Out of the Game: Terms, Metrics, and Mana
By Sean DeCoursey on December 12th, 2005 · Filed in General Magic · Comments not available just now
(Author's Preface Note: If there is not a card that produces mana in a way so weird that it doesn't fit into this framework, one will be printed soon. Wizards routinely breaks and redefines its own rules for mana generation. Mathmatics is all about using numbers to describe a set environment. To use math to describe all the possibilities of every possible Magic: the Gathering manabase, I'd have to go into quantum theory, which is designed to describe environments with inconsistent rules. I'm not going into quantum theory.)
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 Gathering, 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 support all your colors, can leave you with a fairly effective manabase that won't lose you too many games. The key to note is 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 deck in question's theoretical performance. 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.
Unfortunately, Eliza isn't one of my dear
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 one for each creature that produces mana, then add one more for every artifact that produces mana. So, in a deck with sixteen basic lands, four fetchlands, four Birds of Paradise, and two Fellwar Stones 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-winnning GhaziGlare deck for example, runs 23 lands but has a mana potential of 31.
Example: 4x Temple Garden + 4x Brushland + 4x Selesnya Sanctuary + 4x Vitu-Ghazi, the City Tree + 1x Plains + 5x Forest + 1x Okina, Temple to the Grandfathers + 1x Birds of Paradise + 3x Llanowar Elves = 31
Mana Potential is a nice place to start, but what about cards that don't produce mana themselves, but find mana? Things 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 % of the deck they constitue. This is expressed as a (number of finding/producing cards/percentage of the deck those cards make up). Again, using the GhaziGlare deck of Mori, we find that the Mana Percentage is 31/52. 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.
Example: 4x Temple Garden + 4x Brushland + 4x Selesnya Sanctuary + 4x Vitu-Ghazi, the City Tree + 1x Plains + 5x Forest + 1x Okina, Temple to the Grandfathers + 1x Birds of Paradise + 3x Llanowar Elves + 4x Wood Elves = 31
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 it 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 Elves, 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 Blood Pet, Cabal Ritual, and Desperate Ritual would also be included here.
Turn Acceleration % is a simple way to calculate how often you will hit that accelerated relevant turn. To calculate this, 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 will 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 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. The entire thing is expressed as a pair of ##/## expressing % on the play before the /, and percentage on the draw after the /, with the second ##/## being the probability of hitting all the land drops necessary to accelerate to this point. Note that none of these values will ever be higher than 99.
Turn Acceleration Actual is the final and most relevant metric out of all of these, as it tells you how often you will actually accelerate your turn. Turn Acceleration Actual is expressed as Turn Acceleration (turn you're accelerating to) = xx/yy. To calculate Turn Acceleration Actual simply multiply your two sets of Turn Acceleration Percentage numbers. i.e. if your Turn Acceleration Percentage is AA/BB CC/DD your Turn Acceleration Actual would be AA*CC/BB*DD.
Example: 3x Llanowar Elves + 1x Birds of Paradise = 4
4/60 * 7 = 0.46 4/60 * 8 = 0.53 0.87 * 0.46 = 0.40 0.53 * 0.91 = 0.48
Turn Acceleration Actual (3) = 40/48
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 Play Factor metric. Play Factor is what your odds are of having the correct mana to play your ideal drops on your first three turns. Lets use a typical BDW manabase as an example.
And I thought I finally had one up
on that stupid Jackal!
4x Bloodstained Mire, 4x Wooded Foothills, 2x Windswept Heath, 4x Sacred Foundry, 2x Barbarian Ring, 1x Plains, 4x Mountain
The deck wants to drop a Savannah Lions or Isamaru on turn one, so for its ideal turn one play it has a T1 number of 88. On turn two, the deck will ideally play Goblin Legionnaire, which it has a 77 percent chance of doing, giving the deck a T2 number of 77. 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 these spells 67 percent of the time yielding a T3 number of 67. So the Play Factor 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. I believe BDW loses a lot of games it doesn't need to because these numbers are so low, and because its manabase, while appearing successful on the surface, is actually quite subpar.
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 Play Factor. 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.
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, it will be, and there is a very big difference between going 4-2 and 5-1 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 much mana a deck realistically produces. 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 last season. The deck only ran three spells that cost more than one mana, yet it had a Mana Percentage of 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 Potential + nonmana producing mana sources - cards that pull lands out of your deck - lands/mana sources with a non mana primary job - cost of activating those abilities. In this case we would take 31 (Mana Potential) + 4 (Wood Elves) - 4 (Wood Elves) - 4 (Vitu-Ghazi lands) - 16 (Vitu-Ghazi cost) = 11. This means that in general, when firing on all cyclinders, the deck will behave as though it only has 11 actual basic lands in it, with the rest of the deck being gas. You must remember not to count fetchlands twice when calculating this; Krosan Verge however, would be calculated as +1 (Mana Potential) -1 (land with nonmana primary job) -1 (pulls an additional land from your deck), while Kodama's Reach and Explosive Vegetation would be calculated as +1 (non mana producing mana source) -2 (pulls lands from your deck). Another example of calculating this is the RDW build from last season. 24 - 16 (fetchlands, Ports, Wastelands) - 4 (Port cost) = 4. So the reason RDW never got mana flooded, even with all those lands and all those one-drops, was because it played like it only had four actual lands. 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.
Not only do I screw up your mana,
but I also count as negative lands
for my controller!
Example: 8x Mountain + 4x Bloodstained Mire + 4x Wooded Foothilss + 4x Wasteland + 4xRishadan Port - (4x Bloodstained Mire + 4x Wooded Foothilss + 4x Wasteland + 4x Rishadan Port) - 4x Rishadan Port = 4
Building a Balance
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. Basically:
What I propose is using the Play Factor metric as the basis for a new way to calculate mana that takes into account what turn you need the mana on. Lets say you're using a hypothetical aggro deck in Extended that wants to play Kird Ape on turn one, Watchwolf on turn two, and Raging Kavu on turn three. To pull this off you need on turn one, on turn two, and on turn three.
- Determine how many cards of each color you have.
- Determine how many mana symbols of each color you have.
- Assign values to how important they are.
- Ratio your results to get percentages.
- Finally, multiply the percentages by the number of colored mana sources you.
So of these three colors which is the most important, Green (appears twice) or Red (needed on the first turn)? The answer is Red, followed by Green, and then finally White. 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.
The following cards could be used to produce R/W and R/G mana on turn one AND two. Windswept Heath, Wooded Foothills, Bloodstained Mire, Flooded Strand, Sacred Foundry, Battlefield Forge. (Karplusan Forest and many other multi-color lands aren't included because we want a land that counts as a Forest to be played on turn two to power up the Ape.) We'll assume an eight fetchland manabase for this calculation, with Windswept Heath and Wooded Foothills taking the slots.
We want to hit one of these R/W sources on our first land drop at least 90% of the time, sio we need 16 of these mana producers to hit the mark. Eight fetchlands, four Sacred Foundries and four Battlefield Forges would do the trick. Next we want to hit the second turn Forest every time we get the Ape, 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. Eight fetches, four Temple Gardens and two Forests does the job here. Now for turn three, we only have to hit the third land drop, since if we made the first two we'll definitely have the colored requirements with this manabase. To hit our third land drop 90% of the time would require the deck to go up to 28 lands, and that's obviously too many for an aggro deck like this.
Getting the Numbers Right
We decide that we're good if we can cast Kird Ape/Watchwolf 90% of the time when we draw them and we'll settle for 75% on the Raging Kavu. To do so requires 24 lands. We have 22 lands so far. Assuming we just add in a basic Mountain and Plains, let's calculate our metrics to see if this is a good manabase for an aggro deck. The Mana Potential is 16. The Mana Percentage is 24/40, the Turn Acceleration is 0, the Play Factor is 90/90/74 and the Mana Density is 16. 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 can add some nonbasics with activated abilities, and some more fetches to offset the color loss. So let's add two Bloodstained Mires and two Barbarian Rings for a Mountain, two Battlefield Forges, and a Plains. This gives us a Mana Potential of 14 and a Mana Density of 12. This is much better than we were, but still doesn't approach the ideal of 4 epitomized by RDW of seasons past. If we look to the future and include such Guildpact cards as Skargg, the Rage Pits* and the R/G Dual, we can maintain our Play Factor while dropping the Mana Density significantly, perhaps even as low as the 4 achieved by RDW.
So, how does this apply to an existing deck and what can it tell us? Let's continue with the Ghazi-Glare example for Standard, and we'll use the BDW from earlier for Extended.
Fortunately, this math is easy enough
that people besides 'Bert here
can do it.
GhaziGlare - Standard
Mana Potential - 31
Mana Percentage - 31/52
Turn Acceleration(4) - 4
Turn Acceleration Percentage(4) - 53/60 76/82
Turn Acceleration Actual(4) - 40/49
Turn Acceleration(5) - 8
Turn Acceleration Percentage(5) - 99/99 57/68
Turn Acceleration Actual(5) - 56/67
Play Factor - 85/65/75
Mana Density - 11
BDW - Extended
Mana Potential - 11
Mana Percentage - 21/35
Turn Acceleration - 0
Play Factor - 88/77/67
Mana Density - 9
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.
Mana Potential - add up the total amount of mana that all the cards in your deck can produce on a repeated basis. (Lands, Artifacts, 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 every time you use them as part of the calculation for another metric, 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.
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.
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 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, 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 as may be.
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 % of the time you will accelerate a turn.
Target Number: This really depends on your deck's Fundamental Turn. Many decks have a Fundamental Turn of four. Four mana is Fact or Fiction, Wrath of God, Gifts Ungiven, Cranial Extraction, Psychatog with Circular Logic backup, and others.
Play Factor - 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.
Target Number: this is mostly a measuring stick for aggresive 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.
Now get the effect without using the card.
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 decks mana base 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. The bounce duals and other lands that always produce more than one mana, like Ancient Tomb, work out fine.
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 Potential + mana search cards - lands found by mana search cards - mana producers with activated abilities - cost of those abilities IF they are recurring = Mana Density.
Target Number: Aggressive decks want as low of a number here as possible while still keeping up thier Play Factor. 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.
So, to reiterate in order of importance by deck type:
Aggro: Play Factor, Mana Density, Mana Percentage, Mana Potential, Turn Acceleration
Control: Turn Acceleration, Mana Percentage, Mana Density, Mana Potential, Play Factor
Combo: Play Factor, Turn Acceleration, Mana Percentage, Mana Potential, Mana Density
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 Play Factor. 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.
To correct this, the deck should run a full four Barbarian Rings, and a few copies of either Blinkmoth Nexus, Petrified Field, or a singleton copy of Sunhome, Fortress of the Legion or Keldon Necropolis. Another option is to increase the number of Legendary creatures in the deck and run Eiganjo Castle and Shinka, the Bloodsoaked Keep.
A revised BDW manabase created using these metrics could look something like this:
Much like the Kangaroo-Pocket Shoe,
Barbarian Ring's time
has finally come.
This would give you numbers of:
Mana Potential: 14
Mana Percentage: 24/40
Turn Acceleration: 0
Play Factor: 88/85/78
Mana Density: 6
At this point, you've come fairly close to matching the level of efficiency created by the old RDW manabase. There is a slight drop-off in the Play Factor for turn one and two, but in 95% of your hands, you should still have something relevant to do on those turns. There is also a drop off in the Mana Potential, but this is largely offset by the higher Mana Density. The higer Mana Density is in turn partially offset by a higher curve. Here is a more visual illustration of tMana Density's effect.
How BDW looks
The Shocks and Arcbound Stingers in the density list represent the "spells" you get from Blinkmoth Nexus and Barbarian Ring.
Now, if you were guaranteed to draw your Sacred Foundrys early in every game, which of these two lists would you rather play at a tournament?
That's the power of a properly designed manabase.
*Skargg, the Rage Pits - Land, Uncommon, Guildpact. T: add to your mana pool. T: target Creature gets +1/+1 and Trample until end of turn.
Editing: Dr. Tom
By Sean DeCoursey on December 12th, 2005 · 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.