainly thanks to Frost Bite, but Blizzard Brawl and Blessing of Frost also find a good home here.

In conclusion, successful Gruul snow builds take the traditional Gruul shell and build on it by incorporating snow synergies. The cost related to having to pick snow lands is compensated for by access to more cards that fit in the decks, some of them very powerful even with relatively low snow counts. The strength of this build is related to draft flexibility (Snow lands not available? Just revert to regular Gruul aggro) and to how the snow cards synergise well with the deck plan.



Most common cards

Successful Simic snow builds look very much like a midrange deck. Playing defensively early on, the deck aims to turn the corner in the midgame and annihilate the opponent. Early stabilising is achieved with Mistwalkers, Masked Vandals, Littjara Kinseekers, and Sarulf's Packmates as great defensive creatures aided by spells like Bind the Monster. But in the midgame it can start deploying Berg Strider, Icehide Troll, Moritte of the Frost, and Spirit of the Aldergard to turn the corner and quickly run away with the game.

The deck is different from Gruul in several aspects. Firstly, it splashes more readily. Over 85% of the decks from the cluster had a splash, mainly splashing red. This was normally a small splash of 1-2 cards (most commonly Svella, Narfi, and Squash). Second, it is heavier on snow. 1 extra permanent and land seems small but makes a big difference in what can be played reliably. Third, this is a deck that looks designed to go on the defensive from the first turn. Its 2-drops don't scream aggro: the commonly played creatures have higher toughness than power. It looks to clog the board and then win either in the air or using something like Icehide Troll, Frostpeak Yeti, or Avalanche Caller to force damage through (most decks from this category had at least one of those three).

Between Moritte and Littjara Mirrorlake, the deck has plenty of tools to copy one of your own creatures later in the game. This plays well with the Lindwurms, Berg Striders, and any other value creatures. It also can act as another quick finisher, Copying Yeti with Moritte is a very fast clock.

In conclusion, UG snow wants to clog the board early and win the game holding the fort while attacking with evasive threats. The decks splash frequently (in small quantities). They have a middle-heavy mana curve with many 4- and 5-drops. Card draw looks essential to avoid missing land drops and to be able to deploy the threats as early as possible.



Most common cards

The Golgari snow decks are surprisingly creature heavy. Surprising until you realise that they depend on Priest of the Haunted Edge as their prime source of removal. Priest wheels reliably and, therefore, you can count on having 2-3 of them in your deck. With some graveyard recursion (think returning 2 Priests with Raise the Draugr) it can take over the game, and since almost everything else in your deck is a creature, you have a good chance to win.

If the Priests are the early control package, big creatures ramped out with the help of Glittering Frost, Sculptor of Winter, and, to a lesser extent, Binding the Old Gods are the way of making sure they hit the board early enough to stabilise. Golgari works practically like a ramp deck, in a way similar to Simic, where you start on the defensive and with a plan to come back in the late game once you start dropping your Lindwurms and Outriders.

Since it needs quite some snow lands to make sure Priest works well, successful Golgari snow decks splash regularly. All the decks had a 1-2 card splash, mainly red. Most commonly a Svella, which fits perfectly to the ramp plan. Outside of Svella, splashes were more likely to be good rares (Immersturm Predator, Bloodsky Massacre) or uncommon value cards (Kardur's Vicious Return, Kardur himself) rather than removal spells or run-of-the-mill creatures.

Being relatively snow-heavy and midrange but still aggressively slanted, two cards that were common in the deck were Icehide Troll and Hailstorm Valkyrie. The latter one can be a potent threat but also works defensively against any skies deck. The 2 mana cost is offset by the ramp present in the deck, making the cards easy to use even early and making it possible to use multiple times later thanks to Binding, Glittering Frost, and Spirit of the Aldergard.

The deck uses "speed bump" cards to perfection. This is a great home for Elderfang Disciple. Nabbing a card from an opponent's hand, and then chumping to save 4-6 life is a great value in this particular build. To a lesser extent this deck also used Guardian Gladewalker. The 1/1 left behind was also a potential trap with Jarl of the Forsaken.

To conclude, Golgari is the ramp deck, using Priest to stop getting the damage and later eliminate most dangerous threats, ramping to large beasts who will finish the game. You survive till then by a combination of removal and speed bump utility creatures that can be chucked away, recouped, and reused.



Most common cards

Are you starting to get the idea Svella is good in the snow decks? This card seems to be the lynchpin of all red-containing snow decks. It is one of the very few cards that are an enabler and a reward in one, ramping snow mana early and using it later to generate value. Especially in eclectic, but potentially bomb filled multicolour snow decks this has to be a recipe for success. And same goes for successful Jund snow decks – almost all of them have Svella in. And in general, among the most common cards we see a whole lot of them present in the earlier archetypes. Troll, Sculptor, Spirit, Frost, and Lindwurm seem to form a core of good snow decks. Part of it must be because of the fact they are good cards. But part is related to their availability, more so if the archetype is open at the draft table. And I expect to see more decks drafted when it was right to draft snow among the successful decks.

With low competition for snow, you will be able to get at least 4 of those 5 cards reliably. Spirit (or Svella) on the other hand is trickier to get, and therefore, seeing it in so many decks is a much stronger signal that this card is actively good in snow. Not to say the other cards are not good; they still should contribute to the success of their decks. Not all snow cards are common in them: Grim Draugr is readily available, but it doesn't make the most common cards list, and most likely for a very good reason.

Good snow Jund decks are not really Jund to be fair. They are a slightly different, Black-leaning version of 5c snow, but it clusters separately and has a mana composition sufficiently different I decided to call it Jund. This deck is really heavy on snow lands. It's hard to say if the 5-colour nature of it is related to wanting more snow lands and ending with all colours or vice versa, drafting all colours was a plan from the beginning.

This deeper dive into a multicolour deck is most likely the reason why we see Horizon Seeker among the most prevalent cards in the archetype. The ability to kill a creature and draw a missing colour land or, in a perfect scenario, draw multiple lands is amazing for this archetype. One of the cards that are in multiple of those decks is Path to the World Tree, which is an okay turn 2 play, but you really want to have it online at some stage of the game to get the full value. The Jund decks also seem to be happy putting in bombs that are not necessarily on the plan but can be included. In a way it does look like a more durdly version of the Gruul deck with some snow payoffs and off-colour bombs put in instead of non-snow aggro cards.



Most common cards

Temur snow looks, again, surprisingly similar to previous archetypes. I was expecting more of a giants- and shapeshifters-themed pile; instead I can see a midrange deck using Gruul creatures for early and late game and some blue to keep the cards running and to help and turn a corner. Lots of blue was not sufficiently represented to be in over 50% of games, but Augury Raven, Berg Strider, Avalanche Caller, Frost Augur, and Littjara Kinseekers were just below the cut. This is also something we didn't see a lot in recent sets: blue is the colour that contributes creatures, not spells.

The most common card in this build is Glittering Frost. It seems a bit odd, but after giving it a thought, you have a tremendous draw power across Behold the Multiverse, Sarulf's Packmate, and cantrips, and lots of mana sinks: Svella, Icehide Troll among those and Path to the World Tree does both. Glittering Frost is a tempo loss but ensures you can dominate the mid to late stages of the game and makes sure you are never short on snow mana. Another card present in almost all snow decks is Masked Vandal. It seems like having one of those to deal with some annoying enchantment or killing a key equipment is really important for your chances of success. And early it is a very serviceable speed bump that lets you enter the late game with sufficient life.



Most common cards

Sultai, looking at the data, is a focused 3 colour deck. Not many splashes, unlike Jund and Temur. It uses an advantage it has over any other snow pile (barring 5 colours): being able to play Narfi. This is likely the impetus for playing Sultai snow: taking Narfi early and drafting around it. And you can see it in the builds. Glittering Frost lets you play Narfi (and Berg Strider) on turn 4 and then reliably reanimate it if it dies. Pilfering Hawk lets you put Narfi to play early and get a card advantage by discarding it to the ability. All the commonly used creatures get the bonus from Narfi making them significantly better. A 2/5 Mistwalker is way better than a 1/4 one and even the 2/3 Hawk is surprisingly annoying. It even uses the 3/3 Draugr Recruiter more frequently than any other snow deck.

Aside from Narfi being the centrepiece of the deck, Sultai is a controlling deck but still relies on creatures more than on spells, for a good reason. Spells in KHM are not that great. And snow creatures like Priest or Berg Strider promote your control plan well. That is why Blessing of Frost pops out as a common spell: unlike some creatureless control decks, you can use it to the fullest and draw several cards. But there is space for some spells as well. Ravenform and Disdainful Stroke are good insurance policies against larger threats that Narfi can't take care of. Bind the Monster can take care of early threats before they limit your possibilities. This is also a natural home for Icebind Pillar. The deck is pretty heavy on the blue cards and black is used as a support colour in most cases.



Most common cards

Perhaps unsurprisingly, the core of 5-colour snow is designed to make you survive until the late game. Glittering Frost, Path, Binding, Horizon Seeker, Packmate, and Svella make sure you don't miss your land drops and fix your mana, with the latter three also ensuring you can survive the early onslaught. Frost Bite, Priest and Demon Bolt take care of early threats. There is no dominating late game finisher, and for a good reason. With 5C you are not limited in any way on what to use to kill your opponent. You can pick one of the many bombs from any colour combination to win, and if not you can lean on the trusty Lindwurm. 5C decks had finishers ranging from Vorinclex through Cinderheart Giant up to Kaya. It seems to matter little as long as you have something for the late game. And even if not, a couple of Icehide Trolls would do the job just fine. The secret is to focus on cards that let you survive, and then your superior late game should be more than enough to do the trick.

This seems to be an overarching theme of the snow archetype that emerges from the data we analysed. The decks, even though different from each other, have a large overlap. Except for a more aggro tinted Gruul variant, most of the successful snow builds focus on early development and survival, and then start generating card advantage with the most powerful stuff available. Cards that can be seen over and over again are Svella, Glittering Frost and Icehide Troll. Any black version leans hard on Priest of the Haunted Edge. Not only because the card is good, but also because it is so easy to get in a draft while fitting your plan.

Individual Cards

Apart from looking at decks and their relatedness, I also looked at individual cards and their general performance in snow decks. Busted rares aside, the cards with highest win rates when drawn in snow decks were Arni Slays the Troll, Basalt Ravager, Squash, Frostpyre Arcanist and Dwarven Reinforcements. All those cards are not played in snow universally, which is logical: cards played in almost every deck will have a win rate close to the average win rate, so you should treat this data with a grain of salt. It most likely is a proxy of the fact that the Gruul version of snow looks like the most powerful one.

There are some cards that increase your win rate when drawn (during game or opening hand) as opposed to when you don't draw them, which is a slightly stronger signal that a card is good. Some examples of those are Frostpyre Arcanist, which increases your win rate when drawn by as much as 7 percentage points. This card is busted when you have reliable targets to draw an extra spell and should be speculated on more often it seems. Another card that increases your win rate is Runed Crown (5 percentage points) which is a credible way to close the game or stabilise it when you pick some runes during draft. The best rune for the deck seems to be the Rune of Might (also increases win rate when drawn by 5 percentage points), with trample playing really well with cards like Spirit of the Aldergard and Lindwurm. The last card to showcase is Bind the Monster, which may be undervalued at the moment. It increases the win rate when drawn by over 2 percentage points, being most likely a very good alternative to Frost Bite for early game removal.

Snow looks very interesting and has infinite capabilities to build a deck around it. I really hope that this analysis sheds at least some light on the subtle but key differences between some of the successful snow builds, but more importantly I really hope it shows that the similarities across the archetypes are equally important and highlight crucial cards responsible for winning strategy: cards that stabilise the game. Snow is at its weakest in the early stages of the game and the data clearly suggests that removing that problem is the key to winning and trophying. The late game threats are secondary to the early plays and you should draft prioritising early stabilisers, speed bumps and lands rather than focusing on late game drops. Svella and Narfi seem like great snow payoffs but, looking at their individual win rates, are not good just in any build. They definitely make the good builds win more reliably though. Once you pick one of those cards you can use this analysis to set your pick priorities and hopefully increase your win rate. This analysis is by no means complete (I didn't look at unsuccessful builds for example) but I hope we can use a similar analytic strategy in the future to dig deeper in more narrow archetypes to see what makes them tick. Rest assured, if you follow 17Lands, you will know when it happens.

Methods note:

The data was taken from 17lands.com. The dataset was extracted on the 9th of February, so do not be surprised if it is not exactly the same as the current one. To analyse the snow decks, I used a Bray Curtis dissimilarity, first described in "An ordination of upland forest communities of southern Wisconsin." in 1957. I mean come on Bray and Curtis, why not Highland Forest to make my KHM land analogies better? Was that too hard? Would swapping Up with High kill you? Anyway, this is a weighted measure, so it cares not only about what cards are in the deck but also in which quantities (so decks with 1 and 9 Forests are not treated the same like in an unweighted metric that cares only about presence/absence of a card). The choice of weighted metric will result in better clustering of decks based on colours in those decks; this is something I chose on purpose, but in the future I am planning to compare clustering using unweighted metric to see if it leads to large differences. The dissimilarity matrix was converted to a 2-dimensional plot using Nonmetric MultiDimensonal Scaling (NMDS). Since this is a trial analysis I clustered the decks based on their proximity on the 2D graph rather than on the dissimilarity matrix, a choice based on how legible the plots would be to an average reader. In the future I will look at the dissimilarity matrices as the background for the analysis. The distances were calculated using the Pythagorean theorem, based on the distances on the X and Y axes on the plot. Just because I wanted to be able to tell in a future discussion that I actually used it in practice so school was not a complete waste of time.

As always this analysis is only possible thanks to dedication of the 17Lands team. Thanks guys, you are relentless and deserve all the credit for all the amazing things you do. Thanks to Hululu, Viralmisnomer and Grantwu for all the suggestions and corrections and to SLKerstens for comments on the article that helped clarify it.