Opinions/Feedback on Mana Base Calculations
Deck Help forum
Posted on Jan. 20, 2012, 9:12 a.m. by ZaLiTHkA
I'm not really asking for help with a specific deck (although the contents of this post are related to a specific deck: Artificer's Toys). Just did a little experiment with calculating the mana base for this deck, and it's actually pretty interesting.. I was wondering if anybody else uses a similar method, or maybe has some criticism/suggestions for this method. :)
I put a list of all non-land cards into a spreadsheet (have a look here), followed by the card count, and the mana cost per symbol per card. Then using formulas, I summed up different ways of looking at the CMC of each card and all cards together. I'm sure I could find a better layout and labels, but this was just a quick 5 minute job to test a theory.
Looking at the spreadsheet I linked to, looking at individual mana symbols, there's a total cost of 41 Colourless, 16 White, 23 Blue and 4 Black (note: I counted the White/Black symbol from Esper Stormblade as one-half for each because for statistical purposes, it is actually 'one or the other'). Total 'Card Count CMC' for this deck is 84 excluding reductions or casting modifiers (such as those from the Sculptors or Heralds).
In addition to the colour balance, seeing the total 'Card Count CMC' also gives an impression of whether you need more lands or not.. No direct calculations there, it's really just a judgement call, but obviously if that value is over 100, you'll need more lands than if it's only sitting at 60 or 70.
So, crunch time.... :) What do you guys think? Is this a good way to work out colour balance for the mana base? Are there maybe other factors I should be taking into account? Keep in mind I'm not considering card draw odds or 'mana at turn X' in game turns, this is just a straight-forward individual mana count.
Thanks Anarchnachist, that's actually pretty helpful... But it seems more geared to finding the optimal number of land cards to match the non-land cards. My idea is focused on balancing the colours produced by the land cards. :)
I'm only just getting into three colour decks, so balancing the ratio of (for example) Plains/Island/Swamp is pretty important if you want the deck to be reliable.
Also, with the exception of decks with lots of high cost cards, I'd say mana search search cards are only necessary in four and five colour decks. In a three colour deck if it's balanced well enough, then you don't really need it. Well, at least not for casual play anyway (I don't play tournament level, there's nowhere nearby where I can)..
January 20, 2012 11:21 a.m.
If you guys can nail down a formula, I can build this into the interface
January 20, 2012 12:15 p.m.
Arachnarchist I don't think that's the correct calculation, since card draw chances are modelled by a hypergeometric distribution, you can use the hypgeomdist function in excel to work it out. I normally use this http://ark42.com/mtg/land.php to work out land numbers and according to that you need 27 land to have an average of 5 land by turn 5.
January 20, 2012 12:25 p.m.
Arachnarchist says... #6
I checked out that website. In my analysis above, I assumed you drew first, not played first. If you play first your right with 27 lands for 5 by turn 5. If you draw first, it's 25 according to that chart as well as my calculations.
January 20, 2012 3:06 p.m.
Maybe I should outline what I'm trying to achieve here... :)
Small colourless cards like Steel Overseer or even large ones like Blightsteel Colossus are dead easy to plan for; It's simple supply and demand, you need this much of any mana to cast it.
Now take a card like Praetor's Counsel or Stormtide Leviathan for example. Looking at your usual graphs, it's simply "a blue card" or "a green card". But in game, those cards require much more specific mana draw, and even more specific in multicoloured decks.
Cards such as Prince of Thralls or Sphinx Sovereign make things even more difficult because of the number of colours involved.
I've put up a slightly more refined spreadsheet to try explain it better than the first one (link). Pay particular attention to the values marked in blue in the bottom-right corner; those are the values that I think should be used when deciding on the distribution of colours in your deck's mana base of X cards (however many you decide you need).
@yeaGO!: As for how to integrate this idea into the website, maybe something styled the same as the Mana Curve graph (i.e.: a bar graph) with simply the total number of symbols in each colour would work pretty well? Here's a mockup for reference. After all, that is the bottom line in my spreadsheet... I was just trying to explain how I got there and asking for any suggestions on if / how that calculation could be improved.
January 20, 2012 3:18 p.m.
Oh, and just some food for though: with that mockup bar graph, I used the exact same cards to do the 'Mana Symbol Count' graph (with my calculations) as the site already used for 'Mana Curve' graph. :)
January 20, 2012 3:22 p.m.
Would trying to isolate each card to have a "Castability" score help? Is this in the direction you are going?
January 20, 2012 3:25 p.m.
Also, above what you've done is give the distribution of how many mana symbols appear in your deck--how is that different from what the Card cost (outer ring) of the top chart does? You've gone one further and added colorless, but that's the only difference I see.
January 20, 2012 3:29 p.m.
When you say 'castability', you're referring to the mana cost to actually cast a spell? If so, then yeah, that's dead right.
AS far as I can tell, the ring chart (or double pie chart if you will) shows the number of cards in each colour. So for 2x Redirects for example, it would show 2 Blue. While casting two of them would actually cost 4 Blue.
Essentially I like to look at cards by the number of coloured symbols in the cost, not just it's overall cost and card colour. See what I mean?
January 20, 2012 4:26 p.m.
My reasoning behind this is having a deck with an equal number of both White and Blue doesn't necessarily mean it will work with equal White/Blue mana..
Many Blue cards require multiple Islands; so to make the deck more viable, it may actually need (for example) 12 Island and 8 Plains, as opposed to 10 of each.
Arachnarchist says... #2
The first thing I would do is take all non-land cards and find the average converted mana cost. I would then take that number and round up and add 1 to it. That's the number of land drops I would want to hit every turn starting from the first.
I know my method is confusing, so let me give an example:
Average converted mana cost is 4. Add 1 and you want to hit your first 5 land drops
You start with 7 and draw one each turn so on turn 5 you will have drawn 12 cards.
5/12 is about 0.42. So the number of lands you want to have is 0.42 * 60 = 25.
Obviously this doesn't account for any mana acceleration or extra card draws. But the reason I use it is so I know I can play the majority of my cards at the earliest possible time.
January 20, 2012 9:45 a.m.