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Elements the Game => Card Ideas and Art => Design Theory => Topic started by: OldTrees on February 27, 2011, 06:54:48 am

Title: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on February 27, 2011, 06:54:48 am
By now most are familiar with my card cost theory derived from the current cost of cards in the game. Despite how well it describes the cards in the game it has some large intuitive flaws in it. This series of design theory threads will attempt to cover in detail the components of a more intuitive design theory even if the result will be a more complex formula.

To start with we will discuss Resilience.

Resilience is a characteristic of a card that describes the duration of that card's effects. No effect is permanent although some are only stopped by the end of the match.

To make the start of the discussion even simpler we will start with HP of creatures.

Part of this discussion will be the attempt to quantify relative value between hp values.
To work as a baseline 4hp will be worth 1unit. If a creature with 5hp lasts on average 150% as long as 4hp then 5 would be worth 1.5 units.

So begin. What is relevant to the discussion of resilience?

Lightning|Thunderbolt
Thunderstorm|Lightning Storm
Unstable Gas|Unstable Gas
Shockwave|Shockwave
Snipe (Weapon Skill)
Unstable Gas (Creature Skill)
Infection (Creature Skill)
Nightfall|Eclipse
Drain Life|Siphon Life
Liquid Shadow|Liquid Shadow
Voodoo (Creature Skill)
Liquid Shadow (Creature Skill)
Plague (Sacrificial Creature Skill)
Scavenger (Creature Skill)
Skull Shield|Skull Buckler
Plague|Improved Plague
Alfatoxin|Alfatoxin
Alfatoxin (Creature Skill)
Plate Armor|Heavy Armor
Basilisk Blood|Basilisk Blood
Guard (Creature Skill)
Basilisk Blood (Creature Skill)
Paradox (Creature Skill)
Lycanthropy (Creature Skill)
Chaos Seed|Chaos Power
Pandemonium|Pandemonium
Fire Bolt|Fire Lance
Fire Shield|Fire Buckler
Rain of Fire|Firestorm
Growth (Creature Skill)
Rage Potion|Rage Elixir
Rage|Rage (Creature Skill)
Gravity Pull (Creature Skill)
Gravity Shield|Gravity Shield
Momentum|Unstoppable
Devour (Creature Skill)
Gravity Pull|Gravity Force
Chimera|Chimera
Catapult|Trebuchet (Permanent Skill)
Thorn Carapace|Spine Carapace
Holy Light|Holy Flash
Heal(Creature Skill)
Blessing|Improved Blessing
Endow(Creature Skill)
Swarm (Creature Skill)
Ice Bolt|Ice Lance
Inflate (Creature Skill)
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: az4rel on February 27, 2011, 07:27:34 am
well I suppose the first thing we should consider are the early game damaging or creature removing  spells
- the "cheap" CC-.
 spell                   |      damage

fire bolt                       3 in early game
rage potion                 5
rain of fire                  3  in early game
pandemonium            max.5 in early game
chaos seed                 max. 5 in early game
ice bolt                       2  in early game
drain life                    2   in early game
reverse time              only quinted, mummy and skelly immune.
poison all kinds         hp/potion counters.  usually 1, if coming from a creature it can and will grow.
Lightning                    5
Shockwave               4/ instakill if frozen
gravity pull                could be a situacional instakill
rain of fire?               3
thunder storm          1
holy ligth                   10 for dark and death.

since spells are the most imediate way of killing a creature they chould be used to balance the standart resilience vaiues.
 I've always feel safe at +5Hp.
resilence could be derived from the average turns a creature could survive and work as intended with its given Hp, also low attack ability creatures have less resilence due to reverse time and lobo.

tell me what you think is this what you intendes or am I doing it wrong ???

                                     
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on February 27, 2011, 03:51:13 pm
Yes the CC should be considered first when attempting to quantify relative lifespans. I think that only the hp dependent CC will change its effect when hp changes so things like reverse time would be useful in calculating the actual baseline but can be ignored when quantifying the relative resiliences.
5 Lightning|Thunderbolt
1 Thunderstorm|Lightning Storm
1 Unstable Gas|Unstable Gas
4 Shockwave|Shockwave
3x Snipe (Weapon Skill)
1 Unstable Gas (Creature Skill)
(x^2-x)/2 Infection (Creature Skill)
2y Drain Life|Siphon Life
x Liquid Shadow|Liquid Shadow
x Liquid Shadow (Creature Skill)
x Plague (Sacrificial Creature Skill)
x/2 Skull Shield|Skull Buckler
x Plague|Improved Plague
2x Alfatoxin|Alfatoxin
2x^2-x Alfatoxin (Creature Skill)
nx Guard (Creature Skill)
Paradox (Creature Skill)
Chaos Seed
Pandemonium|Pandemonium
3y Fire Bolt|Fire Lance
x Fire Shield|Fire Buckler
3 Rain of Fire|Firestorm
5|6 Rage Potion|Rage Elixir
5|6 Rage|Rage (Creature Skill)
Gravity Pull (Creature Skill)
Gravity Shield|Gravity Shield
Devour (Creature Skill)
Gravity Pull|Gravity Force
Thorn Carapace|Spine Carapace
10 Holy Light|Holy Flash (exception to the norm)
2y Ice Bolt|Ice Lance
(x^2+x)/2 Inflate (Creature Skill)
So how do we calculate/measure/gather data on how much more resilient 5hp is than 4hp?
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Rutarete on February 27, 2011, 04:17:03 pm
Yes the CC should be considered first when attempting to quantify relative lifespans. I think that only the hp dependent CC will change its effect when hp changes so things like reverse time would be useful in calculating the actual baseline but can be ignored when quantifying the relative resiliences.
5 Lightning|Thunderbolt
1 Thunderstorm|Lightning Storm
1 Unstable Gas|Unstable Gas
4 Shockwave|Shockwave
3x Snipe (Weapon Skill)
1 Unstable Gas (Creature Skill)
(x^2-x)/2 Infection (Creature Skill)
2y Drain Life|Siphon Life
x Liquid Shadow|Liquid Shadow
x Liquid Shadow (Creature Skill)
x Plague (Sacrificial Creature Skill)
x/2 Skull Shield|Skull Buckler
x Plague|Improved Plague
2x Alfatoxin|Alfatoxin
2x^2-x Alfatoxin (Creature Skill)
nx Guard (Creature Skill)
Paradox (Creature Skill)
Chaos Seed
Pandemonium|Pandemonium
3y Fire Bolt|Fire Lance
x Fire Shield|Fire Buckler
3 Rain of Fire|Firestorm
5|6 Rage Potion|Rage Elixir
5|6 Rage|Rage (Creature Skill)
Gravity Pull (Creature Skill)
Gravity Shield|Gravity Shield
Devour (Creature Skill)
Gravity Pull|Gravity Force
Thorn Carapace|Spine Carapace
10 Holy Light|Holy Flash (exception to the norm)
2y Ice Bolt|Ice Lance
(x^2+x)/2 Inflate (Creature Skill)
So how do we calculate/measure/gather data on how much more resilient 5hp is than 4hp?
Look at what it CAN survive and what takes multiple spells (of the same one) to kill it. 5hp can survive an upped Oty for a bit. It can also survive drain life/ice bolts for 4hp, (while the 4hp creature dies) which, the time required to get the 10 quanta (without spending any) would be (i'm guessing here) an average of 3 turns. 5hp can take one more turn with poison.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: TimerClock14 on February 27, 2011, 05:02:35 pm
I had started working on a spreadsheet that listed all the creatures in the game (with HP greater than 0), and next to it, all the cards that deal damage to creatures. I forgot about it and eventually stopped working on it, so it's unfinished, but here it is: >link< (https://spreadsheets.google.com/ccc?key=0AokbSsM9MdkzdG5ldHR5NV8wSTlEbEhNZGxxSU05SGc&hl=en&authkey=CPyHs94H)
I think it might be helpful for you guys here ^_^
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: az4rel on February 27, 2011, 07:32:48 pm
not sure if this would do any help but here is some stuf i made bases on timers spread sheet.

https://spreadsheets.google.com/ccc?hl=en&hl=en&key=tNn6j2JpVjqocgYt2z1dIVQ&authkey=CJSt5Hc#gid=0

edit: is unfinished but i got to make some homeworks.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on February 27, 2011, 07:40:30 pm
not sure if this would do any help but here is some stuf i made bases on timers spread sheet.

https://spreadsheets.google.com/ccc?hl=en&hl=en&key=tNn6j2JpVjqocgYt2z1dIVQ&authkey=CJSt5Hc#gid=0

edit: is unfinished but i got to make some homeworks.
That spread sheet is useful. Thanks.
Now we just need someone to give their quantified opinion on the relative resiliences.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: ZephyrPhantom on February 27, 2011, 08:01:44 pm
First of all, it's good to know a new theory is coming out.

Second of all, there should be 2 known facts about resilence -
Spell = 0 (Spells trigger immediatley)
Rs of Permanent > Rs of Creature (there is much more CC than PC).

The bolts and Antimatter are probably the trickiest to calculate here because their effect grows over time or has a long term effect respectively.

Third, regarding this discussion  of creature HP, I say we begin at 0 and 30  (Lowest/Highest, Spark and Massive Dragon/Elite Armagio respectively), and work inward until we find a medium that requires no guessing.

So, where do 0 HP and 30 HP fit on the scale of resilence?

0 HP is probably worth 0-1 units (possible decimal value here) due to the fact it requires a second card for the creature to become useful and can trigger death effects.

For 30 HP, I will use Massive Dragon to calculate first since it has less factors to judge.
Massive Dragon is an 8 | 30 creature with Airborne.
This means it alone takes -
12 :aether | 6 :aether for 6 Lightnings to kill it.
101 :fire quantum for 1 fire bolt to kill it.
151 :water or :darkness quantum for 1 of their bolts to kill it.
8 :entropy to turn the card into a creature that heals your opponent for 8 HP each turn.
7 :life + Shield Slot or 2 :darkness + 7 :death to kill it within 8 turns through poison.

With Armagio how important is the CC factor in relation to it's attack and effect, Gravity Pull?
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Rutarete on February 27, 2011, 09:06:10 pm
Perhaps a factor tree should be made of the list in the first post, the branches being the means of affecting. Then could use the card usage statistics if necessary.
I think the biggest branches would be Instant Removal (IR) and Removal over Time (RoT).

Then, to more appropriately put cards in their respective branch, take percentages of creatures' base stats for IR and RoT.
RoT mainly includes poison.
IR includes damaging spells.

@OT What methods did you use to create your previous theory?
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on February 27, 2011, 09:40:22 pm
Perhaps a factor tree should be made of the list in the first post, the branches being the means of affecting. Then could use the card usage statistics if necessary.
I think the biggest branches would be Instant Removal (IR) and Removal over Time (RoT).

Then, to more appropriately put cards in their respective branch, take percentages of creatures' base stats for IR and RoT.
RoT mainly includes poison.
IR includes damaging spells.

@OT What methods did you use to create your previous theory?
I am slightly unsure as to what you are describing. If you create such a tree I will add it to the OP.
However does anyone know how to create automatic updating card usage charts? I could update them once a week manually but automatic would be better.

My previous theory was derivative which means it assumed that the game was balanced and then calculated what formula would achieve the same results. So it mostly involved graphing one variable against cost and then mapping a second variable against cost-first variable. This lead to a simple arithmetic formula. While the formula is probably accurate for most ideas it has holes like a 0|10 creature is worth <0 not 3 as the formula suggests.
This theory is meant to be constructed meaning that it could be used to test how balanced the game is.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Glitch on February 27, 2011, 09:52:25 pm
I've always thought of HP as having a point of "null-neccessity", at around 6 HP.  Once a creature reaches 6 HP, the net gain in effectiveness of a card is approximately 0 as the HP increases.

How I came upon this conclusion:

CC can be sorted into tiers of how much damage it does.

The lowest tier is one dmaage, done by poison and fire shield.
Next is tier two, where only drain life, ice shield, and unupped otyugh deal exactly 2 damage.  This tier is the MOST IMPORTANT for unupgraded cards.  If a card only has 2 HP, it's worth is dramatically less than something with three HP.
Tier three is where firebolt lies.  I believe chaos seed deals 3.4 damage on average.  This tier is the MOST IMPORTANT for upgraded cards.  In the upgraded setting, the difference between 5 and 6 HP is innumerable.
Tier four is where upgraded otyugh and shockwave lie.
Tier five is for lightning bolt and rage potion.
And lastly, we arrive at tier 6.  There is no damage spell that does six damage.  Save cards like gravity pull and lobotomize, the target might as well have quintessence.  Any attempt at controlling it either requires saving up large amounts of quanta, or wasting two forms of CC.  In 90% of instances, it would be detrimental for the opponent to use spells to kill the creature.  Lobotomization, CC on a stick or reverse time are the better options.

Moving towards the stratosphere, you arrive at the tiers where voodoo doll, armagio, titan, and colossal dragon lie.  Marked only occasionally by the amount of quanta needed for a pump spell, these are the pointless areas, where only gravity pull has a use with the increased HP.  At 6 HP, adding one more point of HP no longer buffs the creature.


Mah 2 cents.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on February 27, 2011, 10:08:37 pm
Thank you Gl1tch!
That is precisely the kind of response I was hoping to find.
Now just for a few more expert gamers to post their comments upon your breakdown and or post breakdowns of their own. +1karma.

I would especially love GirlsGeneration's comment about hp 6+
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Rutarete on February 27, 2011, 10:28:44 pm
Is this going to be based on the effector - spells/abilities - or effected -hp?
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on February 27, 2011, 10:52:47 pm
Is this going to be based on the effector - spells/abilities - or effected -hp?
effected [hp]
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: jumpoffduck on February 28, 2011, 11:55:26 pm
Even though HP is probably going to be the dominant factor here, attack also plays a part (as seen in the 0/10 example stated before).

Crimson dragon and horned frog both have the same amount of HP; however, a diamond shield essentially "removes" the frog from the game, whereas the crimson dragon still can do 9 damage per turn. This fits in with the original definition of resilience, since the shield ends the duration of the frog's effects.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 01, 2011, 12:03:27 am
Even though HP is probably going to be the dominant factor here, attack also plays a part (as seen in the 0/10 example stated before).

Crimson dragon and horned frog both have the same amount of HP; however, a diamond shield essentially "removes" the frog from the game, whereas the crimson dragon still can do 9 damage per turn. This fits in with the original definition of resilience, since the shield ends the duration of the frog's effects.
Correct we will get to observing the other effects on resilience after a few more posts like Gl1tch's on hp.

Once we have hp understood then we can go into non HP CC and even non creatures.

Also Resilience will only be 1 part of the final value equation. I will make another thread for the next topic when this is done/further along.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: az4rel on March 01, 2011, 02:00:14 am
ok, part 1 of my spread sheet  (https://spreadsheets.google.com/ccc?hl=en&hl=en&key=tNn6j2JpVjqocgYt2z1dIVQ&authkey=CJSt5Hc#gid=0)is finished proving what Gl1tch said.
but i would leave the null point at 7-8 because of owlseye, upped oty , upped rage and maybe some poison spells and abilities and paradox.

now how to give a value to each hp amount?

Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 01, 2011, 03:42:52 am
ok, part 1 of my spread sheet  (https://spreadsheets.google.com/ccc?hl=en&hl=en&key=tNn6j2JpVjqocgYt2z1dIVQ&authkey=CJSt5Hc#gid=0)is finished proving what Gl1tch said.
but i would leave the null point at 7-8 because of owlseye, upped oty , upped rage and maybe some poison spells and abilities and paradox.

now how to give a value to each hp amount?
To estimate the value of each hp amount just make an educated guess after setting an arbitrary hp as 1unit

For example
HP
0Special Case
19/24|9/24
23/8|3/8
33/4|1/2
41|1
54/3|4/3
616/9|16/9
I guessed that each tier shift was a multiplier of 4/3 except the most important shifts 2.5|3.5 that were a multiplier of 2. This was using my poor guess work and Gl1tch's divisions. For HP 7+ I would prefer to get a sceond opinion from a Gravity expert to double check Gl1tch's wisdom. Gl1tch having been a Master of Life knows a lot about low hp from the Life creatures.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Boingo on March 01, 2011, 04:53:35 am
I've always thought of HP as having a point of "null-neccessity", at around 6 HP.  Once a creature reaches 6 HP, the net gain in effectiveness of a card is approximately 0 as the HP increases.

How I came upon this conclusion:

CC can be sorted into tiers of how much damage it does.

The lowest tier is one dmaage, done by poison and fire shield.
Next is tier two, where only drain life, ice shield, and unupped otyugh deal exactly 2 damage.  This tier is the MOST IMPORTANT for unupgraded cards.  If a card only has 2 HP, it's worth is dramatically less than something with three HP.
Tier three is where firebolt lies.  I believe chaos seed deals 3.4 damage on average.  This tier is the MOST IMPORTANT for upgraded cards.  In the upgraded setting, the difference between 5 and 6 HP is innumerable.
Tier four is where upgraded otyugh and shockwave lie.
Tier five is for lightning bolt and rage potion.
And lastly, we arrive at tier 6.  There is no damage spell that does six damage.  Save cards like gravity pull and lobotomize, the target might as well have quintessence.  Any attempt at controlling it either requires saving up large amounts of quanta, or wasting two forms of CC.  In 90% of instances, it would be detrimental for the opponent to use spells to kill the creature.  Lobotomization, CC on a stick or reverse time are the better options.

Moving towards the stratosphere, you arrive at the tiers where voodoo doll, armagio, titan, and colossal dragon lie.  Marked only occasionally by the amount of quanta needed for a pump spell, these are the pointless areas, where only gravity pull has a use with the increased HP.  At 6 HP, adding one more point of HP no longer buffs the creature.
Some initial thoughts starting with a refinement of Gl1tch's post (which did a lot of heavy lifting for this thread):

1.  Ice shield does not do damage.  It removes attack ability (temporarily) for those with high enough attack to be affected but it does not actually affect hp.
2.  As for "tier 6": upped rage potion does 6 damage.  if a creature has 7 hp or more, it benefits from RP, if not it simply dies

Consider special situations:
     a.  freeze/shockwave:  essentially any targetable creature can be killed with this combo, independent of hp.  Ice shield now becomes a factor if attack >1 (2 for permafrost).
     b.  airborne/guard considerations:  guard will only lower hp if creature is not airborne.  Therefore airborne creatures might deserve some small token of added resilience.
     c.   phoenix:  the low hp is deceptive in these creatures.  They are the epitome of resilient as the can be "reborn" at very low cost.  Only liquid shadow, lobotomize + other CC or a large enough otyugh/scarab/mutant with devour (to eat the ash) can remove them from the game.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: az4rel on March 03, 2011, 02:19:33 am
maybe
 average turns in field ~  resilence aproach could be better
things like phoenix got low Hp but high resilense.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 03, 2011, 03:32:55 am
maybe
 average turns in field ~  resilence aproach could be better
things like phoenix got low Hp but high resilense.
This is already the case
Resilience is 1 of 3 large variables for my new constructed theory.

Each of these 3 large variables has both a primary definition and components

Resilience is the average duration of a card's effects per effect against an undefined competitive deck.

Resilience is made of many components
A) Resistance to Control
 a1) HP
 a2) means of attack (Immaterial, Momentum, Dark/Death, Water/Other)
 a3) Recovering (Heal, Growth, Ablaze, Steam, Rebirth ...)
B) Lasting Effects
 b1) Damage
 b2) Poison
 b3) Destruction (quanta, creatures, permanents)

However we always start with the easiest steps so we are currently analyzing HP's effect on resilience.

Since nobody has responded to my previous bait of a probably wrong relative Resilience based on hp I decided to try a better version to see if it agrees with the intuitions.

How does this look?
HPUnupped Relative Resilience
1.70
2.85
3.95
41
51.15
61.20
101.30
151.60
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: az4rel on March 06, 2011, 03:41:04 am
How does this look?
HPUnupped Relative Resilience
1.70
2.85
3.95
41
51.15
61.20
101.30
151.60
I think the resilense shoul grow more on 6-7 hp as it can survibe much more than 4.

a graph resilience- hp would be losely like this https://docs.google.com/drawings/edit?id=1rRUARv0B8laXW87ibLxaO1dqNv4XAvskHrZ9Sl-pQJI lol.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 06, 2011, 03:48:06 am
I think the resilense shoul grow more on 6-7 hp as it can survibe much more than 4.

a graph resilience- hp would be losely like this https://docs.google.com/drawings/edit?id=1rRUARv0B8laXW87ibLxaO1dqNv4XAvskHrZ9Sl-pQJI lol.
The google doc is not public access. aka I can't see it.

I think you are right because those higher hp creatures I looked at had higher costs which decreases resilience (due to being played later.)

PS: This thread is related to Resilience. If anyone can answer my question and or offer assistance once the question is answered I would Greatly appreciate it.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Rutarete on March 06, 2011, 04:03:17 am
Literally, what affects it. But that's already in the first post.
But what's really relevant to resilience is its' comparative worth. You can compare it to (broadly) games, ex. MTG, ETG, etc. Or on a different scale, compare it to current resilience, attack (in some ways the opposite of resilience), costs and more.
But even if everything had zero hp which is (ex.) worth a value of zero, they'd all still not be the same due to the other factors.
I'm not sure if this is relevant, but there's also the scale to consider. For example Yugioh is in the thousands while ETG is in the ones and tens.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 06, 2011, 04:15:24 am
Literally, what affects it. But that's already in the first post.
But what's really relevant to resilience is its' comparative worth. You can compare it to (broadly) games, ex. MTG, ETG, etc. Or on a different scale, compare it to current resilience, attack (in some ways the opposite of resilience), costs and more.
But even if everything had zero hp which is (ex.) worth a value of zero, they'd all still not be the same due to the other factors.
I'm not sure if this is relevant, but there's also the scale to consider. For example Yugioh is in the thousands while ETG is in the ones and tens.
Exactly relative resilience is more important then objective resilience. Hence I set an arbitrary hp (4) as resilience 1 and compared the other hp to the resilience of that hp.

I think comparing True Vanilla creatures that are also considered exemplary balanced would be a good point once I have a means to account for the effect of casting cost on resilience.

Also 0hp is definitely not a resilience of 0, as long as it survives to make a single attack then it has some resilience.

I was specifically talking about the scale of Nhp vs (N+1)hp in ETG.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Rutarete on March 06, 2011, 04:30:32 am
The zero as zero value was an example.
(off topic) I wonder if we can compare resiliences like different currencies...
Anyway, the problem with with setting an arbitrary hp and comparing is that while resilience is relative, it doesn't have the right 'ways' to be compared more 'correctly'.
Another way of saying that is 1/2 plus 2/3. you have to make them the same scale 3/6 + 4/6 to add them, or in this case, compare them
so that should be a big focus
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 06, 2011, 04:53:14 am
The zero as zero value was an example.
(off topic) I wonder if we can compare resiliences like different currencies...
Anyway, the problem with with setting an arbitrary hp and comparing is that while resilience is relative, it doesn't have the right 'ways' to be compared more 'correctly'.
Another way of saying that is 1/2 plus 2/3. you have to make them the same scale 3/6 + 4/6 to add them, or in this case, compare them
so that should be a big focus
Yes. What I did was make guesses at
1hp/4hp=A
2hp/4hp=B
3hp/4hp=C
4hp/4hp=D
5hp/4hp=E
6hp/4hp=F
10hp/4hp=G
15hp/4hp=H
2hp/1hp=B/A

on a side note. I do not expect a lot of addition with this theory. mostly multiplication.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Rutarete on March 06, 2011, 05:13:28 am
The zero as zero value was an example.
(off topic) I wonder if we can compare resiliences like different currencies...
Anyway, the problem with with setting an arbitrary hp and comparing is that while resilience is relative, it doesn't have the right 'ways' to be compared more 'correctly'.
Another way of saying that is 1/2 plus 2/3. you have to make them the same scale 3/6 + 4/6 to add them, or in this case, compare them
so that should be a big focus
Yes. What I did was make guesses at
1hp/4hp=A
2hp/4hp=B
3hp/4hp=C
4hp/4hp=D
5hp/4hp=E
6hp/4hp=F
10hp/4hp=G
15hp/4hp=H
2hp/1hp=B/A

on a side note. I do not expect a lot of addition with this theory. mostly multiplication.
That means an equation is needed
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 06, 2011, 05:15:55 am
That means an equation is needed
I am not sure an equation more than a set of values is needed for this factor (hp).
After all it is discrete values we are dealing with not a continuous line.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Rutarete on March 06, 2011, 09:35:21 pm
That means an equation is needed
I am not sure an equation more than a set of values is needed for this factor (hp).
After all it is discrete values we are dealing with not a continuous line.
Maybe to find a comparative value take an ETG card and see how it's affected/affects the normalcy of a different game. The bigger the difference, the bigger the range of values.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Midnar on March 08, 2011, 09:07:10 pm
At this point I start wondering if anybody read this (http://elementscommunity.org/forum/index.php/topic,16655.msg294132#msg294132). I added the big part in an edit a week ago, so it may have gone unnoticed. The formula I suggest is based on logarithm (sorry for the complicated math). Since it fits this topic better, I'll just copy-paste it:

I tried a formula and was amazed by how well it works with every vanilla creature ! First, the ideas behind the formula:
- The more HP a creature has, the less important it is to give it more hp. Therefore, resilience is not a linear function of hp's, but rather a logarithmic one.
- Many vanilla creatures are X/5 with a cost of X quantas, suggesting that resilience of 5hps creatures is 1. I thus tried the base-5 logarithm, but it was no good. This is because...
- All creatures (except 0hp creatures) have a "base resilience", because it's possible that the opponent will not have any creature control, making hp's uninmportant.
- In other words, resilience = (chance to survive despite CC) + (chance to survive because the opponent lacks CC) = logarithmic part + static part

And now, the (temporary) formula:
Resilience = (log5(hp)+1) / 2
With only one adjustment to make: Life creatures get one free hp.

Here are the theoretical costs of all unupped vanilla creatures, using this formula:
Abomination: 5
Purple dragon: 10
Flesh Spider: 2.52, rounds up to 3 (not taking Web into account)
Mummy: 4.27, rounds to 4 (not taking it's passive into account)
Bone dragon: 10
Skeleton: .5, rounds to 1 (version 1.27 will boost it with a new ability, making it less UP)
Graviton mercenary: 3 =/= 4
Colossal dragon: 9.39, rounds to 10
Hematite golem: 4.23, rounds to 4
Gnome rider: .72, rounds to 1 (this one will generate quanta with next update)
Horned Frog: 2.15, rounds to 2
Cockatrice: 3.37, rounds to 3
Emerald Dragon: 10
Ash Eater: 1
Crimson Dragon: 10.10, rounds to 10
Blue Crawler: 2.52, rounds to 3
Ice Dragon: 9.51, rounds to 10
Photon: .5, rounds to 0
Golden Dragon: 12.15, rounds to 12
Dragonfly: 0.72, rounds to 1 (same as Gnome Rider)
Azure Dragon: 9.51, rounds to 10
Devonian Dragon: 10
Black Dragon: 10
Phase Spider: 2.86, rounds to 3 (not taking Web into account)
There's only one discrepancy : Graviton Mercenary. Now just look at card usage statistics: Graviton Mercenary is underused. Meaning that it is probably UP, which is what the formula suggests. The only non-rare creatures used less than Graviton Mercenary are Blue Crawler (also slightly UP according to the formula) and Hematite Golem (balanced, but overshadowed by the OP Graboid).

About upgraded creatures: using either -1 or -2 depending what we need to match the actual card cost isn't the good way to do. We could take inspiration from spells. Low-cost spells get a 1-quantum reduction to their cost when upgraded. High-cost spell get a 2-quanta reduction. I'll work on this later, time for dinner now  :P
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 08, 2011, 10:14:51 pm
Wow...
Wow...

That is great. It had gone unnoticed thanks for repeating it.

It has a good constructed theory.
[Resilience = Constant x Probability of no CC + Function of Hp x Probability of CC]
I personally think that the underlined part is incomplete because cheaper cards are more resilient that expensive cards. (currently testing this to see if is significant enough for an official version of the theory.)

Also it has already been tested for accuracy by comparing to creatures already in the game and the general wisdom about those card.

For now the CPR theory has no determined function between unupped and upgraded (aka the CPR theory does not use the -1.5 function yet.)

I owe you karma. You did what I have been waiting for. You beat me to a solution/model that fit better.

I petition everyone who is reading this thread to give Midnar at least 1 point of karma.
Midnar I will add you in the list of authors in the final thread.

For now I will quickly see how this works on the difficult dragons and other true vanilla creatures (non  :darkness :death :water :rainbow).

Once again thank you!
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Midnar on March 08, 2011, 10:46:08 pm
Wow, my first point of karma ! I'm grateful  :D
I said I was going to work on the upgraded formula, but finally I didn't because the lack of any response kinda demoralized me. Now I'm really motivated, but tired (it's quarter to midnight in France). I'll work on this tomorrow, promise !
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Midnar on March 09, 2011, 01:38:24 pm
After doing the calculations for the upgraded cards, I found that the resilience formula I suggested overrates high-hp creatures and underrates low-hp creatures. I changed the formula slightly, giving more weight to the base resilience; this mostly fixed the problem.
New formula: Resilience = (log5(hp)+2) / 3

Recalculation for unupped vanilla and semi-vanilla creatures using the new formula:
CreatureTheoretical costActual costNotes
Abomination55
Purple Dragon1010
Flesh Spider2.683Ignoring web
Mummy4.474Ignoring the passive
Bone Dragon1010
Skeleton.671Ignoring the passive
Graviton Mercenary34Discrepancy
Colossal Dragon8.9610New discrepancy
Hematite Golem4.154
Horned Frog2.432
Cockatrice3.583
Emerald Dragon1010
Ash Eater1.331
Crimson Dragon10.7310
Blue Crawler2.683
Ice Dragon9.3410
Photon.670
Golden Dragon11.4412
Azure Dragon9.3410
Devonian Dragon1010
Black Dragon1010
Phase Spider3.243Ignoring Web
Graviton Mercenary was already discussed. Colossal Dragon is also UP imo (i was actually surprised when my first formula assessed it as being balanced).


Upped vanilla and semi-vanilla creatures, always accounting upgrade as a 1-quantum cost reduction:
CreatureTheoretical costActual costNotes
Micro Abomination.911
Amethyst Dragon11.4511
Flesh Recluse4.373Ignoring web; Discrepancy
Elite Mummy3.473Ignoring the passive
Ivory Dragon1010
Skeleton.621Ignoring the passive
Graviton Guard22
Massive Dragon10.7911
Steel Golem5.734Discrepancy
Giant Frog3.052Discrepancy
Elite Cockatrice3.773
Jade Dragon12.1712
Ruby Dragon11.1512
Abyss Crawler5.234Discrepancy
Arctic Dragon1211Discrepancy
Light Dragon13.1813
Sky Dragon12.9112
Silurian Dragon11.4012
Black Dragon11.4512
Phase Recluse4.674Ignoring Web
All 5 discrepancies can be fixed by accounting upgrade as a 2-quanta cost reduction, as initially suggested by OldTrees. However, I currently do not understand why some creatures should get a 2-quanta bonus from the upgrade, while most of them only get 1.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 09, 2011, 04:51:24 pm
After doing the calculations for the upgraded cards, I found that the resilience formula I suggested overrates high-hp creatures and underrates low-hp creatures. I changed the formula slightly, giving more weight to the base resilience; this mostly fixed the problem.
New formula: Resilience = (log5(hp)+2) / 3

All 5 discrepancies can be fixed by accounting upgrade as a 2-quanta cost reduction, as initially suggested by OldTrees. However, I currently do not understand why some creatures should get a 2-quanta bonus from the upgrade, while most of them only get 1.
As you said in the other thread HP should be a factor in the Power variable due to catapult and acceleration.
I assume these calculations were under the old Power=attack model.

The 1-2 cost reduction was the old formula. This formula uses a different basis and thus most likely will have a different resulting upgrade factor. As you said before that factor will probably proportional to the original total Cost.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Midnar on March 10, 2011, 09:55:54 am
As you said in the other thread HP should be a factor in the Power variable due to catapult and acceleration.
I assume these calculations were under the old Power=attack model.

The 1-2 cost reduction was the old formula. This formula uses a different basis and thus most likely will have a different resulting upgrade factor. As you said before that factor will probably proportional to the original total Cost.
Indeed, I used the Power = Attack (+ HP/50) model I mentionned in the other thread. HP/50 is only added for gravity creatures (for all other creatures it would barely make a difference of .1 or so).
I tried to make the factor proportional to the original cost, but this definitely doesn't work. For some reason, the creatures that get the best upgrades are the small ones (e.g. Flesh Spider gets +3|+0 for free, while Crimson Dragon gets +3|-1 and +2 CC).
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Rutarete on March 24, 2011, 01:59:28 am
How goes this? Is Part 1 done?
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 24, 2011, 02:22:54 am
How goes this? Is Part 1 done?
No part one is not done yet. Midnar got too busy to return my PMs and I was not able to duplicate his results when I tried to derive it.

Although the values of his constants have not been confirmed, his structure seems accurate.

Resilience = Base Resilience relative to the prevalence of relevant Control in the metagame + Fraction of control that can affect it x Resilience to that control.

Resilience to HP control is a function of HP with a decreasing slope like a Log function.

However I am not sure what function to use or what to set the constants at.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: Manipul8r on March 30, 2011, 11:21:50 am
I'm fairly new to the metagame, but wouldn't those previously mentioned special cases normalize the values to some extent?  Unless the 'freeze', 'delay', 'reverse time', and 'invert attack' effects aren't used very often, I would think that might be the case.  -HP effects would be replaced by those effects when facing a higher HP creature in actual gameplay, so in my opinion, resilience would not increase so drastically from 5 to 6 HP.  Could resilience against special effects be quantified?

Anyhow, I love this thread, it's an excellent idea.
Title: Re: Constructed Design Theory [Part 1:Resilience]
Post by: OldTrees on March 30, 2011, 01:12:56 pm
I'm fairly new to the metagame, but wouldn't those previously mentioned special cases normalize the values to some extent?  Unless the 'freeze', 'delay', 'reverse time', and 'invert attack' effects aren't used very often, I would think that might be the case.  -HP effects would be replaced by those effects when facing a higher HP creature in actual gameplay, so in my opinion, resilience would not increase so drastically from 5 to 6 HP.  Could resilience against special effects be quantified?

Anyhow, I love this thread, it's an excellent idea.
You are right that since the only hp difference from 5-6 is against Lightning and Rage Potion that the increase should be minor.

HPUnupped Relative Resilience
1.70
2.85
3.95
41
51.15
61.20
101.30
151.60
So the resilience from 5->6 is 1.20/1.15=1.04 or a 4% increase in resilience

Unfortunately this numbers do not fit a significant amount of vanilla(no effect) creatures and thus are likely to be flawed.
blarg: