Mage Wars > Spells
Most efficient creature
fas723:
See next post for explanation.
Equation:
Cost_calc = 0,46 x Max Attack + 1,18 x Armor + 0,55 x Health +
+2,42 x Major Trait + 1,13 x Mid Trait + 1,03 x Minor Trait - 0,65 x Negative Trait.
Ranked creatures:
Name Cost Max Attack Armor Healt Major Trait Mid Trait Minor Trait Neg Trait Cost_calc index 1 Hugin, Raven Familiar 11 1 0 5 3 2 1 0 13,86 1,26 2 Blue Gremling 7 3 1 7 0 3 0 1 9,33 1,33 3 Firebrand Imp 5 2 0 6 0 1 2 0 7,23 1,45 4 Emerald Tegu 9 3 3 8 0 1 0 0 11,03 1,23 5 Asyrian Cleric 5 2 1 6 0 1 0 0 6,84 1,37 6 Dark Pack Slayer 13 4 2 14 0 1 1 0 14,68 1,13 7 Skeletal Sentry 8 4 0 11 0 0 2 0 9,51 1,19 8 Necropian Vampiress 16 5 2 15 1 0 2 0 17,40 1,09 9 Gray Angel 12 4 2 10 1 1 0 0 13,40 1,12 10 Steelclaw Grizzly 17 7 3 15 0 2 1 0 18,16 1,07 11 Whirling Spirit 12 4 0 13 1 1 3 3 13,16 1,10 12 Goran, Werewolf Pet 15 4 3 12 1 1 0 0 16,15 1,08 13 Mana Leech 8 3 1 8 0 1 1 0 9,15 1,14 14 Highland Unicorn 13 3 2 9 1 2 0 0 13,91 1,07 15 Malacoda 16 4 3 13 1 1 0 0 16,83 1,05 16 Timber Wolf 9 4 2 10 0 0 0 0 9,82 1,09 17 Tarok, the Skyhunter 13 3 2 9 0 3 1 0 13,70 1,05 18 Darkfenne Bat 5 2 0 4 0 2 0 0 5,33 1,07 19 Sosruko, Ferret Companion 7 2 0 5 1 1 1 1 7,27 1,04 20 Moonglow Fearie 8 2 0 5 1 1 2 1 8,16 1,02 21 Thunderift Falcon 6 3 0 5 0 2 0 0 6,07 1,01 22 Mountain Gorilla 16 4 2 16 0 1 1 0 16,05 1,00 23 Brogan Bloodstone 15 4 4 11 0 2 0 1 15,03 1,00 24 Feral Bobcat 5 2 0 4 0 1 1 0 4,98 1,00 25 Stonegaze Basilisk 12 4 2 10 1 1 0 2 11,94 1,00 26 Bitterwood Fox 5 3 0 5 0 1 0 0 4,82 0,96 27 Royal archer 12 4 1 9 1 1 0 0 11,33 0,94 28 Flaming Hellion 13 4 2 9 0 1 2 0 12,16 0,94 29 Darkfenne Hydra 16 4 1 15 2 0 0 2 15,06 0,94 30 Fella, Pixie Familiar 12 2 0 6 2 1 1 0 11,02 0,92 31 Redclaw, Alpha Male 16 5 3 12 1 0 0 0 14,96 0,94 32 Knight of Westlock 13 5 3 10 0 1 0 1 11,77 0,91 33 Valshalla, Lightning Angel 21 4 1 14 1 3 2 0 19,01 0,91 34 Gorgon Archer 16 4 1 13 1 2 0 2 13,85 0,87 35 Adramelech, Lord of Fire 24 6 3 14 1 2 2 0 20,65 0,86 36 Samandriel, Angel of Light 21 5 1 14 0 3 3 0 17,62 0,84
fas723:
Hi,
I have been reading around at various forums about which is the best creature, and it seems like a mix of opinions. So here is my contribution to the discussion.
Method
What I wanted to do was to find an equation that could tell me if a creature is worth its mana cost or not, or more like; what is the efficiency of this creature compared to other creatures. A linear equation should do the work, you just have to find the proper coefficient for each attribute a creature have.
Like: Coefficient1 x Attribute1 + Coefficient2 x Attribute2 +…+ CoefficientN x AttributeN = True Mana cost.
This value could later be normalized towards the actual mana cost and a relation between creatures can be established.
I started defining which attribute a creature could have. This was harder then I thought since there are tons of them when you start looking. For example; how do you evaluate range attack vs. melee attack? Or how much is +3 piercing worth towards +2 piercing, and how does that relates to flying?
On top of all this there are too few creature cards out there to populate the sample space if more than 5-6 attributes were used.
I came up with the following model as attributes:
- Attack (max number of attack dice)
- Armor
- Health
- Major Trait
- Mid Trait
- Minor Trait
- Negative Trait
What is Major, Mid and Minor Trait then? Well in there goes all abilities that didn't have a discrete value as their property. 10 Health is always 10 Health, which is always twice as high then 5 in Health. To get discrete values for Traits I instead said; How many trait does this particular creature has in each category? After that I evaluated every Trait if it was Major, Mid or Minor. In here I also treated range attacks, defense and spell casting as Traits.
Major:
Defens inf and low
Range attack
Triple strike
Counterstrike
Raven spell cast
Raven peck card
Incorporeal
Redclaw special
Vampiric
Malacoda speciality
Sweeping
Doublestrike
Unicorn speciality
Gray Angel healing
Valshalla speciality
Fella spellcast
Mid:
Defence normal
Blue Gremling spec
Piercing
Cripple 7+
Flying
Regenerate 2
Weak 4-9 2 Weak 10+
Taunt 7+
Rot 8+
Fast
Charge +2
Rage +3
Rot 9+
Burn 8+
Piercong +2
Burn 5-9 2 Burn 10+
Goran speciality
Asyrian Healing
Unavidable
Aegis
Mana Drain
Daze 7-10 2 Daze 11+
Minor
Defence with estriction
Ethereal
+2 vs. Incorporeal
Elusive
Climbing
Defrost
Flame imunity
Necropian flying
Frost -3
Frost -2
Lightning -2
Psychic Immunity
+2 vs. Flying
Lightning immunity
Nonliving
Negative Traits got one combined category since they are too few for statistical insurance to treat separately. Instead they were getting 1,2 or 3 points.
Upkeep +1 - x3
Slow - x2
Lightning +2 - x1
Pest - x1
Curve generation:
Now all creatures were evaluated and the curve which fit the best towards all creatures could be created. I minimized the equation by using a Least Square method, with a simple Monte Carlo sampling, to generate the coefficient for the equation.
Min->(Sum (Cost_cal – True Cost)^2)
I did this back and forth a couple of times with split half method to not fall into any local minimum points.
Ranking:
Now the coefficients were optimized and all that was left was to apply the equation to every creature. Now every creature had a value which corresponds to its true mana value, not just to itself but to all other creature as well. By subtracting their stated mana cost for each creature a normalization between all creatures was done.
Summary:
The table above is my result, and it displays the ranking of all creatures with the calculate value to it. Blue gremling is the one with highest difference to is stated cost and therefore also the top ranked in this evaluation. The index column tells you how much you will get out of your mana once you casted the spell.
piousflea:
Interesting chart (and a lot of work!) but I don't think it's the greatest statistical method. There's no way to say that "Fast is exactly as good as Flying, and both of them are always inferior to Incorporeal."
The most efficient creature is the creature who's stats and abilities synergize best with your deck.
the_iron_troll:
Fascinating.
I agree, piousflea, there are some obvious methodological issues here, but this such a good idea that I'm willing to overlook them and see where I get to. I disagree that the most efficient creature is the creature that synergizes best with your deck - you also need to consider your opponent, and what kind of strategy you should choose in the first place. This kind of analysis lets you decide so many things: how many Bitterwood Foxes you should summon for each Steelclaw Grizzly, say, or whether you'd be better off leaving that Angel out of your deck. You need to take the analysis with a grain of salt, but, it's still valuable.
fas723:
I think you meant "divided", to determine the index value.
You left "Triplestrike" off the list of Traits.
If you look closely at Pest, it's not a bonus at all, it's just a penalty.
I have a large problem with the way you have calculated the coefficient for Armour. I can't do the math for it, I'm afraid, but I think if you examine how Armour works you will realize that it is much more valuable at first and then declines in value as you get more and more of it. The coefficient for Armour thus likewise needs to be nonlinear.
I have no idea how you would then calculate the value of Piercing. It's obviously more valuable as it becomes closer and closer to reducing your opponent's armour to 0. But it should probably be weighted per point of Piercing.
I don't believe your weighting of Max Attack either - there is no way it can be that low. This seems like a similar problem to Armour, but much worse - the usefulness of your attack is dependent on how much Armour your opponent has, how hard you can be hit back, and how much Health they have left (as killing a creature before it can act is Awesome).
I'm also uncertain exactly how you are calculating these sums (maybe the commas are confusing me, but I'm sure that's not all of it). Let me do a full example of Huginn, Raven Familiar to show you what I mean:
cost_calc = 3.26 x Max Attack (1) + 6.90 x Armor (0) + 4.28 x Health (5) +
+14.80 x Major Trait (3) + 9.41 x Mid Trait (2) + 3.78 x Minor Trait (1) - 3.28 x Negative Trait (0)
= 3.26 + 21.4 + 44.4 + 18.82 + 3.28
= 91.16.
Just looking at the chart seems to show other errors. Bitterwood Fox vs. Feral Bobcat, for example - if the Bobcat's extra Minor Trait of Charge +2 is worth 3.78, but the Fox's extra point of Max Attack is worth 3.26 and it's extra point of Health is worth 4.28, how exactly is the Fox ranked lower? Is Health supposed to be worth 0.428? That seems a bit low.
Klaxas:
i agree with pious. most of the traits cant be quantified. for example i dont think resistances or immunities should figure into effiency at all simply because they are either really good or worthless depending on your opponent. however i think that general effiency isnt tuned to a certain deck.
also i dont see pest listed under negative traits, which the blue gremlin should have 1.
in general when i think of effiency i think 1 how long will this creature be alive, and how much damage will it do while it is alive. so for example, if you take flying out of it, and put 2 timber wolves vs say one of the angel creatures. the 2 timber wolves are less mana and i believe with average rolls all around, the timber wolves would kill the angel (too tired to check the math though)
ok aldramelech vs 2 timber wolves. the wolves are guarding so they will get strikes back.
round 1
aldreamelech sweeps. rolls 4 damage, 2 crit 2 non (average roll) to each wolf. each wolf does the same to him.
Ald-4 damage, each wolf 2 damage.
round 2 Ald 8 damage, each wolf 4 damage.
round 3 Ald 12 damage, each wolf 6 damage
round 4 Ald 16 damage, each wolf 8 damage.
so average rolls it is a very close battle after you add in the extra damage the wolves will take from fire. but also remember the wolves are 18 mana where alramelech is 24. we need a whole other 2/3rds a wolf of life and damage output. that is what i mean by effiency
however general effiency isnt the end all of how good a creature is. in the end the best creature for your deck may not be the most effiecent one. if youve got a warlock burn deck whos whole point is to sear things to char, aldramelech will be better than the timber wolves simply because by stacking the burn they all become more effective. if youve got a pestilance deck then non living creatures will be better for you
sorry for rambling its late. night
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