The next generation of Cost Theory- Net effectiveness?

[eaglgenes101]

More qualitative analyses:

Crimson dragon:
12 Attack equivalent
3 Defense equivalent
1/11 Speed
You might object that this is more powerful than ash eater, but note its high cost. It takes a lot of time to put this card on the field; with the same amount of quanta you could put tons of ash eaters on the field (With fractal, mitosis, or what), and with this on the field, the game tends to end quickly if it stays on the field. And don't forget the possibility of being outrushed while you are collecting the quanta to play it.

Collosal dragon
7 Attack equivalent
15 Defense equivalent
1/11 Speed
This thing doesn't have nearly as much attack as a crimson dragon, but it makes up for that using its very high HP, where you can stick rage pots, accelerations, or play pandemonium with less fear. Even with that, it's still considered kind of underpowered.

Spark
3 Attack equivalent
0 Defense equivalent
1 Speed
Don't think that 0 defense equivalent means it can't help you stand. Alone, this thing is only useful as a finisher, but with other cards, it can be quite good. It makes a good fodder card to stick immolations, mutations, or what to gain from it (as with photon, ash eater, and a fair number of other cards, explaining their seemingly low stats). Also, you could stick blessing, plate armor, or what to turn it into a cheap, efficient attacker. It also generates death effects automatically, so one can easily create several death effects to boost vultures, bone walls, or generate quanta with soul catchers and generate skeletons with boneyards. 

(If you noticed, I'm doing vanilla creatures first. We should build the framework using vanilla creatures, then put skills onto it. Spells have an advantage in speed compared to creature abilities, but a disadvantage in attack and defense equivalent (They can't attack like a creature, and they can only be used once per card). Defense equivalent also measure how well it can make you stand.Besides HP, other defense equivalent boosters include gravity pull (skill), heal, and vampire. )

[Pineapple]

I really think we should think of speed as a multiplication factor rather than an effectiveness additive (as suggested by your "sum up these three variables" statement)

[Zaealix]

Speed being a multiplier works...IF speed is defined properly.
That said, the vanillas are very simple, nothing more than a grid of numbers.
I'm more interested in making sure the theory can handle various types of cards.
Now for break attempt number 3. Permanents.
Permanents, in a reveral of spells, can be said to have a general Defense equivilant to the length of the game, considering the limited means of Permanent Control out there.
Explosion requires  , Pulvy needs  & ,  is needed for steal, and while  's shard is PC, it's also a very rare card, due to it's nature of being a shard.
As such, Permanents defense equivilant are almost unquantifiable, due to general lack of PC.
For the most part, it equals the time from being played to whenever the opponent gets a method of PC. Given the Lack of PC, this usually means a permanent will last until the end of the game, unless it has a built-in 'destroy condition' like BoneWall, or Phase Shield.
Can anyone find a way around this issue, or has this theory been disproven?

[OldTrees]

Speed being a multiplier works...IF speed is defined properly.
That said, the vanillas are very simple, nothing more than a grid of numbers.
I'm more interested in making sure the theory can handle various types of cards.
Now for break attempt number 3. Permanents.
Permanents, in a reveral of spells, can be said to have a general Defense equivilant to the length of the game, considering the limited means of Permanent Control out there.
Explosion requires  , Pulvy needs  & ,  is needed for steal, and while  's shard is PC, it's also a very rare card, due to it's nature of being a shard.
As such, Permanents defense equivilant are almost unquantifiable, due to general lack of PC.
For the most part, it equals the time from being played to whenever the opponent gets a method of PC. Given the Lack of PC, this usually means a permanent will last until the end of the game, unless it has a built-in 'destroy condition' like BoneWall, or Phase Shield.
Can anyone find a way around this issue, or has this theory been disproven?

Defense equivalent is a measurement for the duration of the source of the effect. While this is difficult to calculate for permanents, it could be estimated using the average number of turns the permanent stays around. This distribution would have a great deal of variance but would necessarily have a mean.

I would like to highlight a few things
The difference between 1&2 hp and between 3&4 hp are not the same.
The difference between 0&1 cost and between 1&2 cost are not the same.
A Steel Golem that cost 4 would be in play longer than a Steel Golem that cost 8 .

[eaglgenes101]

What I've been tinkering with is this:
P = K_p(A+K_f1)(S(D)+K_f2)(s+K_s)
P = Power
K_p = Constant of power (Optional)
K_f1 = Constant of fodderability
K_f2 = Constant of fodderability
K_s = Constant of speed adjustment
A = Attack equivalent
S(D) = A function of staying power for the defense equivalent (Which, ideally, would give the average number of turns survived for a 1|D creature.)
s = Speed

The "fodderability" constant refers to the ability to use cheap creatures for things other than their stats (immo, mutate, etc.) As the creature gets more expensive, the temptation to do this decreases. I think it will probably end up smaller than A or S(D).

We might need to measure these constants by recording a lot of games in different levels (AI3, FG, PvP1/2, Arena) and figuring out if they're the same in different places.

Am I on the right track?

[OldTrees]

[I do not imply anywhere in this post]
Why is the fodder constant in the defense section?

Where do you calculate how much something should cost? P1=P2?

[Zaealix]

Hrm....If Defense equivilant is how long the source lasts, then that automatically means that Spells have a defense equivilant of 0. At least with working with that theory.
Permenants are another thorny issue, with a high, and wildly varying Defense Equivilant, assuming the permenant does not have a built-in 'Timer' to it...
Anyhow, I'm going to try and create a few data entries for a few cards.
Cockatrice-Cost 3 , Attack Equivilant 4 melee damage per turn, no ability. Defense Equivilant 4 HP. Upgraded modifier: Cost+1 , +1 Melee damage, +1 HP.
Spark-Cost-0, Attack Equivilant 3 melee damage, no ability. Defense Equivilant 0 HP. Upgraded Modifier: +2 Melee damage.
Fire Bolt-Cost 3 , Attack Equivilant 3+3*( /10)
I feel the attempting to  predict how long a card lasts in a match is an inelegant method of figuring out the durability of cards, as it's less a matter of 'how long will this card last' as 'what card on my side of the field will the opponent target first?' and it would be more productive to simply view the resistance a card has to being removed from play.

[OldTrees]

Hrm....If Defense equivilant is how long the source lasts, then that automatically means that Spells have a defense equivilant of 0. At least with working with that theory.

-snip-

I feel the attempting to  predict how long a card lasts in a match is an inelegant method of figuring out the durability of cards, as it's less a matter of 'how long will this card last' as 'what card on my side of the field will the opponent target first?' and it would be more productive to simply view the resistance a card has to being removed from play.

I would mark spells as having the lowest defense equivalent however I do not believe a defense equivalent of 0 (no time at all) is possible.

In most cases the resistance a card has to being removed would have a high correlation with its average duration. Comparing relative resistances would serve the same purpose as comparing relative durations.

Durations: Instant, Next card, 1 turn, 0hp, 2 turns, 1hp, 2hp, 2 turns, 3hp, 3 turns, 4hp, 4 turns, 5hp, 5 turns, 6hp, 7hp ...
(very crude estimates of order)

[darkrobe]

I think looking at this from a defense equivalence perspective is incorrect. If you are talking about staying power of a card you have to look at the number of cards that can remove that card from play. Basically the number of hard/soft counters that are available.

A card that has 4 hp will last longer than a 1 hp card, because there are less cards that can kill a 4 hp card in one shot than there are that can kill a 1 hp card in one shot.

spells are good because the lack direct counters. not simply because they are instantaneous.

Edit: for a bit of perspective.

From a Rage potions point of view: all cards with hp <= 5 that are not immaterial are removable at 1 turn. not 5 turns in the case of a 5hp creature

[OldTrees]

I think looking at this from a defense equivalence perspective is incorrect. If you are talking about staying power of a card you have to look at the number of cards that can remove that card from play. Basically the number of hard/soft counters that are available.

A card that has 4 hp will last longer than a 1 hp card, because there are less cards that can kill a 4 hp card in one shot than there are that can kill a 1 hp card in one shot.

spells are good because the lack direct counters. not simply because they are instantaneous.

Edit: for a bit of perspective.

From a Rage potions point of view: all cards with hp <= 5 that are not immaterial are removable at 1 turn. not 5 turns in the case of a 5hp creature

Counting card by card is a bit inaccurate.
1) Infection can kill both 1hp and 4hp but the speed of death is significantly different.
2) Cards can be combined to greater effect. Thunderstorm cannot kill a Frog but multiples can.
So it is not the number of card that is relevant but rather the threat to the defense which would involve the Speed, Strength, Quantity and Nature of the counters.

The 5hp and 5 turns thing was relating how long I expected an effect with a 5 turn doom clock and a creature with 5hp to survive on average (vs the meta) relative to each other.

Spells are bad because they are instantaneous. They are good because they tend to lack reactive counters (Reflective is the only direct counter).

[eaglgenes101]

Created a sync.in public note for this:
http://sync.in/neteffectiveness

[Zaealix]

I would mark spells as having the lowest defense equivalent however I do not believe a defense equivalent of 0 (no time at all) is possible.

In most cases the resistance a card has to being removed would have a high correlation with its average duration. Comparing relative resistances would serve the same purpose as comparing relative durations.

Durations: Instant, Next card, 1 turn, 0hp, 2 turns, 1hp, 2hp, 2 turns, 3hp, 3 turns, 4hp, 4 turns, 5hp, 5 turns, 6hp, 7hp ...
(very crude estimates of order)

This data may be crude, but the idea behind it probably will work well to compare timed durations like Phase Shield or Wings to something like Bone Shield, and from there, we might even be able to create a value for everlasting permanents like pillars or Empathetic Bond.