Just had a thought: When evaluating colour balance, how about subtotalling gold cards by their respective colours? For example, if your entire gold selection was Lightning Helix and Electrolyze, that would give you totals of 1 white, 2 red and 1 blue. That way each colour can get it's fair share of the gold pie, without having a rigid colour scheme that forces you to play suboptimal cards to 'fill out' the quota for a colour combination.
Hybrid can be accounted for with the same system, but with hybrid totals.
I think we then should count Lightning Helix as 0.5 red and 0.5 white. This way Nicol Bolas, Planeswalker doesn't count as three cards in the colour pie, but as 3 times 1/3. Otherwise gold cards would have more relative weight then mono coloured cards.
Just had a thought: When evaluating colour balance, how about subtotalling gold cards by their respective colours? For example, if your entire gold selection was Lightning Helix and Electrolyze, that would give you totals of 1 white, 2 red and 1 blue. That way each colour can get it's fair share of the gold pie, without having a rigid colour scheme that forces you to play suboptimal cards to 'fill out' the quota for a colour combination.
Hybrid can be accounted for with the same system, but with hybrid totals.
Could be an interesting experiment.
Without having run the numbers, I know for example that in our cube some color combinations have no hybrids, and others have 50% hybrids. Having Kird Ape under RG kinda skews the numbers too. I don't like the idea to have a separate gold/hybrid section because some color combinations have great hybrids and others don't, and quota would force me to include sub-par cards, but using a weighting system could mean that it's ok to include one more card in a certain color combination than in others, because the overall 'color weight' remains similar.
I'm running the numbers on this one, thanks magicmerl.
I think we then should count Lightning Helix as 0.5 red and 0.5 white. This way Nicol Bolas, Planeswalker doesn't count as three cards in the colour pie, but as 3 times 1/3. Otherwise gold cards would have more relative weight then mono coloured cards.
But gold cards ARE heavier to play than mono colored cards, so this should be reflected in the color weight. I do think that it might make sense to count hybrid mana in this fashion, each mana symbol having a weight of 1/2 for each color.
EDIT: For perfect weight calculation, it should be taken into account what the CMC of the card is. RR is heavier than RR6. This might be taking it to far, though. I am going to see if it's a lot of trouble to include this parameter.
One of the arguments for doing this could be that you can actually run more RG cards than WU cards. This would make sence because there's many good RG cards, that are better than mono-green/mono-red cards. Therefor you could run a single RG card instead of ½ red and ½ green one.
On the other hand there aren't many good WU cards, and you might have to run some mediocre ones instead of just ½ white and ½ blue card more.
If you can devise a more flexible organization system, while still maintaining overall balance between the colors, then you have improved your ability to include the best cards magic has to offer.
Let's not keep our goal out of sight here before we start crunching any numbers without a practical application.
What exactly is this trying to accomplish?
The goal is to find out the 'weight' of each color combination in the multi-color section, to see if there are large difference between sections.
With the basic 'number of slots' method, Kird Ape will have the same weight in RG as Niv-Mizzet in UR. It could also factor in the easier-to-cast hybrids without having to resort to sub-sections.
If it means I can include an extra RG card without upsetting the color balance, I'd hate to pass it up!
Before we start to figuring out how to balance hybrid and multicolored cards, we need to figure out how to balance the colors themself, according to the number of colored manasymbols in their casting cost.
For instance how do we weigh WW vs 1W?
How do we weigh 2WW vs 3W?
And how do we weigh a WWWW card?
Bonda's Mana Weight Formula:
I would say the formula for weight should be something like M^2/CMC, where M is the amount of colored manasymbols in the cost.
For instance:
W will be weighed at 1^2/1 = 1
1W will be weighed at 1^2/2 = 0.5
WW will be weighed at 2^2/2 = 2
1WW will be weighed at 2^2/3 ~ 1.3
2WW will be weighed at 2^2/4 = 1
3W will be weighed at 1^2/4 = 0.25
WWWW will be weighed at 4^2/4 = 4
I think this simple formula captures what we want to do with weights on cards, without complicating things to much. I've thought of many formulas for this, but I likes this most because of the simplicity, while it still gives us what we want.
Cards that weigh lower than 1 are generally cards that can be splashed. While cards with weigh of higher than 1 are generally more difficult to splash. Further more a cards with a weight between 1 and 2 are cards that you can play in a two-color deck quite easy. While cards with weigh over 2 are cards that are hard to play in non mono-color decks (or close to mono-color decks).
Bondafong, I like that idea, but I'm worried about the actual numbers. A 1W card seems more splashable than a W card, but is it two times more splashable? And is a 3W card four times as splashable as a W? That seems a bit extreme. I would suggest something a bit more conservative when it comes to the colorless mana symbols, like each 1 = -.1 or at most .2. So:
You could reduce the impact of high cost exponentially as Phantizle described by dividing by the root of the total CMC in each instance, rather than the total CMC. That will normalize the numbers slightly. EDIT: I need to rethink this, it doesn't quite work yet.
Bondafong, I like that idea, but I'm worried about the actual numbers. A 1W card seems more splashable than a W card, but is it two times more splashable? And is a 3W card four times as splashable as a W? That seems a bit extreme. I would suggest something a bit more conservative when it comes to the colorless mana symbols, like each 1 = -.1 or at most .2. So:
W = 1 1W = .9 or .8 2W = .8 or .6 3W = .7 or .4
The weight is only a guideline for splashability (especially for the low CMC cards), as it doesn't factor in how soon the cards needs to be played. Expensive cards are usually late game cards, and most cheap ones are early game cards, but this is not always true. In general though, I think this formula works perfectly. In fact, I had come up with the exact same one and am crunching numbers on my multi-color section using it.
For this formula, I'm counting hybrids as weighing in at only 0.25 instead of 0.5, otherwise a RG2 card will have the same weight as a (R/G)(R/G)2card, which is obviously not right.
There's several reasons why I like this formula (some described above).
I call weight W.
It's simple.
There's a linear dependency between W and CMC (W=CMC) in the subset of cards where M=CMC.
If you add more colorless mana to a castingcost the W of the card will drop. This works very well with splashing, because the best cards to splash are often ones with high CMC, but only a single colored mana symbol. A rule of thumb is that a card that cost 5U are more desirerable to splash, than a card costing 3U.
Cards that have CMC=1 and M=1 have W=1. Cards that have CMC=4 and M=2 have W=1. I think this is important because these two cardtypes are the backbone of most decks, and that these sets of cards are most often played in two-color decks, and aren't splashed.
So even though there's a lot of difference between 0.5 and 0.25 I don't think this is a problem, unless we will add the Weights together to determine something more complex.
So even though there's a lot of difference between 0.5 and 0.25 I don't think this is a problem, unless we will add the Weights together to determine something more complex.
Ahhh. I thought this was the whole idea, to try to balance the "intensiveness" of each color. If that's not the point, I must be missing the purpose. What is it?
Ahhh. I thought this was the whole idea, to try to balance the "intensiveness" of each color. If that's not the point, I must be missing the purpose. What is it?
Well, you should be able to compare certain sets of cards, but not necessarily just 5 random cards, to another 5 random cards, and make any sence out of it. The idea is ofcourse in the end to find each colors total Weight, so we can balance that way.
I wouldn't balance each color for its weight. Different colors perform differently, and go in different archetypes. It's the same reason that you shouldn't balance CMC perfectly across all colors. Some will be higher, and others will be lower, playing of of the color's strengths. Likewise, some colors will contain more actual colored mana symbols than others do, and I think it should be that way.
Well, you should be able to compare certain sets of cards, but not necessarily just 5 random cards, to another 5 random cards, and make any sence out of it. The idea is ofcourse in the end to find each colors total Weight, so we can balance that way.
I don't think that you need to come up with a total weight for a color. Instead just figure out how many cards are suited for mono-color decks, two-color decks and how many are good for splashes. I can't think of a good reason to balance these distributions evenly within the colors, but it should help point out any glaring problems, such as having too many mono-color cards.
While I like the calculations that are being explored here, that wasn't what I was saying originally.
What I was meaning is that if you have for example, no good UR cards in your cube, you can run the following card counts:
0 UR
6 UW
6 UG
6 UB
6 WR
6 GR
6 BR
3 BG
3 BW
3 GW
And each colour has exactly the same number of gold cards.
Edit: Sorry that that didn't really contribute to where the thread currently is at. I like the 'splashability index' that is proposed here, although it's something that I've always understood at a more intuitive level. I'd regard a card as needing a weight of <0.5 to be splashable. And X spells I'd put down X as being 3 or 4 depending on the card.
I wouldn't balance each color for its weight. Different colors perform differently, and go in different archetypes. It's the same reason that you shouldn't balance CMC perfectly across all colors. Some will be higher, and others will be lower, playing of of the color's strengths. Likewise, some colors will contain more actual colored mana symbols than others do, and I think it should be that way.
I agree. Colors shouldn't be balanced by weight, cardtype or CMC's. That is taking it too far. But more numbers are always fun.
I certainly wouldn't want to draft white in your cube. Those mana consistency figures are shocking...
I think there is a limit to how much mathematical analysis can help with cube design. In my mind, this analysis has gone beyond that limit.
I do, however, think that Eidolon deserves one of those trophy things for his polite, detailed and high quality advice in response to almost every new cube posted in this forum
"When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean - neither more nor less." -Lewis Carroll, Through the Looking Glass
eidolon gets props from me too. Very friendly, and goes the extra mile for each new cube thread posted in this forum. We may not agree on every point, but his input is always appreciated.
Hurray for Eidolon! The attention he gives to any cube and the depth of his analysis never ceases to amaze me. Thumbs up!
As for the number crunching, I couldn't get very useful information out of it.
But the re-ordering of the sections did open my eyes to certain things. For instance, I never realized how few cards our cube has that can actually go in every deck (only 66, and that's including the colorless lands). Mishra's Workshop is probably a wasted slot as there are just not enough cards to cast with it, even if our artifact section was as big as the color sections (not very surprising actually with all the mana stuff).
Do you guys think it could be worthwhile to add some more artifacts, so that there are more cards in the cube any color could play? Or do you think there aren't enough artifacts to add that are good enough?
Do you guys think it could be worthwhile to add some more artifacts, so that there are more cards in the cube any color could play? Or do you think there aren't enough artifacts to add that are good enough?
Sorry to bump this, but - anyone care to share his thoughts on this?
I don't think that's necessary. If all decks end up with enough playables at the end of the draft, why add more cards that specifically go in all decks?
Well, having enough playables surely hasn't been a problem in our cubes - sometimes it hurts to see insane cards sitting in sideboards!
So, good point - I suppose the colorless section doesn't need to be as large as the color sections.
So, if I compare my cards per manacost with eidolon's, I'll get similar numbers. Cool! The calculations seem interesting.
The cubability of a card is linked to the question, if the card can be played reliably and splashed easily. Therefore I think that a balance of the casting costs is unnecessary, whereas the evaluation of a card relies heavily on its casting cost.
Cards with a casting cost like Cryptic Command should be as good as Cryptic Command to be considered cubeworthy.
I follow what seems to be the consensus on this board in balancing the amount of cards, which act like colours and adding nonbasics and cards like Vedalken Shackles and Crystal Shard to their respective colours.
I guess the evaluation under the aspect of splashability and reliability plus the balance of the uncolored cards/lands which work only in a certain colour is enough to keep it cube.
Your ideas serve as good food for thought for the development the cube. People should always keep the balance in their cubes between the colours and archetypes.
@artifacts:
Nope, your cube looks like there shouldn't be any problems with enough playable cards after the draft. We got some crazy sideboards and hatepicks sometimes. For example: Player A firstpicks Dark Confidant, but doesn't end up being aggro, so it stays in the sideboard. No worries, it's the cube after all.
Private Mod Note
():
Rollback Post to RevisionRollBack
To post a comment, please login or register a new account.
I think we then should count Lightning Helix as 0.5 red and 0.5 white. This way Nicol Bolas, Planeswalker doesn't count as three cards in the colour pie, but as 3 times 1/3. Otherwise gold cards would have more relative weight then mono coloured cards.
I feel compelled to repeat everything I hear
Could be an interesting experiment.
Without having run the numbers, I know for example that in our cube some color combinations have no hybrids, and others have 50% hybrids. Having Kird Ape under RG kinda skews the numbers too. I don't like the idea to have a separate gold/hybrid section because some color combinations have great hybrids and others don't, and quota would force me to include sub-par cards, but using a weighting system could mean that it's ok to include one more card in a certain color combination than in others, because the overall 'color weight' remains similar.
I'm running the numbers on this one, thanks magicmerl.
But gold cards ARE heavier to play than mono colored cards, so this should be reflected in the color weight. I do think that it might make sense to count hybrid mana in this fashion, each mana symbol having a weight of 1/2 for each color.
EDIT: For perfect weight calculation, it should be taken into account what the CMC of the card is. RR is heavier than RR6. This might be taking it to far, though. I am going to see if it's a lot of trouble to include this parameter.
On the other hand there aren't many good WU cards, and you might have to run some mediocre ones instead of just ½ white and ½ blue card more.
My Tribal cube
My 93/94 old school cube
My Artifact cube
My Hearthstone Quiz App for iOS
The goal is to find out the 'weight' of each color combination in the multi-color section, to see if there are large difference between sections.
With the basic 'number of slots' method, Kird Ape will have the same weight in RG as Niv-Mizzet in UR. It could also factor in the easier-to-cast hybrids without having to resort to sub-sections.
If it means I can include an extra RG card without upsetting the color balance, I'd hate to pass it up!
EDIT: what Phantizle said.
For instance how do we weigh WW vs 1W?
How do we weigh 2WW vs 3W?
And how do we weigh a WWWW card?
Bonda's Mana Weight Formula:
I would say the formula for weight should be something like M^2/CMC, where M is the amount of colored manasymbols in the cost.
For instance:
Cards that weigh lower than 1 are generally cards that can be splashed. While cards with weigh of higher than 1 are generally more difficult to splash. Further more a cards with a weight between 1 and 2 are cards that you can play in a two-color deck quite easy. While cards with weigh over 2 are cards that are hard to play in non mono-color decks (or close to mono-color decks).
My Tribal cube
My 93/94 old school cube
My Artifact cube
My Hearthstone Quiz App for iOS
W = 1
1W = .9 or .8
2W = .8 or .6
3W = .7 or .4
On spoiled card wishlisting and 'should-have-had'-isms:
The weight is only a guideline for splashability (especially for the low CMC cards), as it doesn't factor in how soon the cards needs to be played. Expensive cards are usually late game cards, and most cheap ones are early game cards, but this is not always true. In general though, I think this formula works perfectly. In fact, I had come up with the exact same one and am crunching numbers on my multi-color section using it.
For this formula, I'm counting hybrids as weighing in at only 0.25 instead of 0.5, otherwise a RG2 card will have the same weight as a (R/G)(R/G)2card, which is obviously not right.
I call weight W.
My Tribal cube
My 93/94 old school cube
My Artifact cube
My Hearthstone Quiz App for iOS
Ahhh. I thought this was the whole idea, to try to balance the "intensiveness" of each color. If that's not the point, I must be missing the purpose. What is it?
Well, you should be able to compare certain sets of cards, but not necessarily just 5 random cards, to another 5 random cards, and make any sence out of it. The idea is ofcourse in the end to find each colors total Weight, so we can balance that way.
So I agree with you in some sence.
My Tribal cube
My 93/94 old school cube
My Artifact cube
My Hearthstone Quiz App for iOS
My 630 Card Powered Cube
My Article - "Cube Design Philosophy"
My Article - "Mana Short: A study in limited resource management."
My 50th Set (P)review - Discusses my top 20 Cube cards from OTJ!
I don't think that you need to come up with a total weight for a color. Instead just figure out how many cards are suited for mono-color decks, two-color decks and how many are good for splashes. I can't think of a good reason to balance these distributions evenly within the colors, but it should help point out any glaring problems, such as having too many mono-color cards.
What I was meaning is that if you have for example, no good UR cards in your cube, you can run the following card counts:
0 UR
6 UW
6 UG
6 UB
6 WR
6 GR
6 BR
3 BG
3 BW
3 GW
And each colour has exactly the same number of gold cards.
Edit: Sorry that that didn't really contribute to where the thread currently is at. I like the 'splashability index' that is proposed here, although it's something that I've always understood at a more intuitive level. I'd regard a card as needing a weight of <0.5 to be splashable. And X spells I'd put down X as being 3 or 4 depending on the card.
Edt2: bondafong, please humour me:
(out->in)
sence->sense
I agree. Colors shouldn't be balanced by weight, cardtype or CMC's. That is taking it too far. But more numbers are always fun.
My Tribal cube
My 93/94 old school cube
My Artifact cube
My Hearthstone Quiz App for iOS
My 630 Card Powered Cube
My Article - "Cube Design Philosophy"
My Article - "Mana Short: A study in limited resource management."
My 50th Set (P)review - Discusses my top 20 Cube cards from OTJ!
I think there is a limit to how much mathematical analysis can help with cube design. In my mind, this analysis has gone beyond that limit.
I do, however, think that Eidolon deserves one of those trophy things for his polite, detailed and high quality advice in response to almost every new cube posted in this forum
My 380 Beginners’ Cube on Cube Tutor
"When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean - neither more nor less." -Lewis Carroll, Through the Looking Glass
My 630 Card Powered Cube
My Article - "Cube Design Philosophy"
My Article - "Mana Short: A study in limited resource management."
My 50th Set (P)review - Discusses my top 20 Cube cards from OTJ!
As for the number crunching, I couldn't get very useful information out of it.
But the re-ordering of the sections did open my eyes to certain things. For instance, I never realized how few cards our cube has that can actually go in every deck (only 66, and that's including the colorless lands). Mishra's Workshop is probably a wasted slot as there are just not enough cards to cast with it, even if our artifact section was as big as the color sections (not very surprising actually with all the mana stuff).
Do you guys think it could be worthwhile to add some more artifacts, so that there are more cards in the cube any color could play? Or do you think there aren't enough artifacts to add that are good enough?
Sorry to bump this, but - anyone care to share his thoughts on this?
Well, having enough playables surely hasn't been a problem in our cubes - sometimes it hurts to see insane cards sitting in sideboards!
So, good point - I suppose the colorless section doesn't need to be as large as the color sections.
Thanks for the feedback guys.
The cubability of a card is linked to the question, if the card can be played reliably and splashed easily. Therefore I think that a balance of the casting costs is unnecessary, whereas the evaluation of a card relies heavily on its casting cost.
Cards with a casting cost like Cryptic Command should be as good as Cryptic Command to be considered cubeworthy.
I follow what seems to be the consensus on this board in balancing the amount of cards, which act like colours and adding nonbasics and cards like Vedalken Shackles and Crystal Shard to their respective colours.
I guess the evaluation under the aspect of splashability and reliability plus the balance of the uncolored cards/lands which work only in a certain colour is enough to keep it cube.
Your ideas serve as good food for thought for the development the cube. People should always keep the balance in their cubes between the colours and archetypes.
@artifacts:
Nope, your cube looks like there shouldn't be any problems with enough playable cards after the draft. We got some crazy sideboards and hatepicks sometimes. For example: Player A firstpicks Dark Confidant, but doesn't end up being aggro, so it stays in the sideboard. No worries, it's the cube after all.