[Editor's note: It's been almost seven months since this article ran. With Worlds over, Standard still popular, and Extended on the near horizon, this seemed like a good a time as any for the Classic treatment. Enjoy! -Dr. Tom]
Author's Preface Note: This work is primarily intended to be utilized in conjunction with Standard, Extended, and Block Constructed formats. The Eternal Formats (Vintage and Legacy) have vastly different theories and rules for mana construction due to the presence of cards such as Wasteland, Strip Mine, the Power Nine, and the original duals. Fixing your mana in Limited formats has already been covered in far greater depth and accuracy than anything I could do by many other writers.
The single most common reason people lose games in Magic is because of mana issues, be it mana flood, mana screw, or color screw. Whether you're a dedicated Netdecker or regular Rogue, this article will teach you how to avoid experiencing any of these any more than is absolutely necessary as dictated by the laws of probability.
When building any deck for Magic, the single most important decisions you can make are often among the least considered – namely, your mana base's design and draw frequency. The general rules of thumb – twenty-four lands and enough fixing to support all your colors – can leave you with a fairly effective manabase that won't lose you too many games. The key is to note that it won't win you too many games, either.
If you netdeck, this is still a very important topic for you. Even if you don't make the common one or two tweaks to a build, you still need to be able to objectively analyze the theoretical performance of the deck in question. Boros Deck Wins' poor performance at Worlds could have been predicted (and somewhat prevented) by a careful analysis of its manabase using these metrics. You may recall that, at Pro Tour: LA, BDW took lands out of the deck during sideboarding against 'Tog. This is because the players intuitively realized the deck was too mana heavy, but didn't really understand why or how to fix it. This article will explain both why that is true and how to solve the problem. More recently, at PT Honolulu, whether or not a Zoo deck won was often decided by whether or not its mana worked out.
Boros Deck Wins and Zoo are arguably the two "best" aggro decks in Extended and Standard, but only if their mana works out. The source of both decks' mana problems and solutions for them will be explored during the course of this article.
To help you, dear reader, understand how to build a better manabase, I'm going to introduce several terms and figures you can use to improve your ability to draw mana of the correct colors early, but not late.
The first term we're going to explore is Mana Potential. Mana Potential is pretty easy to calculate. Simply add up how much mana each land in your deck can produce, then add up how much mana creatures in your deck can produce, then add up how much mana artifacts, enchantments, instants, and sorceries can produce in one turn. So, in a deck with sixteen basic lands, four fetchlands, four Birds of Paradise, and two Boros Signets we would have a mana potential of 16+4+2 = 22. Mana Potential can be much higher than the number of lands you have if you have many lands that produce more than one mana, such as the Urzatron, or the common bounce duals from Ravnica. The Worlds-winning GhaziGlare deck, for example, runs 23 lands but has a mana potential of 31.
Mana Potential is a nice place to start, but what about cards that don't produce mana themselves, but find mana? This includes cards like Wood Elves, Eternal Dragon, Sakura-Tribe Elder, fetchlands, and Sylvan Scrying. For this we have the term Mana Percentage. That is, how many cards in your deck can find OR produce mana, and what percentage of the deck they constitute. This is expressed as a pair of numbers with a slash between them, where the first number is the total number of mana cards in your deck, and the second number is the percentage of mana cards in your deck. Again, using the GhaziGlare deck of Mori, we find that the Mana Percentage is 31(cards)/52(percentage). Unlike Mana Potential, Mana Percentage has absolutely nothing to do with how much mana your deck produces; it is simply a way to deduce at a glance how likely you are to draw mana sources early in the game. Note that’s mana sources, not lands; running 15 signets and 9 lands might give you a decent percentage, but it won't lead to a very consistent deck.
Turn Acceleration is a measure of how often you will accelerate your relevant turn. For example, in a deck with eight cards that put additional mana in play – be they artifacts, creatures, or extra lands – if your relevant turn to accelerate to is turn four, then only sources which cost two or less mana would be considered. For example, in a GhaziGlare deck with four Llanowar Elfs, your relevant turn to accelerate to is turn three, and your Turn Acceleration number would be four. If you ran four Elves and two Birds, then your number would be six. One-time acceleration effects such as Wild Cantor, Cabal Ritual, and Lion's Eye Diamond would also be included here.
*I'm using the Expected Value here rather than the actual value because the Expected value is much, much easier to calculate off the top of your head and nearly as accurate as the Actual value. To calculate the actual value, you simply take 1 - (probability that card 1 in hand is not the accelerant) * (probability that card 2 is not the accelerant given card 1 was not the accelerant) * ... = 1 - 56/60*55/59*54/58*53/57*52/56 *51/55*50/54 = 1 - .6005 = 40%. This is the calculation for your opening hand; to determine if you'll have said card by turn two or three, simply carry the equation forward for however many more cards you will have drawn by the time you need to use it.
Turn Acceleration % is a simple way to calculate how often you will hit that accelerated relevant turn. To calculate your expected value*, divide the number of cards in your deck by the Turn Acceleration number, then multiply the resulting number by the number of cards you will have drawn by the turn you have to play your accelerator. In this case, to hit turn three on turn two, the accelerator must be played on turn one. So you will have drawn seven or eight cards depending on if you drew or played first. In the first example, with just the four Elves, you expect to hit three mana on turn two 46% of the time on the play, and 53% of the time on the draw. With six accelerators, you will expect to hit three mana on turn two 70% of the time on the play, and 80% of the time on the draw. These figures do assume playing a land on each of the first two turns, which, in a deck with twenty three lands, will only happen 87%/91% of the time. Finally, you multiply the two sets of number by each other to get the % of time you will accelerate your relevant turn. Note that when these values are higher than 100%, it simply means that you can expect to draw more than one accelerator by that point in the game.
Turn Acceleration is great for measuring the early game of a control deck, but what about aggro decks? To determine how successful the mana for an aggressive deck will be, I use the Color Curve metric. When designing an aggressive deck, you should spend at least as much time on the color curve as you do on your mana curve. The Color Curve is what your odds are of having the correct mana to play your ideal drops on your first three turns. Color Curve is expressed as a series of three numbers (which correspond to the first three turns of the game) divided by slashes, with each number representing the percentage of the time you will have the correct colors of mana to cast your ideal spell on that turn. Let’s use typical Zoo and BDW manabases as an example.
The deck wants to drop a Savannah Lions or Isamaru on turn one, so there is an 88% chance the deck will have a source on turn one. On turn two, the deck will ideally play Goblin Legionnaire, and BDW has a 77% chance of having both a and source on turn two. On turn three, the deck is ideally playing a land destruction spell, either Molten Rain or Pillage. The deck will have the appropriate mana () to cast one of these spells 67% of the time.
So the Color Curve for a typical Boros Deck Wins manabase would be 88/77/67. Obviously, BDW has a LOT of plays and things to do with its mana that don't involve this theoretical ideal. However, with any aggro deck, you will need to draw "the nuts" at least somewhat regularly over the course of a tournament to win, and this is a good way to measure just how often that you will have the mana to support the god draw. BDW loses a lot of games it doesn't need to because these numbers are so low, and because its manabase, while appearing solid on the surface, is actually quite subpar.
Now let's do Zoo. Zoo has a much harder time hitting good numbers here because of the lack of fetchlands in Standard.
On turn one your ideal play is either Isamaru or Savannah Lions, and you will have the to do this 87% of the time. On turn two you want to be dropping Watchwolf, which you will have a 71% chance of doing. On turn three, you want to play Burning-Tree Shaman, and you will have the correct mana to do that 57% of the time. Now, 87/71/57 probably won't cut it most of the time; however, since we don't have fetchlands to smooth out the color requirements, we won't be quite as demanding as we would be in Extended. We'll say that Kird Ape, Kami of Ancient Law, and Flames of the Blood Hand are just as good as their buddies. This gives us numbers of 95/83/63, which is much, much better.
So let's sum up what we have as mana metrics so far: Mana Potential, Mana Percentage, Turn Acceleration, Turn Acceleration Percentage, Turn Acceleration Actual, and Color Curve. This still leaves quite a few things out. For example, what about deck thinning?
A few notes on deck thinning in general: yes, many math Ph.D.s and very respected Magic writers have written extensively and conclusively that using a fetchland or Sakura Tribe-Elder or Kodama's Reach will not significantly alter your chances of drawing land or nonland cards later in the game. This is true. But what happens if you use a fetchland, an Elder, then a Reach, then another fetchland? At this point you rapidly begin to approach the level of statistical significance.
Now you can get the effect without
using the card!
Let's say you're playing a Boros deck. It's turn three, you're on the play, and you've used three fetchlands so far. There are now 48 cards left in your deck, of which (assuming a 21 land build and no lands in hand) 15 are lands. This means you now have around a 31% chance of drawing a land on your next turn. At the start of the game, you had a 35% chance of drawing a land on any given turn. So by using three fetches, you've reduced your land draw chances by 4%. That isn't a giant massive number, but it is big enough to make a difference once every two or three games. Or, in other words, once every match. Is drawing one extra card every match enough by itself to swing the match? Probably not most of the time, but sometimes, and especially with aggro decks that use burn, it will be, and there is a very big difference between going 5-2 and 6-1 in the Swiss.
How can we apply this type of effect as a reasonable metric along with things such as lands which actually consume mana, rather than producing it? I'm looking at you here, Vitu-Ghazi.
Mana Density is the term I use to analyze how likely your deck is to draw into "dead" lands. The lower your number, the less likely you are to pull useless land instead of something relevant. For an example of a deck with a seemingly too high Mana Percentage, but an actual low Mana Density, let's look at Red Deck Wins from two years ago. The deck only ran three spells that cost more than one mana, yet it had a Mana Percentage of 24/40 and rarely experienced mana flood. How? The deck had a very low Mana Density. Eight fetchlands simply meant you'd just pulled two lands out of the deck whenever you drew them, while the Wastelands rarely stayed around and the Rishadan Ports almost always consumed, rather than produced, mana.
Mana Density assumes that Ports and Wastelands will be used, that Cycling Lands will be cycled, and that Svogthos will suck down five mana then turn sideways more often than it will tap for . Again, using GhaziGlare as an example, you would calculate the deck's Mana Density as follows:
Mana Percentage - cards that pull lands out of your deck - lands/mana sources with a nonmana primary job - cost of activating those abilities - cost of activated abilities of nonland permanents.
In this case we would take 31 (Mana Percentage) - 4 (Wood Elves) - 4 (Vitu-Ghazi) - 16 (Vitu-Ghazi cost) - 4 (Selesnya Guildmage cost) = 7. This means that in general, when firing on all cylinders, the deck will behave as though it only has 7 cards that are "dead mana" draws, with the rest of the deck being gas. Fetchlands are a special case and are only counted once unless they grab more than one land; Bloodstained Mire would be calculated as: +1 (Mana Percentage) - 1 (pulls a land from your deck). Krosan Verge however, would be calculated as: +1 (Mana Percentage) -1 (land with non mana primary job) - 1 (pulls an additional land from your deck besides its replacement). The reason for this is because the Onslaught fetchlands still take up a land drop and don't produce mana on thier own. Kodama's Reach and Explosive Vegetation would be calculated as +1 (non mana producing mana source) -2 (pulls two lands from your deck). Another example of calculating this is the RDW build from last season. 24 - 16 (fetchlands, Ports, Wastelands) - 4 (Port cost) - 3 (Cursed Scroll cost) - 1 (Grim Lavamancer cost) = 0.
So the reason RDW never got mana flooded, even with all those lands and all those one-drops, was because it never drew lands it couldn't profitably use. The cycling cost of cycling lands and the activation cost of Threshold lands is not included when calculating this metric because they are one-time expenses. If your Mana Density is negative, you will often have more to do with your mana than mana to do it with.
Mana Density is a very important statistic to your decks' long term success, but it's also a statistic that's ridiculously easy to manipulate by throwing in a few junk lands with high activation costs like Keldon Necropolis or Nivix, Aerie of the Firemind. This isn't to say those cards can't be well utilized by a very specialized deck, but you shouldn't throw them into something just to get your density down a bit lower.
To that end here is a quick list of some of the more efficient and powerful activated abilities in Standard that can be thrown into most decks utilizing the necessary colors.
Okina, Shizo, Minamo, Eiganjo, and Shinka should always be run if your deck contains six+ legendary creatures in it, otherwise, they're probably not worth it.
Skarrg, the Rage Pits - this is probably the best activated ability land in Standard, and it's got quite a bit of competition for that title. It does exactly what its colors / want to do, and acts as an amazing threat to combat math as well, allowing it to have a powerful impact on the board without ever being used.
Rix Maadi, Dungeon Palace - number two on our list, but number one in pain, is the Rakdos land. Uncounterable discard for four mana is quite the treat, especially as most Rakdos decks are trying to get rid of their hands anyways.
Vitu-Ghazi, the City Tree - while it costs more than Kjeldoran Outpost did, there is no denying the power of a land that just keeps making a new army over and over again.
Svogthos, the Restless Tomb - expensive, but potentially huge, this card works exceptionally well with its guild mechanic of Dredge, acting as a solid finisher that recurs with Life from the Loam and flat out abuses people trying to get by with only sorcery-speed removal.
Ghost Quarter - unless your opponent forgot to put any basic lands in his deck, this won't break his back, but it does provide a nice way for every color to deal with some of the more annoying lands on this list and slow down the Urzatron.
An incorrectly filled out Form 7b, Mr.
"Triple-S" clearly prevents you from
lodging a complaint against Mr.
Planeswalker today, please go to the
back of the line now.
Mikokoro, Center of the Sea - giving your opponent cards is often a bad idea, but if you really need a source of draw and aren't in one of the colors Wizards has given draw to, this is a very solid answer.
Prahv, Spires of Order - much maligned due to its fairly insane activation cost, this land would be ridiculous and dominant at a lower number. Considering how much good mana acceleration is in the format right now, a / controllish deck can use this to force an opponent to commit additional creatures to the board, or hold off burn spells that don't come in multiple doses. This is currently very underrated as a way to hold off a topdecked threat in the late game while you search for answers. Honestly, how often has a control player sat at three or so life while he and the aggro player desperately try to topdeck an answer? All of a sudden, your opponent needs two Chars to kill you instead of just one. If you read Prahv carefully, you'll also note that it can stop damage from untargetable sources like NorthsideTriple-S and Creepy Crawly.
Orzhova, the Church of Deals - lifegain and burn on a land is pretty powerful, and the fact that you can wait until your opponents' EOT to use it makes the two point life swing something that’s definitely worth springing for.
Novijen, Heart of Progress - another underrated land, this basically gives your creatures a +1/+1 kicker cost. Its best uses, though, come when more than one creature is played in a turn or with mass removal/return effects like Ghostway. It can also be used to give your opponent’s creatures +1/+1 counters for things like Cytoplast Manipulator and Experimental Kraj.
Sunhome, Fortress of the Legion - barely playable in the right deck, but at one mana less it would be very playable, borderline abusive. Since any deck that wants to use this would get almost the same power boost from Skarrg, it just doesn't cut it.
Duskmantle, House of Shadow - this is a case of a card being killed by Limited. If this mills enough to be relevant, it ruins RRR drafts. The emphasis Wizards places on draft is the reason we will probably never see a competitive milling deck in Standard, unless every single card in it is Rare. At Uncommon, Duskmantle was doomed.
Well, that covers the lands with repeatedly activated abilities in Standard right now, so let’s go over some of the better repeatedly activated abilities on nonland permanents that you may want to include in your decks. First, the Guildmages. I've divided them into three tiers which are basically auto-include, very solid, and barely worth it.
Tier One: Selesnya Guildmage - builds a new army, pumps an existing one, or both, this is the best Guildmage out there. Rakdos Guildmage - number 1a behind the tree-huggers, his ability to fling 2/1's or turn dead cards into removal is too good to be overlooked. Dimir Guildmage - provides nearly insurmountable card advantage if he lives for more than one or two turns.
Tier Two: Gruul Guildmage - not as good at pumping as his Selesnya friend, he makes up for it with the ability to fling trees at your opponent. Izzet Guildmage - expensive to use multiple times, but giving spells like Boomerang and Lightning Helix replicate can be backbreaking. Orzhov Guildmage - the only source of untargeted life loss on a Guildmage, he can get around Worship or burn your opponent out. But the White half is very, very meh for its cost. Boros Guildmage - dominates the combat phase like no other, and randomly gives your guys a Haste Kicker, but doesn't have any way to deal damage or increase it on her own.
Tier Three: Azorius Guildmage - expensive for what she does, but there are still a lot of worse options out there. Simic Guildmage - in very limited situations he's insane, the rest of the time, you wonder why his abilities aren't relevant . . . to anything. Golgari Guildmage - he can be very powerful in a long, slow game where nothing messes with him, but realistically, that game doesn't exist outside of Limited, and not even that often there.
Next, we have a bunch of random creatures/artifacts with activated abilities that cost mana and are also worth using. I'm only hitting the very playable highlights here as there are a LOT of options in this category, so in no particular order we have:
Lyzolda, the Blood Witch - the Rakdos have so many good things to do with cards in play that it’s not really funny. Of course, I guess if your guild mechanic is to play from the board instead of your hand, you need spells to cast from it.
Pride of the Clouds - slightly cheaper than Vitu-Ghazi, but with the restriction that you have to pay the cost during your upkeep.
Paladin of Prahv - for a very reasonable cost, you can now suck the life right out of your opponent. Feels White in theory, vampiric in practice.
Stormscale Anarch - three mana to turn anything into a Shock? Doesn't remind me of Cursed Scroll at all. Ok, maybe an easy-to-kill Stormbind is a better comparison, but the ability to fire it off more than once a turn is strong, and turning that Putrefy into a Char aimed at your opponent’s head shouldn't be overlooked.
Searing Meditation - this is the kind of card you build a deck around, and several people already have.
Remember, if your deck has a bad Mana Density, putting in bad cards with activated abilities won't make your deck better; it will only give you a deck with a bad manabase and bad cards. However, taking a deck with a bad Mana Density and adding good cards with activated abilities can push your deck right over the top into the territory of "very good."
As a final example of how important Mana Density is, I'm going to show you why Rakdos aggro will be so much better (or at least have a better mana base) than Zoo or Boros aggro. Let's assume a Rakdos aggro deck with the following manabase: 2x Rix Maadi, Dungeon Palace, 4x Blood Crypt, 4x Sulfurous Springs, 6x Swamp, 6x Mountain, 2x Ghost Quarter. Your mana density would come out something like this: 24 - 2 (Rix Maadi) - 2 (Ghost Quarter) - 6 (Rix Maadi cost) - 2 (Lyzolda cost) - 4 (Rakdos Guildmage cost) - 1 (Plagued Rusalka cost) - 1 (Frenzied Goblin cost) = 8. No other aggro deck in Standard comes close to that kind of mana density except some builds of Selesnya aggro/control... the deck that won Worlds. See? These numbers ARE important.
Ach, Hans! It's the Pain!
Closely related to Mana Density (at least in Extended) is the Pain Index of a given deck. The Pain Index is a simple way that you can estimate what your actual life total will be when you take into account the amount of life you're going to lose to your own manabase. The Pain Index is based over the first four turns of a game, because it is assumed that after that point, you can safely play any shock duals tapped and the Ice Age/Apocalypse pain lands can mostly be used for colorless mana. First, we'll go over how to calculate this in Standard.
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First, figure out how many pain and shock lands you have in your deck. We'll use Zoo for this example. We have 12 shock lands and 6 pain lands. You have an 80% chance of having a shock land and a 53% chance of having a pain land on turn one, so we'll use the greater value and multiply 2 (damage) by .8 (% of draws) to get 1.6 damage for the first turn. On turn two we have a 52% chance of a second shockland, and a 59% chance of a painland, so again we'll use the higher value and multiply 1 (damage) by .59 (% of draws) to get .59 damage for turn two. On turn three, we have a 57% chance of drawing a second shockland, and a 28% chance of drawing a second painland, so we have .59 (painland gets used again, so the damage carries over) + 2 (damage) x .57 (% of draws) to get a turn three number of 1.73. For turn four we have a 33% chance of drawing a second painland and a 31% chance of drawing a third shockland. We also have a 52% chance of having drawn our first not painful land, so for turn four we again use the highest value and carry over the damage from the painland to get .59 + 0 (damage) x .52 (%of draws) to get .59 for turn four. This gives us a total of 1.6 + .59 + 1.73 + .59 = 4.51, which rounds up to 5. So, on average, a Zoo player using this manabase starts the game at approximately 15 life rather than 20.
Note that decks without a turn one play automatically assign themselves a zero for turn one, unless they use a fetchland, in which case it's a one in the damage category.
In Extended, we have the fetchlands to add to our misery, so let’s calculate the typical 21-land BDW build. With 10 fetchlands, four shocklands, two painlands (Barbarian Ring), and five painless lands. On turn one our greatest probability is a fetchland at 68%, which will grab us a shockland, so our calculation would be 3 (total damage) x .72 (% of draws) = 2.16. On turn two our highest number is still a painless land at 52%, which gives us a number of 0 (damage) x .52 (% of draws) = 0. On turn three we're back to the fetchlands, at 46% which gives us a number of 3 (damage) x .46 (% of draws) = 1.38. Finally, on turn four, we have a 30% chance of drawing our first painland, which gives us a number of 1 (damage) x .3 (% of draws) = .3. This gives us a total pain index of 3.84, which is rounded up to four, meaning that the typical Boros Deck Wins player starts the game with approximately 16 life.
That's only part of the story, though. You also have to take into account the potential damage a deck’s manabase can do to its controller’s life total so that you can accurately assess worst-case scenarios rather than just statistical averages. So, for Zoo, we take 12 (number of shocklands) x 2 (damage) + 6 (number of painlands) x 1 (damage) to get a total of 30. Now divide this number by the average life loss of the deck (five) to get your variability - 6. This means that, while your statistical average life loss is 5 life points, on any particular draw, you should be prepared to lose up to 11 life from your lands alone. For BDW, we take 4 (number of shocklands) x 2 (damage) + 2 (number of painlands) x 1 (damage) + 10 x 1.5 (fetchlands grabbing shocklands) = 25. Divided by four and rounded up, this gives us a variability of 7, which means that although your average life loss is four, you could, in any given game, easily lose up to 11.
So, to calculate your decks' pain index, figure out your highest percentage land draw for each of the first four turns, then multiply that draw chance by the damage from the land and add the results together (rounding final figures up) to get your average life loss. To calculate the variability, add up the total damage from your manabase (fetchlands count for one if they only fetch basics, 1.5 if they fetch shocklands) and divide by your average life loss, again, rounding results up. The final number is expressed as (average starting life total)/(life total - variability). Or, in BDW's case, 16/9, and in Zoo's case, 15/9.
In the event of a tie in percentages, for example, if you ran four Temple Gardens and four Brushlands as your only nonbasics, calculate both probabilities then average the results.
Mana Curve and Color Curve, United at Last
The hardest thing to do when building a deck is to balance the mana properly. Currently, the best way to calculate mana ratios is found in a ten-year-old book by George Baxter. Players of Magic Workstation will note that this is the statistic used under the "Deep Analysis" tab. Basically:
1. Determine how many cards of each color you have.
2. Determine how many mana symbols of each color you have.
3. Assign values to how important they are.
4. Ratio your results to get percentages.
5. Finally, multiply the percentages by the number of colored mana sources.
You have to decide what is important and assign one of three values to each card.
This system was devised before mana fixing nonland cards were in wide circulation.
The first and second problems are related, Tooth And Nail is obviously more important to a Tooth deck than Zealot, but since you won't realistically be casting Tooth before turn four, you'll have had several more turns to draw the necessary for it. This means you actually need less Green to afford the more important in Tooth than the less important in Zealot. Contradictions like this make it very easy to improperly label the importance of the mana in different cards.
That third statement probably sounds pretty strange given how common mana and color fixing from non land sources are today. It's pretty hard to realize that the first playable "Rampant Growth" effect ever printed was when Rampant Growth was printed in Mirage - Magic's 9th Expansion (Sorry, but Untamed Wilds just doesn't quite cut it, and Thawing Glaciers got banned).
What I propose is using the Color Curve as the basis for a new way to calculate mana that takes into account what turn you need the mana on. Let’s say you're playing Tooth and Nail. The in Tooth and Nail's isn't a problem, but the in Viridian Zealot is nearly prohibitive. Why? Timing. When you need to have a particular color of mana available is just as important a consideration as how much of that mana your deck needs when designing your mana base.
Note that analysis of this metric can also affect your deck design. If you decide to go with the first turn Ape, second turn Forest play then it makes sense to include more red one-drops. If you decide that a two power creature on turn one is your ultimate priority, then it makes more sense to try and drop a Savannah Lion or Isamaru on turn one from a White mana source. But for now, back to the Ape.
To further illustrate this point we'll be looking at the best bad deck in Standard, Zoo. On your first turn, your ideal play is a powered up Kird Ape. This means you want to have a Stomping Grounds out ASAP. Unfortunately for Zoo players, you only have the four Stomping Grounds and no fetchlands or Land Grants to go pick them up for you. This means you either want a first turn land to produce Red mana and a second turn Forest to power up the monkey, or a first turn Forest followed by a Red source to play the Ape.
So, we want to have at least a 90% chance to have both a Forest and a Red source in play by turn two. How do we write a formula to express this? Assuming we always want to have available on turn one, and that we'll want to have it from a land that ALSO produces or so we can cast Watchwolf on turn two, let's look at what lands could produce the colors we want on the relevant turns. Note that this eliminates several lands from consideration because they come into play tapped or will not tap for colored mana on the next turn. However, these lands could be considered when calculating for a turn two, three, or four drop IF you don't need to hit every previous point on the curve.
We want to hit one of these R/W sources on our first land drop at least 90% of the time, so we need 16 of these mana producers to hit the mark. Four Battlefield Forges, and four Sacred Foundrys are a nice start, but after that, we're out of luck. So we'll have to settle for simply a OR source, rather than a / source. This means that adding in four copies of Stomping Ground and four copies of Temple Garden covers us completely. Next we want to hit the second turn Forest every time we get the Ape or Wolf, so that also needs to be a 90% play. However, because this will be on turn two, we can get by with only 14 Forests. Four Temple Gardens and four Stomping Grounds gets us to eight, but after that, we start running into trouble on finding enough Forests without overloading our deck with lands. So what does all this tell us? That Standard, three-color Zoo probably should be running a different Red or Green one drop than Kird Ape because the mana simply isn't there to consistently support the little fella and the rest of the deck you're trying to play. In a two-color / deck, Kird Ape is eminently supportable, but three-color Zoo is probably better off running Frenzied Goblin, Scorched Rusalka, Frostling, Child of Thorns, Boros Recruit, Jukai Messenger, or War-Torch Goblin. Recruit is probably the least appealing card on that list, but he is the easiest to cast, kills x/1's and lives, and with help from some burn, he can take down most anything and survive.
We decide that we're good if we can cast our one drop and two drop 90% of the time when we draw them and we'll settle for 75% on the three. To do so requires 24 lands. We have 16 lands so far, and they provide us 90% on the one drop. If we count Kami of Ancient Law as an acceptable option in the two-slot, we get to 90% on the two drop with any lands we add, although six lands that produce and two Skarrg, the Rage Pits would give us a 90% chance on dropping Watchwolf when we draw him. Assuming the six lands are three Forests, two Karplusan Forests, and a single Brushland, let's calculate our metrics to see if this is a good manabase for an aggro deck. The Mana Potential is 24. The Mana Percentage is 24/40, the Turn Acceleration is 0, the Play Factor is 90/90/74 and the Mana Density is 18. All of these numbers are good, except for the Mana Density, which is way, way, way too high. This means that we'll often be drawing lands when we'd rather be drawing action cards. How can this be fixed? We could add some nonbasics with activated abilities, but then our playability numbers would go down. So let's add some creatures/spells with activated abilities to get some more use out of our mana. Selesnya Guildmage seems like an excellent choice, as anytime we have him in play we'll automatically be able to utilize almost all of our mana. This takes us down to 14 on our mana density, which is still high, but honestly, about as good as we're likely to get with the limitations imposed on us by the lack of fetchlands. Ghost Quarter would be a great way to reduce our density, but we need the colored mana our lands produce a lot more than we need the lower density the Quarter could give us.
So, how does this apply to an existing deck and what can it tell us? Let's continue with the Zoo example for Standard, and we'll use the BDW from earlier for Extended.
Zoo - Standard
Mana Potential - 22
Mana Percentage - 22/37
Turn Acceleration -0
Play Factor - 87/71/57 (da nutz!) 95/83/63 (anything)
Mana Density - 20
Pain Index 15/9
BDW - Extended
Mana Potential - 11
Mana Percentage - 21/35
Turn Acceleration - 0
Play Factor - 88/77/67
Mana Density - 9
Pain Index - 16/9
As you can see, the Zoo deck has a low Play Factor for the nuts, but is fairly consistent if you don't particularly mind what spell you're playing, and has an absolutely horrific Mana Density for an aggro deck. The combination of these two factors led to the majority of the deck’s losses at PT: Honolulu. In fact you can argue that the deck’s second-place finish was simply the result of one Zoo deck going on a continued run of statistical improbability. BDW, on the other hand, has a very solid Mana Density, but this comes at the cost of a slightly lower Play Factor. These are the two best/worst aggro decks in Standard and Extended, and they both have bad mana bases, but putting them side by side, you can see that the reasons for their bad manabases are very different.
Now, for everyone who got burned out by the math and explanations above, this is the quick and simple formula summary, along with reference points for what good numbers are in the various categories and what deck types they are most useful in evaluating. For a printable version of this summary, click here.
Mana Potential - add up the total amount of mana that all the cards in your deck can produce. (Lands, Artifacts, Instants, Sorceries, and Creatures) This is a useful tool to determine if you will have large amounts of mana available on a regular basis. When calculating the mana for things like the Urzatron or Gaea's Cradle that produce variable amounts of mana, count the maximum they could produce when creating your Mana Potential, but when using them to calculate most other metrics, they only count for one.
Deck Types: Aggro, Control, Combo. When calculating Combo, be sure to include "one time" mana generating effects such as Early Harvest and Seething Song.
How to calculate: Take all Lands, Creatures, and Artifacts in your deck that produce mana and add up the total amount of mana they would produce if they were all tapped at the same time. Then calculate the maximum amount of mana you can get from things like Early Harvest and Heartbeat of Spring.
Target number: This really depends on your deck. A deck that wants to make expensive late-game plays, like recurring and playing Eternal Dragon, or resurrecting Firemane Angel, wants a much higher number than a deck whose mana curve tops out at three. However, if your mana curve tops out at three but you have a lot of three and four mana activated abilities (Rix Maadi, Skarrg, any Guildmage) a high mana potential is definitely not a bad thing.
Mana Percentage - the number of cards in your deck that produce or search for mana producers and the percentage of your deck that those cards constitute. This is a good way to tell how likely you are to be mana screwed early in the game.
Deck Types: Control, Combo, Aggro. Every deck needs to hit its early land drops (even Vintage 2-Land Belcher needs mana early, whether it's from lands or not).
How to calculate: Count all of the cards in your deck that produce mana, then count all the cards that search out cards in the first category, add the two numbers, and then divide the result by the number of cards in your deck.
Target Number: Again, this depends on your deck, but you probably want to shoot for around 40%, as this lets you make land drops 1-3 regularly.
Turn Acceleration - the percentage chance that you will draw your mana accelerators and lands in time to use them to accelerate yourself to the relevant turn. This is a good tool to evaluate how "fast" a control deck is at making it to the midgame, where it can begin to take over from an aggro deck or set up defenses against a combo deck. This is also where you calculate how likely you are to be able to do something entirely stupid with your Tolarian Academy on turn two. Or one.
Deck Types: Control, Combo. Some aggro decks use this with cards like Chrome Mox or Llanowar Elves, but they are far less common than their brethren, and usually only care about accelerating on the first turn. One-shot acceleration cards such as Seething Song and Early Harvest are also included here.
How to calculate: Divide the number of cards in your deck by number of accelerators, then multiply the resulting number by the number of cards you will have drawn by the turn when you have to play your accelerator. Now multiply the resulting percentage by the percentage chance you have to draw enough lands to hit all the land drops to accelerate. The result is the expected % of the time you will accelerate a turn.
Color Curve - the odds of having the correct mana to make your ideal plays on turns one through three. This is a very important measuring stick for aggro and combo decks. If you're scoring less than 85-90 on turns one and two, you probably need to rework your manabase. The inverse of your turn one and two scores are a good indicator of the amount of time you'll be mulliganing due to mana issues.
Deck Types: Aggro, Combo. Control also wants to hit its early drops, but these are covered by Turn Acceleration for most control decks.
How to calculate: Count the number of lands in your deck that let you make the ideal play on turn one, divide this number by the number of cards in your deck then multiply the result by seven (expected value).
Target Number: this is mostly a measuring stick for aggro and combo decks. You should be shooting for 85-90 for turns one and two, and 70-75 for turn three. The higher you can get this without overloading your Mana Density, the better.
Mana Density - How land-heavy your deck plays. The differential between this number and the Mana Potential is very telling in trying to assess how much the deck’s manabase does besides produce mana. Remember that sources which produce variable amounts of mana, like Rofellos, or Metalworker, only count for one when calculating Mana Density.
Deck Types: Aggro, Control. Combo decks frequently don't care at all about the mid or late game because they'll either go win or they won't, and in either case they couldn't care less about their odds of drawing/not drawing land in the mid and late game.
How to calculate: Mana Percentage - lands found by mana search cards - lands with a non-mana primary job - cost of those abilities IF they are recurring - cost of activated abilities = Mana Density.
Target Number: Aggressive decks want as low of a number here as possible while still keeping up their Color Curve. Control Decks want a somewhat higher number, but going too high can leave you without enough tools to mount an effective fight. In Extended, if you're over 16, and not playing Heartbeat of Spring or Suppression Field, you need to take a hard look at your mana. In Standard, this number will often be 20 or higher, but decks that can get it lower do have a definite advantage.
Now that's a painland.
Pain Index - how much damage you're likely to take from your own manabase.
Deck Types: Control, Combo, Aggro. Most decks honestly don't care about this number unless they're facing off against a fast aggro deck because it's almost always worth trading in a few life for a more consistent manabase.
How to Calculate: Figure out your highest percentage land draw for each of the first four turns, then multiply that draw chance by the damage from the land and add the results together (rounding final figures up) to get your average life loss. To calculate the variability, add up the total damage from your manabase (fetchlands count for one if they only fetch basics, 1.5 if they fetch shocklands) and divide by your average life loss, again, rounding results up. The final number is expressed as (average starting life total)/(life total - variability). Or, in BDW's case, 16/9, and in Zoo's case, 15/9.
Target Number: this is entirely dependent on how aggressive the general metagame is and how important it is to your deck to maintain a high life total.
So, to reiterate in order of importance by deck type:
Aggro: Color Curve, Mana Density, Mana Percentage, Mana Potential, Turn Acceleration, Pain Index
Control: Turn Acceleration, Mana Percentage, Mana Density, Pain Index, Mana Potential, Color Curve
Combo: Color Curve, Turn Acceleration, Mana Percentage, Mana Potential, Mana Density, Pain Index
I honestly cannot emphasize enough how important the correct manabase is to the success or failure of any deck you play. Using tools like these to analyze your deck and manabase is time-consuming and annoying, but it will often be the difference between winning and losing. Players often tend to ascribe losses to the incorrect source. It is much easier to blame your opponent for topdecking or "lucksacking," or a bad shuffle on your part, than to realize that you made an incorrect mulligan decision or failed to adequately design and consider your own manabase.
To illustrate this point, we'll look at BDW again. At the beginning of this article, I stated that the deck's poor performance at Worlds could have been predicted by examining its manabase with these metrics. The deck attempts to copy the success of RDW but fails because of its manabase. The deck has a lower Mana Percentage, a lower Mana Potential, a higher Mana Density, and, worse yet, a worse Color Curve. This means it runs fewer lands, gets manascrewed more often, mulligans more often, misses critical plays more often, and plays like it has too many lands. The result of all this is that you lose one or more burn spells PER GAME. Oftentimes, that is enough to mark the difference between winning and losing.
Mana Potential: The maximum amount of mana your deck can produce in ideal circumstances.
Mana Percentage: number of lands + number of land search spells/effects + number of creatures, artifacts, enchantments, instants and sorceries that produce mana = Mana Percentage.
Mana Density: Mana Percentage - lands found by mana search cards - lands with a non mana primary job - cost of those abilities IF they are recurring - cost of activated abilities = Mana Density.
Turn Acceleration: [(number of cards in deck / number of accelerators) * the number of cards you will have drawn by the turn when you have to play your accelerator] * the percentage chance you have to draw enough lands to hit all the land drops up to the turn you want to accelerate to = Turn Acceleration.
Color Curve: (The number of lands in your deck that let you make the ideal play on turn one / the number of cards in your deck) * the number of cards you have drawn on turn one = first number of the Color Curve. (The number of lands in your deck that let you make the ideal play on turn two / the number of cards in your deck) * the number of cards you have drawn on turn two = second number of the Color Curve. (The number of lands in your deck that let you make the ideal play on turn three / the number of cards in your deck) * the number of cards you have drawn on turn three = third number of the Color Curve.
Pain Index: Highest percentage land draw for turn one * the damage from the land = turn one number. Repeat this process for turns 2, 3, and 4 then add the four numbers together (rounding final figures up) to get your average life loss. To calculate the variability, add up the total damage from your manabase (in this calculation fetchlands count for 1 if they only fetch basics, 1.5 if they fetch shocklands) and divide by your average life loss, round final results up.
By Sean DeCoursey on December 20th, 2006 · Filed in General Magic · Comments not available just now
About Sean DeCoursey
Sean Decoursey is a veteran of Operation Iraqi Freedom where he served with the 2/124th Infantry from 12/02 through 03/04. He attended Truman State University where he was a member of the rugby team which ranked in the top ten nationally three times. Sean graduated with a degree in Justice Systems and now lives in Kansas City, where he works as a Financial Advisor.