Arcane Wonders Forum

Mage Wars => Spells => Topic started by: fas723 on October 04, 2012, 12:32:36 PM

Title: Most efficient creature
Post by: fas723 on October 04, 2012, 12:32:36 PM

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

Title: Re: Most efficient creature
Post by: fas723 on October 04, 2012, 12:33:01 PM

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.

Title: Re: Most efficient creature
Post by: piousflea on October 04, 2012, 10:18:56 PM

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.

Title: Re: Most efficient creature
Post by: the_iron_troll on October 05, 2012, 02:49:54 AM

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.

Title: Re: Most efficient creature
Post by: Klaxas on October 05, 2012, 03:17:53 AM

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

Title: Re: Most efficient creature
Post by: fas723 on October 05, 2012, 04:55:45 AM

Hi,
Nice that you had some comments! I was excpecting that, to tweak the calculation.
I'm out of town this weekend, so I will comment all your conserns on Monday. I could also attached the Excel I made then, it is kind of big though...

Title: Re: Most efficient creature
Post by: Arcanus on October 05, 2012, 10:54:07 AM

Wow! Very impressive!

The math behind Mage Wars is extremely complicated.  We use over 70 spreadsheets to govern the math.  We called in a team of programmers to help refine and finalize the algorithms used.  In the end, it's what held Mage Wars up the longest.

One of the challenges was determining how much are the attack dice and armor are worth.  The value of the attack dice is based upon the armor of the target.  If typical creatures in your games have high armor, then the value of each additional attack die becomes exponential.  If most creatures have armor 0-1, then additional attack dice tend to "flatline".  The typical armor of creatures will depend upon who you are playing, and the creatures available in the set, their mana cost (frequency of appearance) and their durability (how likely they are to remain in the arena).  The actual formula by necessity has iterations in it based on these factors, and in the end is really more of a "good calculated guess supported by playtesting results"!   :)

The values for Flying, Fast, Incorporeal, are similarly based upon how effective they are based on current creatures and attacks.  For example, if 70% of attacks are Ethereal, then Incorporeal has a lot less meaning. Or, if your opponent is usually low on ranged attacks and flyers, then a single buffed flyer can wreak havoc against him.

The value of each creature trait is dependent on who you are playing against, and the likelihood of encountering creatures or spells which work well or poorly against their traits.  The math shifts slightly too with each new expansion release, as new traits and abilities change the relative values of past traits.  To some degree the math is based on Mage Wars as a whole, including sets that won't be released until 2013.

Another interesting challenge was determining how to scale mana cost based on creature size.  If 2 creatures both have the same attack, but one has twice the Life, how much more is that worth?  Certainly not double,or else you could buy 2 of the smaller creatures for the same price, who would be dealing 2X the damage.  We originally used a logarithm to scale creatures, so that as they double in durability or effectiveness (attack) their value increases by 60%.  Later, as new methods were introduced making it easier to control larger creatures effectively, and as guarding evolved so that smaller creatures were more important, we had to change our scaling to use a square root so that the increase was closer to 41%

The real value of a creature depends upon your own spellbook synergy (what works best with the other spells you have), and what the other player is going to play. However, all of that being said, it is important to determine some average value for each trait, attack, and creature, so that mana costs are in a reasonably fair range, and consistent. In the end, that's what we tried to accomplish.

I am impressed by the math being done here and I am curious what conclusions are drawn and what players think!

Title: Re: Most efficient creature
Post by: Shad0w on October 05, 2012, 11:03:55 AM

You covered most of what I was going to talk about. :cheer:

Title: Re: Most efficient creature
Post by: Arcanus on October 05, 2012, 11:17:07 AM

Sorry Shadow!  Please feel free to elaborate!

Title: Re: Most efficient creature
Post by: the_iron_troll on October 06, 2012, 02:09:16 AM

Arcanus, this is why I love Mage Wars. The dedication to your craft, the sheer amount of effort that has been put into this game; it's just incredible.

Title: Re: Most efficient creature
Post by: Arcanus on October 06, 2012, 12:20:54 PM

Wow!  Thanks - that is so appreciated!  We worked so hard on this for so many years.  We wanted to make the ideal mage combat we as gamers would want to play.  Thanks for noticing!   :)

Title: Re: Most efficient creature
Post by: piousflea on October 06, 2012, 11:00:52 PM

Quote from: "Arcanus" post=1789

Another interesting challenge was determining how to scale mana cost based on creature size.  If 2 creatures both have the same attack, but one has twice the Life, how much more is that worth?  Certainly not double,or else you could buy 2 of the smaller creatures for the same price, who would be dealing 2X the damage.  We originally used a logarithm to scale creatures, so that as they double in durability or effectiveness (attack) their value increases by 60%.  Later, as new methods were introduced making it easier to control larger creatures effectively, and as guarding evolved so that smaller creatures were more important, we had to change our scaling to use a square root so that the increase was closer to 41%

If the mana-cost exponent was exactly a square-root (41%) then a creature with 2x HP and 2x attack would cost exactly 2x as much mana. Interesting that it comes out so close to the "intuitive" figure.

The relative value of Attack and Armor is interesting. Armor has steeply diminishing returns while Attack is linear against zero-armor, but has slightly ascending returns against armored foes.

For example, for a 3 dice attack vs. 0 Armor:
+1 armor decreases expected damage from 3.00 to 2.30 (+0.70 incremental mitigation)
+2 armor decreases expected damage from 2.30 to 1.81 (+0.49 incremental mitigation)
+3 armor decreases expected damage from 1.81 to 1.61 (+0.20 incremental mitigation)

For a 3 dice attack vs. 2 armor:
+1 attack (4 dice) increases expected damage from 1.81 to 2.59 (+0.78 incremental damage)
+2 attack (5 dice) increases expected damage from 2.59 to 3.43 (+0.84 incremental damage)
+3 attack (6 dice) increases expected damage from 3.43 to 4.31 (+0.88 incremental damage)

Regarding the OP,
I disagree with the entire methodology of pre-assigning a point value to major/mid/minor traits. A trait such as "Flying" should be worth a very different amount depending on whether the creature is very weak or very strong. (ie, a Darkfenne Bat vs Samandriel) Other traits such as "nonliving" can be either very strong or totally useless depending on what other cards are in play.

IMO a better methodology (and probably closer to the actual game designer's database) would be to define a number of points ("expected mana value") based on base stats only (that's HP, Armor and melee attack dice). Then we can see how much extra mana we are paying for the abilities.

Judging by Arcanus's post it sounds like they are multiplying HP and Attack. (that is, double HP is worth a *141% multiplier, double attack is worth *141%, together they are worth *200%) I would expect that Armor is a multiplier as well. Using the mitigation numbers posted above (assuming the average source of incoming damage is 4 attack dice), we get:
0 Armor: 0% mitigation, equivalent to *100.0% HP = *100% mana value
1 Armor: Approx. 20% mitigation, equivalent to *125.1% HP = *111.8% mana value
2 Armor: Approx. 35% mitigation, equivalent to *154.3% HP = *124.2% mana value
3 Armor: Approx. 44% mitigation, equivalent to *177.0% HP = *133.1% mana value

Now some attacks have Piercing, so let's decrease the mana value multipliers by ~10%. (totally arbitrary hat-pull number)
0 Armor: *100% mana value
1 Armor: *110.7% mana value
2 Armor: *121.8% mana value
3 Armor: *129.8% mana value
4 Armor: *134.6% mana value

So let's use the Timber Wolf as the baseline - it is the only creature in the game with absolutely no affixes:
Timber Wolf: Mana Cost = 9, HP = 10, Attack = 4, AC = 2, we get:
Mana Value = 1.17 * HPValue * AttackValue * ACValue; where:
HPValue = Sqrt(HP)
AttackValue = Sqrt(Attack)
ACValue = Refer to above chart.

Every other creature in the game has some number of affixes. If we calculate the expected mana cost (this is the cost if it had no affixes at all) and compare it to the actual mana cost, we can start to guess at how highly valued each Affix is. For example, a Bitterwood Fox costs 0.5 mana more than you'd expect, its only affix is "Fast", so this implies that "Fast" is worth 0.5 mana (for the fox - it might be worth more on a larger creature).

For all of the non-Familiar units in the game:
Darkfenne Bat = 3.30 Expected, 5 Actual (+1.70 or +51.3%)
Feral Bobcat = 3.30 Expected, 5 Actual (+1.70 or +51.3%)
Firebrand Imp = 4.05 Expected, 5 Actual (+0.95 or +23.5%)
Asyran Cleric = 4.49 Expected, 5 Actual (+0.51 or +11.6%)
Bitterwood Fox = 4.53 Expected, 5 Actual (+0.48 or +10.5%)
Thunderift Falcon = 4.53 Expected, 6 Actual (+1.48 or +32.6%)
Sosruko, Ferret = 3.69 Expected, 7 Actual (+3.31 or +89.5%)
Blue Gremlin = 5.93 Expected, 7 Actual (+1.07 or +18.1%)
Moonglow Faerie = 3.69 Expected, 8 Actual (+4.31 or +116.5%)
Mana Leech = 6.34 Expected, 8 Actual (+1.66 or +26.2%)
Skeletal Sentry = 7.75 Expected, 8 Actual (+0.25 or +3.2%)
Emerald Tegu = 7.88 Expected, 9 Actual (+1.12 or +14.2%)
Timber Wolf = 9.00 Expected, 9 Actual (by definition)
Royal Archer = 7.76 Expected, 12 Actual (+4.24 or +54.6%)
Whirling Spirit = 8.42 Expected, 12 Actual (+3.58 or +42.4%)
Gray Angel = 9.00 Expected, 12 Actual (+3.00 or +33.3%)
Stonegaze Basilisk = 9.00 Expected, 12 Actual (+3.00 or +33.3%)
Highland Unicorn = 7.39 Expected, 13 Actual (+5.61 or +75.8%)
Tarok, the Skyhunter = 7.39 Expected, 13 Actual (+5.61 or +75.8%)
Flaming Hellion = 8.54 Expected, 13 Actual (+4.46 or +52.3%)
Dark Pact Slayer = 10.65 Expected, 13 Actual (+2.35 or +22.1%)
Knight of Westlock = 10.72 Expected, 13 Actual (+2.28 or +21.2%)
Cervere, Forest Shadow = 9.44 Expected, 15 Actual (+5.56 or +58.9%)
Brogan Bloodstone = 10.43 Expected, 15 Actual (+4.57 or +43.8%)
Goran, Werewolf Pet = 10.51 Expected, 15 Actual (+4.49 or +42.8%)
Gorgon Archer = 9.33 Expected, 16 Actual (+6.67 or +71.6%)
Darkfenne Hydra = 10.02 Expected, 16 Actual (+5.98 or +59.7%)
Malacoda = 10.94 Expected, 16 Actual (+5.06 or +46.3%)
Mountain Gorilla = 11.38 Expected, 16 Actual (+4.62 or +40.5%)
Redclaw, Alpha Male = 11.75 Expected, 16 Actual (+4.25 or +36.2%)
Necropian Vampiress = 12.32 Expected, 16 Actual (+3.67 or +29.8%)
Steelclaw Grizzly = 15.54 Expected, 17 Actual (+1.46 or +9.4%)
Valshalla, Lightning Angel = 9.68 Expected, 21 Actual (+11.32 or +117.0%)
Samandriel, Angel of Light = 10.82 Expected, 21 Actual (+10.18 or +94.1%)
Adramalech, Lord of Fire = 13.90 Expected, 24 Actual (+10.10 or +72.7%)

Title: Re: Most efficient creature
Post by: piousflea on October 06, 2012, 11:17:24 PM

So looking for trends in cost:

Fast Creatures:
Bitterwood Fox = 4.53 Expected, 5 Actual (+0.48 or +10.5%, no other abilities)
Thunderift Falcon = 4.53 Expected, 6 Actual (+1.48 or +32.6%, also has Flying)
Blue Gremlin = 5.93 Expected, 7 Actual (+1.07 or +18.1%, Piercing +1, 1x Defense 8+ Pest, must pay 1 mana to be Fast but gains Teleport)
Tarok, the Skyhunter = 7.39 Expected, 13 Actual (+5.61 or +75.8%, Flying, Piercing +1, +2 vs. Flying, 1x Defense 7+ vs Air Melee)
Cervere, Forest Shadow = 9.44 Expected, 15 Actual (+5.56 or +58.9%, Elusive, 1x Defense 8+)

Flying Creatures:
Darkfenne Bat, 3.30 Expected, 5 Actual (+1.70 or +51.3%, also includes Rot 9+)
Thunderift Falcon, 4.53 Expected, 6 Actual (+1.48 or +32.6%, also includes Fast)
Moonglow Faerie, 3.69 Expected, 8 Actual (+4.31 or +116.5%, also includes Pest, Infinite Defense 6+, Ethereal, +2 vs Incorporeal)
Gray Angel, 9.00 Expected, 12 Actual (+3.00 or +33.3%, can sacrifice itself for 6 dice heal)
Necropian Vampiress, 12.32 Expected, 16 Actual (+3.67 or +29.8%, costs 1 mana to fly, also has Vampiric)
Valshalla, Lightning Angel, 9.68 Expected, 21 Actual (+11.32 or +117.0%, 7-8 Daze, 9+ Stun, can buff attack by up to +4, Aegis 1, Lightning -2)
Samandriel, Angel of Light, 10.82 Expected, 21 Actual (+10.18 or +94.1%, 7-10 Daze, 11+ Stun, Aegis 1, Light Immunity)
Adramalech, Lord of Fire, 13.90 Expected, 24 Actual (+10.10 or +72.7%, 5-9 Burn, 10+ 2 Burn, 4 dice sweeping attack with 7-10 Burn, 11+ 2 Burn, Flame Immunity)

I would venture to guess, based on the cost "floors" of these creatures, that Fast is worth around +10% mana cost, while Flying is around +20-25%. Keep in mind that +20% mana cost is equivalent to +44% HP so it's a fairly steep cost.

Of course, all this reverse-engineering is pure guesswork and subject to massive rounding errors. (ie, a unit can only cost 8 mana or 9 mana, it can't cost 8.246)

Title: Re: Most efficient creature
Post by: fas723 on October 08, 2012, 01:45:57 PM

First I must say that I really enjoy that all of you in here put so much thought into this!  :)

I will try to answer some your comments and add my thinking to it.

Yes, there are some flaws in the method. I was aware of that when I started already. My main target was to make a simple equation that anyone could use to get a decent understanding of what they could expect out of their mana once they had invested into creature. An easy function that was "good enough".

For example; in my evaluation Double strike and Triple strike will have the same "value". They are both Major traits. As all of you know this is defiantly not true. Same goes for quick vs. full attacks. I haven't mad e a difference between these two. But, to not end up with 5000 parameters I instead said; Ok, what is my sampling size? It turned out to be 36 individual creatures. To have 7 parameters to a sample size of 36 is also VERY high. 7 was the lowest number of parameters I could think of, and therefore I kept that.

I like the discussion regarding Armor. I also thought it could not be linear. The first point of Armor is much more valuable than the fourth. To cover this I could add a nonlinear term in the equation. Like: Coefficient1 x Armor^2 or Armor^(1/Coefficient1).

I like your idea of excessive mana for traits, pioudflea. What I came across doing this is that the hardest part was to evaluate each trait. I see if I can give it a try.

My question to you now is: How do we update the evaluation method to incorporate every necessary aspect without doing it too complicated and still keep it statistically insured.


I have now updated my first two posts (table and traits reference).

Error 1: In the first equation every parameter should have been divided by 7 (7 parameters) to be correct. (I was in my table). The coefficient in the present equation now includes "everything". You should use it as it is.
Error 2: Pest is now a Neg Trait x1
Error 3: Triple strike and Counterstrike did get lost in the cut and paste operation into the forum.

Title: Re: Most efficient creature
Post by: fas723 on October 08, 2012, 02:02:06 PM

Excel can be downloaded here:


https://docs.google.com/folder/d/0Bz0fnLKKUKlxaUtBU1dhcDNCTkE/edit

Title: Re: Most efficient creature
Post by: piousflea on October 08, 2012, 02:35:35 PM

The reason that I prefer the "expected mana cost" methodology is that you can estimate how much mana you are spending for the special abilities on your creature.

A highland unicorn has a combat value of 7.4 but costs 12 mana. So you are paying 5.6 mana for the AoE regeneration aura.

A dark pact slayer has a combat value (vs 0 armor) of 10.6 but costs 13 mana. So you are paying 2.4 mana for flame resistance and 2 piercing.

A gray angel has a combat value of 9 and a mana cost of 12. So you are paying 3 mana for Flying and a self-sacrifice heal.

If you don't feel like flying and self sacrifice is worth 3 mana, then you should be less enthusiastic about the Grey Angel.

Better yet is ranged units. The Royal Archer pays 4.2 mana for its ranged attack. Is a 4 dice ranged attack worth 4.2 mana? Almost certainly yes, you can tell it is a very strong unit.

Title: Re: Most efficient creature
Post by: jhsjhs on October 11, 2012, 02:08:46 PM

This is fun, thanks for doing this.  I did the same thing for Dreamblade, a similar game, when it came out--well, pretty close, regression analysis of creature cost.  A few things I learned:
1) trying to cost abilities is really hard, as you basically have one or just a few data points for each.  I ultimately did what one of the respondents recommended, and just tried to figure out the value of the stats, effectively pricing the abilities.  Less neat, but useful--you can decide if a given ability is worth it's cost.
2) several sets in I had enough vanilla (special ability free) guys to run a good regression on just them, which basically cracked the code, but I got decent results from the first set just running the regression ignoring abilities, so you might try that.  The results were biased, of course, as some good abilities are correlated with certain abilities, but it still gave some useful info.  At least I would like to see the results!
3) after a few more releases you may have better luck pricing some of the abilities, if multiple creatures get them.


Keep up the good work, and thanks again.

Title: Re: Most efficient creature
Post by: fas723 on October 15, 2012, 01:47:12 PM

I did look into your model, piousflea. And I must say it will probably work well, but we have too few Timber wolfs at the moment. Just as jhsjhs is saying we need more vanilla creatures before this can be done.

What I get out form Arcanus post is that the eqation must have a shape like this:

Cost = C1 x sqr(HP) + C2 x sqr(Max attack dice) + C3 x ln(C4 x Armor)

To solve this we must have at least 4 vanilla creatures. And if one of them devides from the rules we must start sampeling again. That would requier even more creatures.

Title: Re: Most efficient creature
Post by: piousflea on October 17, 2012, 07:02:50 PM

Actually my belief is that it is purely multiplicative:
Cost = C * sqrt(HP) * sqrt(Max attack dice) * f(Armor) * g(Affixes)
where f() and g() are arbitrarily defined functions.

Alternatively, it could be:
Cost = ( C * sqrt(HP) * sqrt(Max attack dice) * f(Armor) * g(Affixes) ) + h(Affixes)
where g(Affixes) is for multiplicative-cost affixes, and h(Affixes) is for additive-cost affixes.

Title: Re: Most efficient creature
Post by: fas723 on November 06, 2012, 06:06:44 AM

Did some more testing yesterday.
I started to apply non-linear behaviors to the equation as we have talked about here. I tried both natural logarithmic, square root and power functions to various properties. My problem was that no matter how I did it, it never got as good as just a linear function as I started with.

That made me think a bit more. How should we think when we set up the base function? Before the coefficient are set. How does each property behave? Right now we have talked about how armor relates to attack dice, or how
I'm not sure we can do it that way.

Instead I think we should say: What effect does it have if a property is doubled. I.e. is 4 attack dice twice as good as 2? If yes; well then it is linear. If not then we have to say how it behaves.

If we start with the three basic attributes: Attack, Armor & Health. I would say that both Attack and Health have typical linear behaviors.
Armor is a bit harder. 20 in armor is probably not much better than 10. 0 in Armor would contribute with 0 to the mana cost, and the greatest increase must be between 0 and 1.

Mana_cost_Armor = c1*sqrt(Armor).
Armor=0: c1*0
Armor=1: c1*1
Armor=2: c1*1,41
Armor=3: c1*1,73
According to theory above.

Mana_cost = c1*sqrt(Armor)+c2*Attack+c3*Health

Note. This doesn't mean one in health is equal to one in attack. The coefficients will take care of the actual power for each property.

Now we just have to do the same for traits...

Title: Re: Most efficient creature
Post by: fas723 on November 06, 2012, 06:09:46 AM

Quote from: "piousflea" post=2279

Actually my belief is that it is purely multiplicative:
Cost = C * sqrt(HP) * sqrt(Max attack dice) * f(Armor) * g(Affixes)
where f() and g() are arbitrarily defined functions.

Alternatively, it could be:
Cost = ( C * sqrt(HP) * sqrt(Max attack dice) * f(Armor) * g(Affixes) ) + h(Affixes)
where g(Affixes) is for multiplicative-cost affixes, and h(Affixes) is for additive-cost affixes.

piousflea, why would you go with just multiplicatives? That will only give one coefficent, and less ability to control your parameters...