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Author Topic: Most efficient Creature 2  (Read 6141 times)

fas723

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Most efficient Creature 2
« on: February 24, 2013, 01:30:38 PM »
See next post for explanation.

Equations:

Calculated cost = 0.38*Attack + 2.29*Armor^(1/2) + 0.45*Health + 1.74*Trait

Attack = max(Attack1 or Attack2) + 0,3*min(Attack1 or Attack2)

AttackX = Dies * [2*sum(AttackTrait)/max(AttackTrait)+1] * AttackType^(0.74)

Ranked creatures:

   Name      True Cost      Attack      Armor      Health      Trait      Calc Cost      Diff Cost      Index   
   1      Thunderift Falcon      6      1,90      0,00      2,22      5,31      9,43      3,43      1,57   
   2      Blue Gremling      7      2,85      2,29      3,11      1,82      10,07      3,07      1,44   
   3      Gray Angel      12      2,53      3,24      4,45      4,61      14,83      2,83      1,24   
   4      Ludwig Boltsorm      13      8,26      3,24      4,00      0,00      15,51      2,51      1,19   
   5      Earth Elemental      20      7,68      0,00      15,57      -0,84      22,41      2,41      1,12   
   6      Asyrian Cleric      5      1,27      2,29      2,67      0,70      6,93      1,93      1,39   
   7      Bitterwood Fox      5      1,90      0,00      2,22      2,52      6,64      1,64      1,33   
   8      Tarok, the Skyhunter      13      3,23      3,24      4,00      4,05      14,53      1,53      1,12   
   9      Flaming Hellion      13      6,24      3,24      4,00      0,84      14,32      1,32      1,10   
   10      Orc Butcher      8      2,53      2,29      4,45      0,00      9,27      1,27      1,16   
   11      Timber Wolf      9      2,53      3,24      4,45      0,00      10,22      1,22      1,14   
   12      Necropian Vampiress      16      6,33      3,24      6,67      0,98      17,22      1,22      1,08   
   13      Darkfenne Bat      5      1,65      0,00      1,78      2,80      6,22      1,22      1,24   
   14      Feral Bobcat      5      1,27      0,00      1,78      3,07      6,12      1,12      1,22   
   15      Dark Pack Slayer      13      4,30      3,24      6,23      0,28      14,05      1,05      1,08   
   16      Emerald Tegu      9      2,47      3,97      3,56      0,00      10,00      1,00      1,11   
   17      Mana Leech      8      2,20      2,29      3,56      0,84      8,89      0,89      1,11   
   18      Cervere, The forest Shadow      15      2,53      3,24      4,89      5,17      15,84      0,84      1,06   
   19      Sosruko, Ferret Companion      7      2,91      0,00      2,22      2,66      7,79      0,79      1,11   
   20      Psylok      8      3,54      0,00      3,56      1,68      8,78      0,78      1,10   
   21      Skeletal Sentry      8      2,53      0,00      4,89      0,98      8,40      0,40      1,05   
   22      Firebrand Imp      5      1,77      0,00      2,67      0,84      5,28      0,28      1,06   
   23      Dwarf Kriegsbiel      11      3,94      3,97      4,00      -0,70      11,21      0,21      1,02   
   24      Iron Golem      13      3,80      5,13      5,78      -1,54      13,17      0,17      1,01   
   25      Highland Unicorn      13      1,90      3,24      4,00      3,91      13,06      0,06      1,00   
   26      Whirling Spirit      12      5,06      0,00      5,78      1,12      11,96      -0,04      1,00   
   27      Darkfenne Hydra      16      8,11      2,29      6,67      -1,12      15,96      -0,04      1,00   
   28      Steelclaw Grizzly      17      5,94      3,97      6,67      0,28      16,86      -0,14      0,99   
   29      Brogan Bloodstone      15      6,07      4,59      4,89      -0,70      14,85      -0,15      0,99   
   30      Royal archer      12      5,51      2,29      4,00      0,00      11,80      -0,20      0,98   
   31      Goblin Grunt      4      1,90      0,00      1,78      0,00      3,68      -0,32      0,92   
   32      Goblin Builder      5      1,27      0,00      2,67      0,56      4,49      -0,51      0,90   
   33      Goblin Bomber      8      9,27      0,00      2,22      -4,19      7,30      -0,70      0,91   
   34      Sir Corazin, Bladmaster      16      4,54      2,29      5,78      2,66      15,27      -0,73      0,95   
   35      Goran, Werewolf Pet      15      3,28      3,97      5,34      1,54      14,13      -0,87      0,94   
   36      Valshalla, Lightning Angel      21      4,81      2,29      6,23      6,71      20,04      -0,96      0,95   
   37      Knight of Westlock      13      3,16      3,97      4,45      0,42      12,00      -1,00      0,92   
   38      Mountain Gorilla      16      2,53      3,24      7,12      2,10      14,99      -1,01      0,94   
   39      Thorg, Chief Bodyguard      17      3,16      4,59      5,34      2,80      15,88      -1,12      0,93   
   40      Goblin Slinger      7      2,94      0,00      2,67      0,00      5,61      -1,39      0,80   
   41      Redclaw, Alpha Male      16      3,16      3,97      5,34      2,10      14,57      -1,43      0,91   
   42      Samandriel, Angel of Light      21      6,01      2,29      6,23      5,03      19,56      -1,44      0,93   
   43      Adramelech, Lord of Fire      24      8,53      3,97      6,23      3,63      22,36      -1,64      0,93   
   44      Fella, Pixie Familiar      12      1,52      0,00      2,67      6,15      10,34      -1,66      0,86   
   45      Hugin, Raven Familiar      11      0,95      0,00      2,22      6,15      9,32      -1,68      0,85   
   46      Moonglow Fearie      8      1,77      0,00      2,22      1,68      5,67      -2,33      0,71   
   47      Malacoda      16      3,80      3,97      5,78      0,00      13,55      -2,45      0,85   
   48      Gorgon Archer      16      6,53      2,29      5,78      -1,12      13,49      -2,51      0,84   
   49      Stonegaze Basilisk      12      3,25      3,24      4,45      -2,10      8,84      -3,16      0,74   
   50      Selesius, the East Wind      21      4,52      2,29      5,78      5,03      17,63      -3,37      0,84   
   51      Invisable stalker      15      3,80      0,00      3,11      4,19      11,10      -3,90      0,74   
   52      Thoughtspore      8      0,63      0,00      3,11      -0,42      3,33      -4,67      0,42   
[td]   53   [/td]     [td]   Grimson Deadeye, sniper   [/td]     [td]   15   [/td]     [td]   3,74   [/td]     [td]   2,29   [/td]     [td]   4,00   [/td]     [td]   0,00   [/td]     [td]   10,04   [/td]     [td]   -4,96   [/td]     [td]   0,67   [/td]
[/tr]                                                                                       
                                                                                    
[/table]

fas723

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Re: Most efficient Creature 2
« Reply #1 on: February 24, 2013, 01:33:28 PM »
Hi,
Now with the new expansion I thought it would be appropriate to update my calculation of the most efficient creature. If you haven't read the last thread on the topic please take a look here.

I have changed the calculation quite substantially since last time. Good thing is that it shows rather similar results which would indicate that both of them are fairly correct. Last time we have discussion about how to treat trait. I have now changed this to a much more robust model whist is also more discrete.

The equation now only contains 5 variables instead of 6 (which make it more stable) and looks like this now:

Calculated cost = x1*Attack+x2*Armor^(1/2)+x3*Health+x4*Trait

Attack:
The attack part of the equation is described like this:

Attack = max(Attack1 or Attack2)+0,3*min(Attack1 or Attack2)

(This means a creature with two attacks will get a bonus of 30% for its worse attack. It is strictly better to have two vs. one attack opportunity)

Followed by

AttackX = Dies*[2*sum(AttackTrait)/max(AttackTrait)+1]*AttackType^(y1)

(Each attack will hereby include how powerful it is, which effects it has and how fast/slow it is. It also takes care of if it is range or melee type. The AttackTrait part will be in the range of 1-3. In this way I can control that Triple strike is three times better them regular strikes and that double strike is twice as good. max(AttackTrait) is equal to 20 according to the present evaluation setup (see table below))

Attack Type:
This attribute follow this table:
Slow Melee = 1
Fast Melee = 2
Slow Range 1-2 = 3
Slow AOE = 3
Slow Range 1-3 = 4
Fast range 1-2 = 4

Since variable y1 is the power of AttackType it will accommodate exactly how valuable the each AttackType is towards each other, with the lowest number at 1.

AttackTrait:
I have evaluated and ranked each trait in two categories; the ones who takes place with an attack (AttackTrait) and the ones who are always active (Trait).

20   Triplestrike
18   Counterstrik
15   Double strike or Sweeping
13   7+ Taunt
12   Doublestrike
11   Sweeping
10   Vampiric
10   Critical damage
10   Slam 5-10 Stun 11+
9   Slam 7+
8   Weak 4-9 2 Weak 10+
8   Burn 5-9 2 Burn 10+
8   Piercing +3
7   Burn 7-10 2 Burn 11+
7   Piercing +2
7   Daze 7-8 Stun 9+
6   Push 7-10 Push & Daze 11+
6   Daze 7-10 Stun 11+
6   Daze 7-10 2 Daze 11+
6   Unavidable
5   Push 7+
5   Mana Drain +2
5   Piercing +1
4   Taunt 7+
4   Cripple 7+
3   Burn 8+
3   Rot 8+
3   Daze 9+
3   Rot 9+
3   Mana Drain +1
2   Ethereal
2    +2 vs. Flying
2    +2 vs. Incorporeal
1    +1 vs. Nonliving or Dark
1   Defrost
0   None
-5   Grimson Deadeye, sniper

Trait:

Trait =  2*sum(Trait)/max(Trait)

Note that the “+1” from AttackTrait is now gone. We don’t want a positive addition for creatures that doesn’t have any passive traits. max(Trait) is equal to 25 according to the present evaluation setup (see table).

25   Thorg. Chief Bodyguard spec
24   Defence 5+ inf
22   Invisible
20   Defence 6+ inf
20   Flying
19   Defence 6+ 2x
18   Fast
17   Incorporeal
16   Defence 8+ 1x
16   Valshalla speciality
15   Redclaw special
15   Malacoda speciality
14   Rage +3
14   Charge +2
13   Gray Angel healing
12   Goblin builder spec
12   Thoughtspore spell cast
12   Raven spell cast
12   Fella spellcast
11   Goran speciality
10   Aegis 1
9   Defence 7+ 1x no range
8   Defence 8+ 1x no range
7   Regenerate 2
7   Unicorn speciality
6   Flame immunity
6   Psychic Immunity
6   Lightning immunity
6   Wind immunity
5   Asyrian Healing
5   Necropian flying
5   Blue Gremling spec
5   Raven peek card
4   Tough -2
3   Elusive
2   Frost -3
2   Flame -2
2   Frost -2
2   Lightning -2
1   Unmovable
1   Nonliving
1   Climbing
1   Burnproof
0   None
-5   Lightning +2
-8   Pest
-10   Upkeep +1
-15   Slow
-30   Goblin Bomber spec

Method:
The method is as last time. I have improved it a bit to reach convergation a bit faster.

Summary:
No matter how you play around with the figures it always comes down to how you evaluate your traits. I have done my best to evaluate them as good as possible. Now I would like you to comment if you feel some are better or worse than my estimation. Remember all traits are normalized later on in the equation so it is a relative evaluation that must be done.

piousflea

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Re: Most efficient Creature 2
« Reply #2 on: February 24, 2013, 02:29:43 PM »
Fas723, I disagreed with your methodology for the first "most efficient" thread, and I still disagree with it now.

The traits and attributes in Mage Wars have such complicated interactions that it is nonsensical to assign a mathematical "efficiency" to any one trait. Just a few examples:

1) Nonliving. Is it a bonus, or is it a penalty? I would argue that for the Skeletal Sentry it is a major bonus, giving immunity to Pestilence, Deathlock, Malacoda, and Psychic spells. However, for the Earth Elemental it is a really major penalty, because you cannot use Nature enchantments (ie Bear Strength or Cheetah Speed) or heals on Nonliving.

2) Falcons vs Foxes. The falcon has the same stats but gains Flying for only 1 mana. Most people would agree that this makes it very underpriced when you just compare stats. However, the Fox synergizes much better with Redclaw and Animal Kinship, to such a large degree that many swarm decks prefer Foxes over Falcons.

-----
I think it would be far more valid to reverse-engineer the "expected mana value" of Health, Armor, and quick action melee attack die - ignoring all traits, abilities, and ranged attacks.

Then you could say stuff like, "An Emerald Tegu costs 1.83 more mana than it would without any traits or abilities, so you are paying 1.83 mana for 8+ Rot.", or "A Falcon only pays 1 mana for Flying which is pretty sweet.", or "Boltstorm pays 5 mana for his triplestrike 3 dice 1-1 ranged attack, which is really awesome."

fas723

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Re: Most efficient Creature 2
« Reply #3 on: February 24, 2013, 03:10:31 PM »
Piousflea, I see what you are saying and I think I have good news for you.

There are now 4 creatures with no Traits what so ever: Timber Wolf, Goblin Slinger, Orc Butcher and Goblin Grunt.
So I did the same calculation with only these four. What surprised me was that all variables came out almost the same as when all creatures were included (and all Traits variables set to 0). It means the model actually takes care of the Emerald Tegu issue you have as example.

In the Falcon vs. Fox example I agree with you. What you say also shows up in the evaluation, but synergies will not. Still good enough for making a good estimate. When doing these types of calculations you have to remember that combinations of cards, and their benefits, are not included. Same goes for synergies from conjurations, enchantments and incantations.

However I have treated all traits with the "When-you-get-most-out-of-the-trait-approach" when I made my table. Nonliving is a hard one I know...but that is what I wrote in the summary as well.

You can still disagree with me, but in my view at the end all these errors we are talking about will even out and the table will be quite valid.  :P  :)

HeatStryke

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Re: Most efficient Creature 2
« Reply #4 on: February 24, 2013, 04:59:44 PM »
Another, simpler take on efficiency is simply determining how much damage a creature is likely to do ober it's lifespan.
Consider the average damage of all attacks and compare it to the defensive capability of a creature.

I don't have my math on me at the moment.l, but if I remember right in a pure sandbox test the Grizzly comes out on top.

MrSaucy

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Re: Most efficient Creature 2
« Reply #5 on: February 24, 2013, 05:50:21 PM »
Quote from: "piousflea" post=7983
Fas723, I disagreed with your methodology for the first "most efficient" thread, and I still disagree with it now.

The traits and attributes in Mage Wars have such complicated interactions that it is nonsensical to assign a mathematical "efficiency" to any one trait. Just a few examples:

1) Nonliving. Is it a bonus, or is it a penalty? I would argue that for the Skeletal Sentry it is a major bonus, giving immunity to Pestilence, Deathlock, Malacoda, and Psychic spells. However, for the Earth Elemental it is a really major penalty, because you cannot use Nature enchantments (ie Bear Strength or Cheetah Speed) or heals on Nonliving.

2) Falcons vs Foxes. The falcon has the same stats but gains Flying for only 1 mana. Most people would agree that this makes it very underpriced when you just compare stats. However, the Fox synergizes much better with Redclaw and Animal Kinship, to such a large degree that many swarm decks prefer Foxes over Falcons.

-----
I think it would be far more valid to reverse-engineer the "expected mana value" of Health, Armor, and quick action melee attack die - ignoring all traits, abilities, and ranged attacks.

Then you could say stuff like, "An Emerald Tegu costs 1.83 more mana than it would without any traits or abilities, so you are paying 1.83 mana for 8+ Rot.", or "A Falcon only pays 1 mana for Flying which is pretty sweet.", or "Boltstorm pays 5 mana for his triplestrike 3 dice 1-1 ranged attack, which is really awesome."


This exactly. When I think efficiency I think, how much attack and staying power am I getting with a creature considering how much I am paying for it? Here is a suggestion. Give a creature an offensive rating and a defensive rating. Average the two ratings to give a creature a final, tentative rating.

Offensive rating = (# attack dice rolled) + (# attacks available for use) + (3 points for each attack that does an effect outside of damage, like stun, burn, etc.) - (total mana cost) - (points taken up in spellbook).

Defensive rating = (# armor) + (# life) + (3 points for having the Counterstrike ability) + (3 point for having a Defense) - (total mana cost) - (points taken up in spellbook).

Rating = (offensive rating + defensive rating)/2
"See you space cowboy..."

fas723

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Re: Most efficient Creature 2
« Reply #6 on: February 25, 2013, 03:22:00 AM »
Not to dissapoint you MrSaucy, but this is exactly what is done. Just in  a more detailed fashion.  ;)