Mana Ratios: The Basics
mistergreen527 - 18 January 2010
Mana Ratios: The Basics
The Importance of Mana
Try and imagine playing a game of Magic that doesnt use ANY mana. That is, youre not allowed to produce mana in any way. Your card selection would be pretty limiting. I mean, sure, you would have your Crimson Kobolds and your Ornithopters, but these will only get you so far. A Chalice of the Void would completely shutdown your opponent, but would you really want to cast it when your only hope to end the monotony is for a foolish opponent to play a Pact of Negation?
The point here is that mana is the backbone of Magic. Without it, the game is boring and difficult to win. Because mana is essentially the core of Magic, there can be a lot said about it. Im going to split all of these topics on mana into two main realms: mana ratios and mana counts. Mana ratios involve making sure the mana producers in your deck can fulfill color cost requirements of your spells most efficiently. Mana count involves converted mana costs, mana curve, and the number of cards that produce mana.
The Basics of Mana Ratios
Today, were going to focus on mana ratios. So, lets look at the three fundamentals of mana ratios:
1) Some mana requirements are easier to fulfill than others. Each individual mana required to cast a spell can be described in one of three ways. It will either be a colorless mana symbol, a hybrid mana symbol, or a colored mana symbol. As you may have guessed, colorless mana symbols are the easiest to pay for. Mana of any color will do. Hybrid mana symbols are a little bit harder. They require that mana be one of two colors. Colored mana symbols are the most difficult. If it says you need a green, you need a green. For example, Howling Mine (two colorless) is easier to cast than Riverfall Mimic (one colorless, one hybrid). Riverfall Mimic is easier to cast than Negate (one colorless, one colored). Negate is easier to cast than Esper Stormblade (one hybrid, one colored). And, Esper Stormblade is easier to cast than Twincast (two colored).
2) A card that produces mana belongs in some decks, but not others. For example, if your deck only has costs that require white mana, then youre always going to be happier to draw a Plains than a Seaside Citadel. Therefore, Seaside Citadels do not belong in your deck. Similarly, a deck that includes both red mana and green mana costs would probably benefit from using a Stomping Ground over an extra Forest.
3) Math can be used to determine what type of mana producers a deck should use, based on the cost requirements found in the deck.
Wait math? Before you stop reading, let me explain that I am not a fan of doing math. I may be good at it, but I dont like doing it. However, finding the correct ratio of mana producers really isnt that bad. Plus, were going to start off easy. Besides, your decks will improve once you understand the mathematical relationship between your mana costs and your mana producers. For now, were only going to factor in basic lands as our mana producers. Others ways to produce mana will be discussed in later articles.
How to Calculate Mana Ratios for Your Deck
The first thing you need to do is create a count that represents each color in your deck. This count will be based on the mana symbols in the costs of the cards in your deck. Were going to use black as an example, but this applies for all colors. For each card that requires a single black mana, the black count increases by 1. For cards that require two black mana, add 2 to the count for the first one, 1 to the count for the second one, 2 to the count for the third one, 1 to the count for the fourth one, and so on. For cards that require three black mana, add 3 to the count for the first one, 2 to the count for the second one, 1 to the count for the third one, 3 to the count for the fourth one, and so on. I call this the progressive pattern method. (An explanation for why we do this can be found later in this article).
For hybrids, add 0.5 to the count for each half mana symbol on the card. The exception to this is if you plan on using only one of the colors in that hybrid for your deck. In that case, treat the hybrid mana symbol as a regular colored mana symbol for the color in your deck. For example, if youre making a White/Blue deck with Memory Sluice in it, the count for blue would increase by 1.
Colorless mana symbols are ignored completely. Since they can be paid for using any type of mana, they dont have any influence on the mana that our lands are going to be producing.
Im going to pull a deck from the Newb section of the TappedOut home page to illustrate making these counts and how they can be used to determine what lands to put in a deck. Here are the current contents of Mazurkas Grixis Discard Beatdown and the increase to each colors count that the cards would provide:
1x Banefire --- +1 Red4x Bituminous Blast --- +4 Black, +4 Red4x Blightning --- +4 Black, +4 Red4x Cunning Lethemancer --- +4 Black1x Deny Reality --- +1 Blue, +1 Black3x Duress --- +3 Black4x Sedraxis Specter --- +4 Blue, +4 Black, +4 Red2x Terminate --- +2 Black, +1 Red3x Thought Hemorrhage --- +3 Black, +3 Red
These first nine cards on the list are easy to do. Each colored mana symbol increases the count for its color by 1.
These next four cards each had two black in their cost, so I used the progressive pattern method described above. To clarify, I put the amount each individual card added to the count in the parentheses.
1x Cruel Ultimatum --- +2 Blue, +3 Black, +2 RedSince this last card is the only one that has two blue in its cost, it increases the blue by two. The same goes for red. It is also the only card with three black in its cost, so each mana symbol in this cost ends up increases the cost for its color by 1.
This results in each color having these counts:White = 0Blue = 7Black = 36Red = 19Green = 0Total = 62
We can convert each of these numbers into a ratio by dividing each one by the sum of the counts.White = 0/62 = 0.000Blue = 7/62 = 0.113Black = 36/62 = 0.581Red = 19/62 = 0.306Green = 0/62 = 0.000
The next step is to multiply these ratios by the number of land we plan on putting in the deck. Mazurka used 20 land, so lets multiply each ratio in our example by 20:White = 0.00020 = 0.000Blue = 0.11320 = 2.260Black = 0.58120 = 11.620Red = 0.30620 = 6.120Green = 0.000*20 = 0.000
So, if this deck were only using basic lands, it should be using 2 Islands, 12 Swamps, and 6 Mountains. If youre observant you may notice that this makes it extremely unlikely that this deck will be able to play any of its blue spells, especially Cruel Ultimatum. However, since nearly every card requires at least two colored mana in its cost, I assure you this is mathematically correct. There are two ways to alleviate this problem. The first solution is to decrease the number of spells and increase the number of lands. However, this falls under a completely different mana realm (mana count). The other solution is to use nonbasic lands. Well learn how to make intelligent choices about your mana ratios involving nonbasic lands next week.
The Logic of the Progressive Pattern Method
You may be wondering why we dont just increase the count of each color by one for every colored mana symbol that appears. Why does the first card in a deck that costs three white increase whites count by 3, but the third card in that deck that costs three white only increases the count by 1? Well, to simplify the explanation, were going to make up a deck that ignores deck making rules as an example. This deck plans on using 20x Ball Lightnings, 20x Elite Vanguards, and 20x basic land. Using the progressive pattern method we learned, we would get the following results:Whites Count = 20Reds Count = 41Whites Ratio = 20/61 = 0.328Reds Ratio = 41/61 = 0.672Number of Plains = 0.32820 = 6.560 = 7Number of Mountains = 0.67220 = 13.440 = 13
However, if we instead increase each colors count by one for every matching mana symbol, our equation would look like this:Whites Count = 20Reds Count = 60Whites Ratio = 20/80 = 0.250Reds Ratio = 60/80 = 0.750Number of Plains = 0.25020 = 5.000 = 5Number of mountains = 0.75020 = 15.000 = 15
That difference of two in the number of Plains may seem small, but it isnt. By using the progressive pattern method, each card you draw gives you a 12% chance of getting a Plains. Meanwhile, by increasing the counts for every mana symbol, each card draw gives you an 8% chance of drawing a Plains. Since 33% of the deck requires a Plains to cast, we want to keep the chance of drawing a Plains as high as we can get it. However, we must also acknowledge that it is easier to cast an Elite Vanguard than it is to cast a Ball Lightning. By using the progressive pattern method, it creates a happy medium between these two factors.
Until Next Time-
I will be writing another article for next week involving nonbasic lands, and I hope to continue writing new ones weekly in order to cover all of the bases on mana. To help me focus my muse, what mana-related topics interest you? Also, if youre having trouble applying the math to any of your decks, let me know and Ill help you out. Finally, if you have an alternative way of calculating your mana ratio, Id love to know about it. Comment below, I cant wait to read them!
I guess it works. It its essentially a heuristic scoring metric.
There are other (admittedly, more labor-intensive ways) of finding a good mana ratio.
Another way would be to goldfish using make-believe 5-color lands. Whenever you need to tap a color of mana, note which color you needed.
Goldfish maybe ~5-10 games and average the color costs requirements for each turn, and you'll get a good picture of which colors are most-needed by which turn.
Then use the formula for the geometric distribution to apportion your lands correctly. Essentially, this is a maximum-likelihood problem, where you attempt to maximize the probability of meeting your mana requirements on each turn by manipulating the color proportions, constrained to some number of lands.
Once the color amounts are apportioned, you can then play around with different quantities of nonbasic lands to take make things run a little smoother.
January 18, 2010 11:17 p.m.
Yay! A very informative article which I will put to use when the time comes. Thanks, mistergreen527!!!
January 18, 2010 11:55 p.m.
I use, more or less, mistergreen527's method when deciding on color quantity (before I get into things about whether or not it's worth it to have a Rupture Spire or whatever). The big advantage of it is that it's quick, easy, and provides a very solid approximation of what you need in the timed environment of a limited event. I even use it as a starting point for constructed decks, before playtesting.
Incidentally, any weird text issues in this article are my fault, not mistergreen's. I will get them remedied as soon as I can.
January 19, 2010 2:20 a.m.
Wow, I use this exact same method to determine my land distribution.. Though I have learned that sometimes its good to transfer one or two land from the largest color to the lowest color just to ensure you don't get color-screwed.
January 19, 2010 9:48 a.m.
I think I messed up somewhere in my calculations for my deck anti-jund-g/u-needs-comments. For some reason I got 6.3 for Forests and 9.45 for my Blue but I wanted my land count to be 21... Thanks if you could help!
January 19, 2010 11:16 a.m.
hmm....very interesting. maybe I could come up with a chart or some notification to calculate this for users.
January 19, 2010 11:17 a.m.
Excellent article. Although I must admit I much prefer my mana balancing.
January 20, 2010 6:26 a.m.
I love this method, the only things that I think should be mentioned in addition are:
Sometimes colorless mana should absolutely be taken into account, if all your early spells you plan on casting are artifacts and whatnot you should probably consider some land that produces EXTRA colorless mana ala' Cloudpost , card:Mishra's Workshop, or the infamous three uzra lands...
This one is more common sense but if your playing a combo deck that focused on casting a small portion of their cards as opposed to all of them, (Like my most recent submission Turn 2 Hyper Fat ) don't count the cards you will not cast. : P
Thats all, great article.
January 20, 2010 1:23 p.m.
@clustro: I can totally see how that would work. I do agree that it can take a long time to do though, so it may not be applicable in all situations, such as during a draft. I'd definitely recommend trying both methods for high-stakes tournaments though (Pro Tours/Grand Prixs), just to make sure everything is perfect.
@SageRook: Thanks and no problem. :)
@KrazyCaley: Yeah, I figured since it's pretty easy and effective, people should know about it. I wish someone had taught me how to do this when I first started playing. It would have made the decks I made back in the day much less crappy.
@MDragoon423: It's cool to know that other people out there use the same type of method. Also, I agree that actual play should trump what this equation gives you. If you're always running low on one color of mana, then you probably need to up that color, regardless of what the equation told you to use. However, I feel this gives you an excellent start and that it tends to be extremely effective. Nonbasics can help too, which I address in my second article.
@yeaGO!: Maybe it can be an optional addition to a person's deck page? I just wouldn't want to clutter someone's page with this equation if they don't agree with using it, you know?
@Squire : Thanks! Oh, and for some reason user:squire wasn't working, so I apologize for the incorrect link.
@TAMA: Thanks for reading! What's your method of mana balancing?
@Elesdee: I see what you're saying about the extra colorless mana, but I think that relates more to what I called "mana counts." I talk a little bit about this in a later article that will hopefully be up around February 1st and plan to address it further when I start addressing "mana counts" more thoroughly. Also, you're absolutely right about only counting the cards you're planning on casting. For example, I put a Reya Dawnbringer in my Back from the Dead deck, but I never plan on actually casting it, so I included no white mana sources. This also goes for anything with an alternate cost that you plan on paying, rather than the actual cost, such as with Suspend, Morph, etc.
@EVERYONE Thanks again for reading! Keep an eye out for my newest article. It should be getting posted very soon.