Wednesday, 23 November 2016

Land Ratios

In cube decks, especially those in the midrange drafting cube, I almost always pack 16 or 17 lands. I play a 41 card deck more often than I step outside those land counts(and hopefully if you make it at least some way through this epic you will understand why I go 41 cards so much). Typically my RDW, Rock and white weenie lists are 16 lands while my Zoo and Control decks are 17. There are of course exceptions and the more exotic the cube format the more extreme it can get. I have had a no land Belcher deck with I think 3 lands and my all land Seismic Swans deck at about 31/40 lands. When you have Mox and things you can drop lower and so a 14 or 15 land aggressive deck is not at all uncommon, particularly in the powered cube. There is a lot going on in working out mana bases and the cube is of course one of the most involved. Despite this, the frequency with which I find myself packing either 16 or 17 lands is surprisingly high (95%+).

There are two things I have noticed about cube mana bases compared to other formats that felt like it needed further investigation. The first is that there appears to be a smaller range, or a narrower bell curve if you will, for cube decks land ratios than other magic formats. Further to this, on the whole, cube decks tend to play more lands than constructed versions of those archetypes. Take my 16 land RDW list and compare it to a modern burn deck which has 20 lands and a lot more of those that thin the deck of lands. The modern burn decks are at most 33.3% land while a cube version is more like 40% land. Aggressive cube decks typically play significantly more lands than modern constructed counterparts. Cube control decks play slightly more lands than constructed modern counterparts. It is not until you look at some standard decks and limited decks that you find higher land ratios than cube decks. Some limited decks want up to 18/40 lands in them and I have seen loads of standard decks with 27/60 lands. What factors are accounting for this low range of high land ratios in cube decks? Why do both aggressive and control decks play such comparable land counts in cube yet not in other formats?

Obviously this is not even close to a simple answer or even just one answer but I shall do my best to shed light on these factors. One of the more general factors is the stability of a 60 card deck relative to a 40 card one. This stability of which I speak is a mixed blessing. Every card carriers more weight in terms of ratios in a 40 card deck than does one in a 60 card deck. This is significant in how you build the thing but it also has an impact on how it plays. Getting the ratio right to start with is harder with 40 cards as you have less fine tuning capability. When it comes to playing however the instability of the deck plays a significant part in smoothing your draw.

Let us compare two decks with an identical land ratio. A 16 lands out of 40 cube deck and a comparable constructed archetype with 24 lands in 60 cards. Both have exactly 40% lands. Now, let us consider some opening hands that are classically close mulligan calls just because of the ratios you have. A two land hand or a five land hand. In both cases the cube deck is far better positioned to be able to keep the hand compared to the constructed deck and here is some basic maths to demonstrate why!

In the 2 land hands the constructed deck now has a library with 22/53 (41.5%) lands while my cube deck is 14/33 (42.4%). As you can see, the chance of either deck drawing a land is increased but it is more noticeable for the cube deck. The same kind of thing happens for the flood simulations. With 5 lands in hand the constructed deck now has a 19/53 (35.8%) lands in library while the cube deck has 11/33 (33.3%) lands in the deck. Now both decks have a lower chance to draw a land but again, it is more pronounced in the cube deck. Essentially your deck has a negative feedback mechanism in play that helps correct for your previous draws where expected ratios have not occurred. This mechanism is stronger in 40 card decks than in 60 card ones. What might seem like an equally big risk in either format is generally less of a risk in cube.

A difference of three lands in hand for the 60 card deck has a range of 5.7% on how it affects your decks land ratios while the cube deck has a 9.1% range in that same scenario. A constructed deck is stable in that the expectation on your draws changes somewhat less with every draw. Stable is perhaps a bad word in hindsight as a significant result of its affect is that extreme screws and floods occur with greater frequency in 60 card decks than 40 card ones. I have seen so many constructed games lost where people see like ten lands in thirteen or fourteen cards, or just two lands, and the game is over. Flood and screw still occurs in cube but no where near that level.

Now, you may ask, why, if there is less risk with screw and flood in a 40 card deck do you not play fewer lands rather than the more lands we tend to see? That is somewhat the wrong question to ask. All my previous maths was based on the assumption that a 40% starting land count was correct for both decks. The feedback mechanism works towards your starting % not your ideal %, if you missbuild your deck and mana base then the feedback mechanism will mostly work against you. Greater instability in the 40 card deck makes it much more important to have exactly the right land count for your deck. With a greater feedback mechanism forcing your draw towards your starting build's ratios you cannot afford the luxury of playing too few or too many lands. You will more consistently flood with too many lands and screw with too few. Sixty card constructed decks can hedge on various things and are able to employ a higher variance in their initial build land ratios in order to do so.

The question should be, why do constructed decks typically hedge on fewer lands than perhaps they should if they were trying to optimise a goldfish timing. That is basically your answer right there. Real games are interactive and resources are consumed in some attrition. When nothing goes to waste you want exactly the right amount of lands in the shortest time span. The more waste you get the fewer lands you want relative to this perfect start. If you are just looking at goldfish stats then you will think you want way more land than you really do. A goldfish game is super short, you may only see 12 or so cards. Even for an aggressive deck you are absolutely going to want at least 3 lands in those 12 cards and that means you want a very high percentage of lands in your deck. If the games go on longer however you really don't need much more land than the ones you need on your early turns and so the key to working out the mana ratios for a constructed deck is to know how long the average game with the affects of attrition will be, or at least the average length of games you win!  This length will always be longer than the goldfish number and it will significantly reduce your ideal land count. Now, interaction happens just as much in cube as it does in other formats on the whole. For the most part your deck will not be goldfishing against people. I have gone some way to explaining why 40 card decks sensibly have a narrower range of land counts than 60 card decks but I have not done much to explain why cube decks typically have higher land ratios than other comparable decks.

Most of the reasoning from here on in is more down to the kinds of cards used and archetypes in play as to why land rations are not as you might expect them to be as you change from format to format.
Lands have pretty high diminishing returns in most constructed decks and formats. You are typically better off having enough to get started, using mulligans intentionally to help with that, and risk having too few than having more than you need from the outset. Hedging on fewer lands, especially with the option on mulligans greatly increases the late game potential of contstructed decks, particularly aggressive ones and those with a low CMC cap (noting in the modern burn deck costs more than two mana and so the deck can chug along with just two lands and be fine).

Cube decks are generally more powerful than modern decks in that they have more synergy and more powerful cards. This description of cube decks is rather misleading however. A modern deck is far more consistent and direct. Modern decks do their thing and they do it quickly and consistently. Sure, the individual cards may not be quite as powerful as the cube ones but having the redundancy is massive. If you could play a 15 card cube burn deck then it would be more direct and more consistent than the modern one but at 40 cards it feels incredibly midrange by comparison. The very best cube aggressive cube decks have roughly 12 one drops, 8 two drops and 4 three drops. If you compare that to modern burn decks their curve is lower at 24 one drops and 16 two drops. The average CMC of the cube list is at best 1.67 mana per spell while the modern list is 1.3 mana. A 20% price hike is very significant and in typically the case with cube decks and is a significant reason why cube decks play a slightly higher land count than constructed decks. Constructed decks basically play 4 of all the one drops that cube can only play 1 copy of and this gives them lower curves which need fewer lands. This is why we find standard and limited decks with the only higher land counts. They are the only formats that have higher mana curves. The actual power of the cards is pretty irrelevant, it is all just the CMC of them that dictates your mana. It might sounds really obvious to some but for some reason this wasn't immediately apparent to me. I kind of just assumed that increasing power equated to reducing the need of lands. The actual thing going on is that by increasing the power you typically speed up formats and naturally only the cheaper cards remain viable. More powerful formats also have deeper card pools from which there are more options on good cheap cards. Essentially powerful formats have decks with lower average CMCs than less powerful formats. You would think that powerful formats inherently play fewer lands but if and when they do the power of the cards is nothing to do with it. It is what they are doing rather than how well they do it that can give rise to unexpected land counts.

Cube is certainly very powerful but it is limited in a very different way to other formats. Having only one copy of a card means that there is significantly less scope in what you can find to pad out the low curve parts of your deck. There is precious little premium stuff and barely even enough playable cheap stuff to be able to mimic the constructed decks. Constructed burn can play 4 Guides, 4 Bolts and 4 Swiftspear, that is 20% of the deck full of cheap premium cards while a cube deck with all those isn't even at 10%. It is either playing garbage like Jackal Pup to make up the low curve numbers or, more sensibly it is playing Sulphuric Vortex or Fiery Confluence instead. A much more powerful card that is also much more CMC. Cube decks will still typically play a tier of one and two drop cards under that which is considered playable in powerful constructed formats but they don't stoop any lower, instead they use more powerful and more expensive stuff to give the best balance of speed and power that they can with the available tools. All this is to say that yes, generally a cube deck has more powerful cards than a modern deck, and may well be "more powerful" however you would measure that. Despite this the cube decks almost always have higher average CMC in their spells and more things to use mana on. This is the main reason you see a higher % of lands in cube decks than modern ones. Standard and limited are the only formats with card pools small enough that you see them having higher average CMCs than cube decks and hence higher land ratios.

Cube mana bases and decks typically suffer far less diminishing returns than most other formats. Being direct and pure like modern burn is great for playing very few lands but it does leave you with lots of weaknesses. Cube decks tend to be far more rounded, they are forced into just playing some good cards that fit and these cards offer a wide range of utility to archetypes that don't have that sort of thing at all in constructed formats. Mana sinks like Kargan Dragon Lord, card quality like Faithless Looting, lands with utility like Barbarian Ring and Mishra's Factory and many more like them mean that aggressive cube red decks are not just wasting a draw when they see their 4th and later lands. Your higher curve means you want more and your better late game means you don't need to hedge and play fewer than you should.

Almost every cube archetype has these useful lands and ways to put excess or dead cards to some other practical use, not just the red deck as used in the example. Most in fact have far more access to such things than the red deck. Cube decks are happier to continue drawing lands for a little longer than comparable constructed versions. Card quality is another huge thing in cube and there is way more of it in cube than most other magic formats and most importantly, it scales far more effectively in 40 card formats than any other. A scry is arguably 50% more powerful in a 40 card deck than it is in a 60 card one, perhaps more once you take cards already drawn into account. Essentially they just see a much higher proportion of your library and thus offer much more returns for their mana. This is again a little misleading as seeing a higher percentage of your library is only better if that library contains the same percentage of things. A constructed deck will typically have four of each of the cards it needs. Beyond the simple land or not land aspect of card quality the effect it has on a non-singleton deck is more reliable. You need a Bolt or a Path, your Preordain is more likely to hit in your 60 card modern deck than a cube one both containing the maximum possible count for those cards. Card quality in cube typically gives you more options than in constructed and it is more potent at handling screw or flood. On the flip side, it is much more important to be able to get the cards you need with your card quality in cube than it is to sort out your mana base. You feel a little behind if you basically just use your Preordain to hit a land drop. Card quality may be more powerful in cube but it is that much more important not to be using it just to hit your land drops. Those things are best used in cube for helping with the your inconsistent spells rather than your relatively consistent (compared to constructed) lands.

So, in somewhat of a conclusion; cube decks generally have higher average CMC in their spells that their constructed counterpart archetypes. They also typically have better mana sinks both of which lead to wanting higher starting land counts on average and being happier to draw more total lands as the game progresses. The strong feedback mechanism towards initial ratios of the 40 card deck combined with a strong desire to use card quality on spells rather than lands in a singleton format leads to a narrower range of land ratios on the whole in cube decks. It is also noteworthy that the shift in average spell CMC moves less in cube when you move from aggro to midrange and then to control than it does in modern. Ramp cards have way more of an impact on the decks spell CMC than what it is trying to do. With less of a shift in CMC the less you need to add more lands and this helps to keep the range of cube mana ratios narrow.  (Control) Decks that want to cap out at higher land counts generally play more in the way of raw card draw to achieve this if they are not green and playing cards specifically to do this for them asap!

Having started down this epic rabbit hole there is one last little place I want to have a look as it was what got me thinking about this topic in the first place. I recently did an affinity archetype breakdown in which I gave a load of advice and examples on how to build the deck. I was painfully aware however that I was advocating a significantly higher land count than ones finds in constructed versions of the deck. Robots in modern has 16/60 lands which is the terrifying equivalent of 10 and 2/3rds land in a 40 card deck. I don't pack loads in my affinity decks but it is usually 13 or 14 which is still vastly more than it should be if I was taking the modern list as a guide. It is the biggest discrepancy of all the archetype comparisons for land ratios. All of the more general things I talked about in this essay apply to cube affinity when compared to modern robots. It has a slightly higher CMC, it has more mana sinks and more uses for lands late game. Further to this modern affinity has 8 Mox Opal and Springleaf Drum with 7 zero mana dorks to go with them compared to the 2 and 2 that cube can offer. Sure, you can throw in a Chrome or Diamond, perhaps you can get a Frogmite out on turn one in cube but all that jazz doesn't equate to the same kinds of consistency or redundancy. You can probably consider those cards to be worth about seven lands in the modern list while they are not that much more than one in the cube deck. The cube version also has more utility from its lands in that more of them are artifact lands and they have some ramping lands that modern doesn't. Experience taught me that 13 or 14 lands in an unpowered affinity cube deck is about right but evidence from modern lists suggested otherwise. I had to spend ages working through all this to be happy going against the sage wisdom of the robot loving pros. Only with all these many subtle factors on top of the more obvious Opal/Drum count does the difference in land counts seem reasonable.

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