Correct. But since this is a singleton format, the more conservative assumption is that you have a single double-cost spell that you assign a "turn priority" to. So, in almost every cube case (certainly in the average cube case), I'd be looking for 13 sources and not 12. The cube doesn't have a high enough density of double-cost 2cc cards in a single color to change the numbers on the chart from needing more to needing less. Not to mention that some of them would be prioritized differently than one another (like I mentioned in the article, something like Hymn to Tourach I'd be willing to run with only 10 sources because it's still a really powerful spell even on turn 4, whereas Sinkhole is a card I want to play on T2, so I'd be looking for 13 sources).
But again, remember than I was trying to create the most demanding of predictable situations, which in this case would be a single double-color spell I'm trying to cast, and on the play.
Thanks for pointing out that math though; it's certainly interesting.
But if I determine that I need 2 sources of white by T4 on the play (for the 2WW card in that example) the source value is still 10. If I decided I was comfortable playing that spell on T5, I could drop it to 9 sources.
If Wrath of God is my only double-white card in my deck, I want to be able to generate a conservative value for the number of sources I would need to have in order to have double-white on T4. On the play. And that's exactly what those values give me.
I'm comfortable with the values in the chart giving me the most conservative values they can, even if it means assuming they're the only color-demanding spell in a given color.
..........
What it boils down to is this: There's a myriad of things that influence how many sources of a given color you might want to run, like redundancy at that cmc, mulligans, being on the draw, draw/filter/fetch plays ahead of the cmc of the card in question, density of equal color-demand cards, etc. Each of those will raise and lower the source value when you change those factors. This article is a guide, not the end-all of source calculating. I don't think there is a single value you can come up with that can factor in all the potential influences on your mana-demand. I understand there are flaws, but again, nothing is perfect.
Really interesting article. I'm glad I got an opportunity to read it. I think it's a great presentation of initial research. There are some problems and some holes that should be addressed before I'd call it a presentable final product though. It doesn't really provide enough thorough information to draw solid conclusions from just yet. As it stands it shows an area in need of more research to fully understand.
Before we talk about determining how many sources of each color are required, have you ever calculated how difficult it might be simply to curve out? Take a look at this table and see how many sources your deck might need
You are only talking about casting a single card on curve. If you want to really curve out (as in casting a 1,2,3,4 drop in consecutive turns) adding more than 17 lands is actually worse.
This is the biggest issue for me that needs to be included. It gets really interesting when you consider how color splits might correlate with optimal curves for the different theatres.
What it boils down to is this: There's a myriad of things that influence how many sources of a given color you might want to run, like redundancy at that cmc, mulligans, being on the draw, draw/filter/fetch plays ahead of the cmc of the card in question, density of equal color-demand cards, etc. Each of those will raise and lower the source value when you change those factors. This article is a guide, not the end-all of source calculating. I don't think there is a single value you can come up with that can factor in all the potential influences on your mana-demand. I understand there are flaws, but again, nothing is perfect.
The issue is really big and really complex, but it can be understood, at least well enough to draw some general guidelines for optimal mana base construction. I would suggest a revision that avoids the temptation to make conclusions just yet . . . unless the conclusion is that more research needs to be done. In fact, I would seriously consider removing anything that calls up interpretations of the data. There is nothing wrong with presenting your data as just that, interesting data in an area that clearly needs more research. What you have there is data that suggests mana requirements for color restrictive cards may be more prohibitive to being cast than we commonly think. At the moment, there isn't enough information to make it a reliable guide . . . yet.
I really hope you continue looking into this, and don't get discouraged by the complexity. Maybe team up with eidolon and some others on the boards that like this kind of research to co-author a series of articles looking into it. I wish I had more time available to join in because I'd love to. In the mean time, I hope you don't let this topic go where it's at because there is more to be learned.
Basically, there's too many variables to present data that's both readable and all-inclusive. What if I mulligan? What if I mulligan to 4? What if my deck is 12 Plains as 28 Soltari Priests? What if my deck has nothing but cards of the same converted mana cost? What if my deck is full of fetchlands? Or draw spells? Or looters? What about casting the spells AND considering mana demand? Overall sources and color-demand sources together? There is no one value or one table of values that covers all those options, so I opted to keep the information direct and simple. If you consider it unpresentable as a product because of that, that's you're prerogative, I suppose. But I think it presented the information I wanted it to present, and explained what you were looking at and how to use the information relatively well.
Can the information go deeper? Absolutely. And I'd be interested in reading those findings if someone wants to present them in their own way. But doing so would escape the scope of this article and the information I set out to share. Thanks for commenting, Theogony_IX.
You know what, man? A lot of those variables can be discarded as noise. If you want to make a really sweet basic guideline, only a few more things need to be taken into account:
-Optimal mana source counts for curving out. Use actual deck samples to set an average curve for each theatre, i.e. an aggro deck with no 4 drops, an aggro deck with 2 four drops, a midrange deck with 3 five drops, a control deck with 2 six drops, or whatever it comes out to be. This should show how the probability to actually hit your curve changes with differing land counts. It would probably create nice little bell curves.
-Mana base color splits for each theatre using the data generated from the optimal mana source counts for curve. Using the curves from the previous study as a baseline, the numbers will more accurately reflect what you want your deck to look like and thus your color splits. With this you aren't suggesting land counts but are instead suggesting color proportions and showing cost benefit analysis of more land to less land when it comes to actually being able to cast your color intensive spells. Is it worth risking the flood in my midrange deck to fit an 18th - 19th land just so I can be closer to reliably casting that secondary color 2XX card.
-Splashing a third color. A bit of a subsection on the above study but with enough variables to warrant its own section.
-Lastly, and this is more an addendum than a complete section, but look at how the option to mulligan affects your numbers. Do they reduce the strictness of the numbers found previously? Do they change the numbers at all and by how much if they do change?
Now, given any theatre of deck, I know my optimal land count based on my curve, and I know my optimal color split within the boundaries of that land count and just how greedy I'm being with my color intensive spells. Boom! guideline study complete. Make conclusions regarding deck construction and extrapolate for cube composition to provide players with enough fixing. Solid reference guide.
I wasn't kidding when I said I'd love to get down on that kind of study. Give me a couple months and I'll be able to, but if it's really not something you want to do then cool, I get it. The point you wanted to make was made. We could drop some knowledge though, and your experience with the game would be invaluable.
I would gladly be a part of another article that wants to further explore more of the variables involved with mana base construction. I was simply pointing out that it was a bit away from the scope of this article. Again, thanks for the feedback.
I remember calculating this for the case of CC and 1CC cards after I noticed how difficult it can be to reliably cast the likes of the Clique/Sower combinations. The numbers are indeed pretty shocking. This article confirms that for the large part and demonstrates the difficulty of playing the CCC cards in anything but mono-black. I have ended up having to cut most of the CCC cards - particularly the cheap ones - just because of the way we draft. Even the CC cards have to be watched very carefully, and I think that is particularly true for cube construction as much as deck construction. I think the threshold for inclusion for something that costs CC needs to be much higher than something costing 1C. Particularly as many of the aforementioned CC and CCC cards want to be cast on curve - which is often impossible in a 2/3 colour deck. I'm glad you raised that last point, as something like a Garruk, Primal Hunter a) costs more, giving you time to get the right sources, b) doesn't require casting on curve to the same degree as a Soltari Priest, and c) is in the best fixing colour to get you there. The article has made me look again at Cryptic Command, whose days may be numbered.
One last mitigating factor for making those decisions, alongside the quality of mana rocks, ramp and fixing, is filtering and cheap draw. Having a couple of Brainstorm, Top, Recall or Ponder effects available increases the likelihood of seeing both source types and hitting land drops on curve.
Pruning heavily the CC cards was one of the best design decisions we made for our cube, and the next goal is reducing the 1CC options and introducing the much more splashable 2C ones. At the moment that's very difficult indeed so it's a long-term goal. Like wtwlf, I'm a reasonably conservative builder but sometimes can't resist a greedy splash here and there.
I love the math and probability of Magic. Thanks for a great read. I will say it took me a few read-throughs to understand what the charts meant. Maybe an example of a one drop with the one drop chart, step by step, turn by turn-similar to the Hymn to Tourach two drop example would help clarify things. Until I got to the two drop example, I really didn't understand the charts. Maybe it's my reading comprehension, who knows.
Again, thanks for the work involved.
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Thnks for the reply and the feedback. Ya, there definitely could've been some more clarifications, but I added the extra boxes to the sections to help clarify. Sorry it was still a bit confusing. PM me if you have any other detailed questions and I'll try and help make things clearer.
Just discovering this article now, great work man! Really like your writing style, to the point and easy to read. Opposite of mine lol.
We mostly do team drafts around here, and when building decks I'd say I'm definitely among the most vocal about conservative mana bases. I'm glad your work helps support my hypotheses that people underestimate mana requirements of XX cards
Thanks bud. Ya, it's also part of the reason why I consider filter lands a trap in the cube too. In constructed, using Filters to hit your XX cost cards is pretty easy and pretty consistent. But in the cube with 1 lone filter floating around in the deck, it won't be able to help make your mana more consistent for those XX cards, and trying to build easier mana demand is the better solution.
Question regarding fixing: if all I'm concerned about is fixing for stuff that require two sources in two colour decks (ie. curving from Sulfuric Vortex to Braids or from Brimaz to Hero of Oxid Ridge), would the filter lands be better than pain lands? It just looks that way to me, but I'm not good in maths.
The point is to design decks that function without needing Filter Lands, not playing decks that fail to cast their spells without them.
And even so, probably not, because you need to hit your 7/8 sources of your secondary color for available T1 mana, so the Painlands are still more important to the early game in decks that aren't so greedy they need Filters to function.
A filter can help you curve from T3 Brimaz to T4 Oxid Ridge, but the more important thing is to go from your T1 Lions to your T2 Berserker, and Painlands help you accomplish this. I'd rather just drop one of the more color demanding cards for something that's easier to cast and have more consistent early game mana--particularly in a Boros aggro deck.
I find having 9-10 sources fairly easy to do. Literally almost all our 2 colour decks have 9-11 sources for each. It's hitting 12 consistently that becomes an issue for us though.
Right. So a deck with a Brimaz and a Jackal Pup needs to build a 12/8 manabase, which is hard enough. Especially since a Filter won't count as an 8 for your T1 red mana. So trying to build a 12/10 manabase is really hard. A filter might help the top of the curve, but building the bottom baseline is hard enough as it is.
I haven't noticed any problems with missing first turn drops really (even if you whiff on the Pup, if you're playing a Brimaz you have multiple white 1-drops in the deck too). I mean, it does happen on occasion, but not often enough for me to be concerned. What does come up is not getting that second mountain by T3/4. Now I get the exercise discipline and build more consistent decks thing, but I'm going to want to run that Vortex no matter how much discipline I have. And it's that particular part of the curve that I've noticed the problem: going from 1X to 1YY to 2XX.
1 random fixing land in the deck isn't going to increase the consistency of that particular play in a significant way. What will help, is limiting your higher end double-colored cards. Of course there are going to be occasions where you'll be running 1XX and 2YY cards, but keep them to a minimum to ease the burden on your manabase.
I've found that a filter land in my opening hand interferes with my T1 play more often than having a pain land in play interferes with my 3-4cc plays. And as I said above, the math for needing that T1 mana for your secondary color is usually much harder to hit.
I guess the analysis here already answers the gold card issue.
If you wanto to cast Putrid Leech on T2,
you need one black source and one green source.
The table tells you that a 7/7 split is fine,
this is much easier than casting Strangleroot Geist.
Correct, it is easier to cast a Putrid Leech in a 2-color aggro deck than it is to cast a Strangleroot Geist. But exactly how much easier wasn't part of the calculations for this article.
Like many have commented, I found CC creatures too hard to cast for aggro and cut them all.
But I am curious what you think about hybrid one-drops. They may help you plan your game better
so you can cast the 1CC, which are very powerfull (Brimaz, Vortex).
We run Judge's Familiar, Rakdos Cackler, Figure of Destiny, Tattermunge Maniac and Dryad Militant.
But again, remember than I was trying to create the most demanding of predictable situations, which in this case would be a single double-color spell I'm trying to cast, and on the play.
Thanks for pointing out that math though; it's certainly interesting.
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If Wrath of God is my only double-white card in my deck, I want to be able to generate a conservative value for the number of sources I would need to have in order to have double-white on T4. On the play. And that's exactly what those values give me.
I'm comfortable with the values in the chart giving me the most conservative values they can, even if it means assuming they're the only color-demanding spell in a given color.
..........
What it boils down to is this: There's a myriad of things that influence how many sources of a given color you might want to run, like redundancy at that cmc, mulligans, being on the draw, draw/filter/fetch plays ahead of the cmc of the card in question, density of equal color-demand cards, etc. Each of those will raise and lower the source value when you change those factors. This article is a guide, not the end-all of source calculating. I don't think there is a single value you can come up with that can factor in all the potential influences on your mana-demand. I understand there are flaws, but again, nothing is perfect.
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This is the biggest issue for me that needs to be included. It gets really interesting when you consider how color splits might correlate with optimal curves for the different theatres.
The issue is really big and really complex, but it can be understood, at least well enough to draw some general guidelines for optimal mana base construction. I would suggest a revision that avoids the temptation to make conclusions just yet . . . unless the conclusion is that more research needs to be done. In fact, I would seriously consider removing anything that calls up interpretations of the data. There is nothing wrong with presenting your data as just that, interesting data in an area that clearly needs more research. What you have there is data that suggests mana requirements for color restrictive cards may be more prohibitive to being cast than we commonly think. At the moment, there isn't enough information to make it a reliable guide . . . yet.
I really hope you continue looking into this, and don't get discouraged by the complexity. Maybe team up with eidolon and some others on the boards that like this kind of research to co-author a series of articles looking into it. I wish I had more time available to join in because I'd love to. In the mean time, I hope you don't let this topic go where it's at because there is more to be learned.
Thank you for the read. I enjoyed it.
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Can the information go deeper? Absolutely. And I'd be interested in reading those findings if someone wants to present them in their own way. But doing so would escape the scope of this article and the information I set out to share. Thanks for commenting, Theogony_IX.
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-Optimal mana source counts for curving out. Use actual deck samples to set an average curve for each theatre, i.e. an aggro deck with no 4 drops, an aggro deck with 2 four drops, a midrange deck with 3 five drops, a control deck with 2 six drops, or whatever it comes out to be. This should show how the probability to actually hit your curve changes with differing land counts. It would probably create nice little bell curves.
-Mana base color splits for each theatre using the data generated from the optimal mana source counts for curve. Using the curves from the previous study as a baseline, the numbers will more accurately reflect what you want your deck to look like and thus your color splits. With this you aren't suggesting land counts but are instead suggesting color proportions and showing cost benefit analysis of more land to less land when it comes to actually being able to cast your color intensive spells. Is it worth risking the flood in my midrange deck to fit an 18th - 19th land just so I can be closer to reliably casting that secondary color 2XX card.
-Splashing a third color. A bit of a subsection on the above study but with enough variables to warrant its own section.
-Lastly, and this is more an addendum than a complete section, but look at how the option to mulligan affects your numbers. Do they reduce the strictness of the numbers found previously? Do they change the numbers at all and by how much if they do change?
Now, given any theatre of deck, I know my optimal land count based on my curve, and I know my optimal color split within the boundaries of that land count and just how greedy I'm being with my color intensive spells. Boom! guideline study complete. Make conclusions regarding deck construction and extrapolate for cube composition to provide players with enough fixing. Solid reference guide.
I wasn't kidding when I said I'd love to get down on that kind of study. Give me a couple months and I'll be able to, but if it's really not something you want to do then cool, I get it. The point you wanted to make was made. We could drop some knowledge though, and your experience with the game would be invaluable.
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I remember calculating this for the case of CC and 1CC cards after I noticed how difficult it can be to reliably cast the likes of the Clique/Sower combinations. The numbers are indeed pretty shocking. This article confirms that for the large part and demonstrates the difficulty of playing the CCC cards in anything but mono-black. I have ended up having to cut most of the CCC cards - particularly the cheap ones - just because of the way we draft. Even the CC cards have to be watched very carefully, and I think that is particularly true for cube construction as much as deck construction. I think the threshold for inclusion for something that costs CC needs to be much higher than something costing 1C. Particularly as many of the aforementioned CC and CCC cards want to be cast on curve - which is often impossible in a 2/3 colour deck. I'm glad you raised that last point, as something like a Garruk, Primal Hunter a) costs more, giving you time to get the right sources, b) doesn't require casting on curve to the same degree as a Soltari Priest, and c) is in the best fixing colour to get you there. The article has made me look again at Cryptic Command, whose days may be numbered.
One last mitigating factor for making those decisions, alongside the quality of mana rocks, ramp and fixing, is filtering and cheap draw. Having a couple of Brainstorm, Top, Recall or Ponder effects available increases the likelihood of seeing both source types and hitting land drops on curve.
Pruning heavily the CC cards was one of the best design decisions we made for our cube, and the next goal is reducing the 1CC options and introducing the much more splashable 2C ones. At the moment that's very difficult indeed so it's a long-term goal. Like wtwlf, I'm a reasonably conservative builder but sometimes can't resist a greedy splash here and there.
On spoiled card wishlisting and 'should-have-had'-isms:
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Again, thanks for the work involved.
Cheers, and happy cubing!
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We mostly do team drafts around here, and when building decks I'd say I'm definitely among the most vocal about conservative mana bases. I'm glad your work helps support my hypotheses that people underestimate mana requirements of XX cards
Part of the reason I love filter lands so much
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And even so, probably not, because you need to hit your 7/8 sources of your secondary color for available T1 mana, so the Painlands are still more important to the early game in decks that aren't so greedy they need Filters to function.
A filter can help you curve from T3 Brimaz to T4 Oxid Ridge, but the more important thing is to go from your T1 Lions to your T2 Berserker, and Painlands help you accomplish this. I'd rather just drop one of the more color demanding cards for something that's easier to cast and have more consistent early game mana--particularly in a Boros aggro deck.
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I've found that a filter land in my opening hand interferes with my T1 play more often than having a pain land in play interferes with my 3-4cc plays. And as I said above, the math for needing that T1 mana for your secondary color is usually much harder to hit.
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I'm now wondering why do you choose this 75% base line?
I do understand something between 70/90%, but why 75% ? any specific reason for this?
And thanks again for the article, it make my day.
Thanks for the reply!
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If you wanto to cast Putrid Leech on T2,
you need one black source and one green source.
The table tells you that a 7/7 split is fine,
this is much easier than casting Strangleroot Geist.
Thanks for commenting!
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But I am curious what you think about hybrid one-drops. They may help you plan your game better
so you can cast the 1CC, which are very powerfull (Brimaz, Vortex).
We run Judge's Familiar, Rakdos Cackler, Figure of Destiny, Tattermunge Maniac and Dryad Militant.
We also run Porcelain Legionnaire and Spined Thopter as "colorless" 2-drops. They help you set up the 3rd turn too.
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