Mana cost of life, armor, attacks, and traits

[lettucemode]

I was inspired by the "Most Efficient Creature" thread to try and come up with a simple calculation for how much creature stats cost in terms of mana. How much are you paying for Fast or that 8+ 1x Defense? Do any traits cost more on certain categories of creatures but less on others? Why is Steelclaw Grizzly so good, anyway? Let's find out!

Before I start, I'd like to say that I've been analyzing a lot of the creatures with this method and it seems to work out pretty consistently for all of them. The goal is to provide a quick gauge of a creature's worth from just a quick glance at the card. However playtesting is always more valuable than figuring stuff out on paper. So if you notice any discrepancies between what my formula gives and how the creature actually plays, please leave a comment and let us all know! There is also still a lot of gray area at this point, so I hope this post provokes some discussion. Without further ado...

The Method
This method uses the creatures Goblin Grunt, Orc Butcher, and Timber Wolf as a "base reference" against which everything else can be compared. These creatures were chosen because they have no traits and a single quick action melee attack which also has no traits.

Let's start with the Grunt. He costs 4 mana and has 4 life, 0 armor, and 3 attack dice. Based on this, I made the following initial assumptions:

• Each point of health and armor is worth one mana.
• A quick action melee attack of 3 dice is worth zero mana.

Now let's apply this to the Butcher. He has 10 life, 1 armor, and a quick action melee attack of 4 dice. If we figure that every die above 3 is worth 1 mana, his expected mana cost is 12. But his actual cost is 8! Hmm, let's try the Timber Wolf. It has 10 life, 2 armor, and a quick action melee attack of 4. So he should cost 13 mana, but the card says 9!

Notice anything similar about the expected vs. actual cost for those two creatures? The actual cost is 4 below the expected cost. So I made another assumption:

• If a creature's level is 2 or above, their cost is reduced by Level * 2. (this implies that higher level creatures are more mana efficient than lower level ones)

Therefore, the equation for Lettucemode's Simple Cost Calculation (LSC for short) is:

Mana cost = Life + Armor + AttackWorth + TraitWorth - 2 * Level if not level 1

Life, Armor, and the level adjustment should make sense to you by now, so let's go into the other two.

Judging the Worth of Attacks with LSC
As stated above, a quick action melee attack of 3 dice with no traits is worth 0 mana - you can just slap it on any creature without adjusting its mana cost. Every extra or fewer die is worth 1 more or less mana, respectively.

As an example, let's take a look at Darkfenne Bat. Mana Cost = 4 life + 0 armor + (-1 + Value of 9+ Rot) + (Value of Flying) - (0 for level 1). If we assume that Flying and a 9+ Rot are both worth 1 mana, then the formula works out! Pretty neat.

********** Is Flying really worth only 1 mana? Further analysis down in the Traits section. **************

Now that we have an idea how much Rot costs, let's take a look at Emerald Tegu! 8 health, 3 armor, a quick melee attack of 3 with 8+ Rot, and level 2 with an actual cost of 9. We can solve for the cost of 8+ Rot here. Mana Cost of 9 = 8 health + 3 armor + (0 + X) + 0 Traits - (2 * 2). Solving this tells us that 8+ Rot is worth 2 mana. But wait, wasn't Darkfenne Bat's 9+ Rot worth 1 mana above? Why is 8+ Rot valued at 2 mana, but 9+ Rot is only 1? Here's our first interesting discovery: is 8+ Rot really worth 2 mana when 9+ Rot is only 1? That depends on you. If you don't think that an additional 8.3% chance to inflict Rot is worth 1 mana, then it follows that Emerald Tegu is 1 mana overpriced. Cool stuff.

Let's do Dark Pact Slayer. I'll leave the math as an exercise to the reader and just tell you that if we assume that each Piercing +1 is worth 1 mana, and that Flame -2 is also worth 1 mana, then the formula places DPS's mana cost at 14. However, his actual cost is 13! So if you agree with my assumptions from 2 sentences ago, DPS is underpriced by 1 mana! I think we can agree that he certainly feels that way, he's a strong creature for sure.

Ranged Attacks
Some creatures have a ranged attack. What should those be worth? To find out, let's take a look at the Goblin Slinger. If he didn't have the ranged attack, LSC tells us that he should cost 1 mana, woah! That means that his ranged attack of 1-2 zones for 3 dice is worth 6 mana! We can use this as a basis to judge other ranged attacks.

Take the Royal Archer. Without her ranged attack, she's worth a mere 3 mana. So her ranged attack must be valued at 9 to get her up to her actual cost of 12 mana. However, compared to the Goblin Slinger's ranged attack, it should only be valued at 8 (one extra die, piercing +1). So is Royal Archer overpriced, or are extra dice on ranged attacks worth more than on melee attacks? Up to you

Trait Analysis under LSC
For the purposes of keeping this post less than a billion pages long, I am going to judge the worth of just the Flying trait in this section. You all should be able to follow my methodology to guesstimate at the other traits.

What are some creatures that have flying? Darkfenne Bat we've already been over, and that analysis suggested that Flying was valued at 1 mana. Let's go through some other creatures and see what it's worth on them. I am going to make a lot of unwritten assumptions here as the other traits and attacks on the creature could affect the worth of Flying. How much they do is up for debate!

• Thunderift Falcon - 1 mana (note that this implies that Fast is free!)
• Samandriel - 4 or 5 mana, depending on how much her attack is worth (it's a lot)
• Gray Angel - 2 or 3 mana, depending on how much Redeeming Sacrifice is worth
• Adramelech - 3-4 mana, depending on attack worth.

So it looks like the cost of Flying increases as all other stats increase, generally. Also, Samandriel may be a tad overpriced.

Interesting Findings

• Level 1 Animal creatures are about 3 mana underpriced (Fast is free on them, which costs about 3 on other creatures). Level 1 creatures in general are a couple mana underpriced.
• The combination of Nonliving and Psychic Immunity is priced at -1 mana under LCS. Examples: Skeletal Minion, Skeletal Knight
• An 8+, 1x Defense costs 5 mana. Examples: Knight of Westlock, Skeletal Knight
• Steelclaw Grizzly is underpriced by 2 mana, that is the most I've seen for that level of creature so far. If you value the full attack at 1 or 2 mana less due to the difficulty in using it, than the underprice-ing is even greater.
• Thorg's Taunt is worth 8 mana.
• The Familiar trait is worth about 4 mana.
• The combination of traits on Zombies is valued at around +4 under LCS.
• Asyran Cleric's heal ability is priced at -1 under LCS. As in he should cost 6 mana even without that ability.

Take this formula and see what you can figure out!

[Shad0w]

Bryan has stated that "Each Burn mark is worth 3 mana. The reason behind this is that 1 burn mark is expected to do 3 damage on average before it is removed. " Burn has a 1/3rd chance on the damage die of rolling a blank.

[lettucemode]

Thanks for that info, Shad0w. Based on that, the Firebrand Imp's d12 roll is worth slightly more than 1 mana, which means that Adramelech's d12 rolls are way too complicated for me to figure out right now 

[kailas]

What if the values are 0.5 mana for both health and armor, plus every attack dice beyond 1 attack dice +1 mana for each dice.

grunt 4 life * 0.5 + (3-1 atk)= 2+2=4
butcher (10 life + 1 armor) * 0.5 + (4-1)=8.5
timber wolf (10+2)*0.5+(4-1)=9
bat 2*0.5 + (2-1) + Rot (i assume half of removal cost 2/1=1)+ Flying (1 or maybe even 1.5)=5
tegu (8+3)*0.5 + (3-1) + Rot(1, maybe even 1.2, because higher rot chance)=8.5
falcon 5*0.5 +(3-1) +Flying(1)+Fast(0.5)=6
bitterwood fox 5*0.5 +(3-1) Fast(0.5)=5
cleric (6+1)*0.5 +(2-1) + Heal(0.5) =5

[Aylin]

It is impossible to accurately determine the approximate mana cost of Health, Armour, Spell Level, and Attack from a single card. Assuming that School and Subtype are meaningless for determining mana cost, we would need to have at least four "vanilla" creatures, at which point it would just be a simple matter of putting those into a matrix and row-reducing (assuming that mana cost is a linear function, which is a pretty large and currently unprovable assumption).

However, at the moment we only have 3. The best we can do is determine what three of them are as a function of the fourth.


Goblin Grunt: Level 1, Armour 0, Attack 3, Health 4, Mana 4
Orc Butcher: Level 2, Armour 1, Attack 4, Health 10, Mana 8
Timber Wolf: Level 2, Armour 2, Attack 4, Health 10, Mana 9

[   1   0   3   4   |   4   ]
[   2   1   4   10 |   8   ]
[   2   2   4   10 |   9   ]

[   1   0   3   4   |   4   ]
[   0   1   -2  2   |   0   ]
[   0   2   -2  2   |   1   ]

[   1   0   3   4   |   4   ]
[   0   1   -2  2   |   0   ]
[   0   0   2   -2  |   1   ]

[   1   0   3   4   |   4   ]
[   0   1   -2  2   |   0   ]
[   0   0   1   -1  |  1/2 ]

[   1   0   0   7   | 11/2]
[   0   1   0   0   |   1   ]
[   0   0   1   -1  |  1/2 ]

So we have
1 Armour = 1 Mana
1 Level + 7 HP = 5.5 Mana
1 Attack - 1 HP = 0.5 Mana

Looking at the creatures themselves, that looks fairly accurate: Timber Wolf costs 1 more mana than Orc Butcher and has 1 more point of Armour.


So until we get at least one more "vanilla" creature...the best I can say is that 1 point of armour = 1 mana...assuming that mana cost is a linear function of Attack, HP, Armour, and Level.


In order to know of the linear assumption is any good, we'd need an overdetermined system (6+ creatures). If all but 4 rows drop out (or become very very small) then we'll know that our linear approximation is good.

[haslo]

Hey, this calculation appears to make a lot more sense than the other one Interesting, definitely, but I'm sure that what really determined the costs was mostly playtesting, not any formula at all 

[DeckBuilder]

This is great, Lettucemode - more accessible and credible than the other.
I love the way you use deduction to slowly identify the value of any add-on.
That's why I feel so guilty throwing a few spanners into your calculations...

Your base creatures have Soldier or Animal as a subtype.
Consider the synergy value of that subtype - worth mana?
Value because some cards interact with certain subtypes.

If you adjust your base equation for this "trait", everything cascades and may make a bit more sense.
Bats, a level 1 animal, are arguably more valuable for Straywood, even if they costs 2 spell points each.

This brings me to a second characteristic you need to consider, the creature's spell point cost to your mage.
After all, Iron Golem costs 6 spell points for non-Earth mages but still cost 13 mana - so why not play them?
While there is a mana to spell point cost correlation, it is not consistent as level is used for school exclusivity.
3 spell points for a 9 mana Raptor Vine makes it cheap to cast but the creature is level 3 equivalent in power.
However paying 6 spell points yet still the same 9 mana for it makes it over-priced for all non-Nature mages.

The cost of a creature is a function of both its mana cost and its spell points cost - the latter varying by mage.
Hence one mage's bargain is another mage's stinker.

I personally hope there isn't any formula behind costs (it would be like seeing the wizard behind the curtain).
I doubt it as there are under-costed (Iron Golem, Zombie Brute) and over-costed (Earth Elemental) creatures.
I think experienced players easily spot a bargain or a stinker without needing heuristics, just using intuition.

Despite these spanners, Lettucemode, this is great work - please continue calculating your LSC formula!

[fas723]

When I started out with my "Most efficient creature" calculation I did exactly the same thing as you Lettucemode.  . But as Aylin says, you need at least one creature for each unknown properties you what to have in your evaluation (as long as all of them have a linear behavior). 

For me it ended up with a numerical optimazation to fit the function best way possible (as you all know) due to all these cross functionalities that has been mentiond in here already. I really encourage you to keep up thinking about your idea though, and post your thoughts so that we in here can help you.

When I started I figured that I needed to reduce the amount of parameters and only look at the major drivers, and leave the rest as freebees, to have a chance at all. My choice fell on: Health, Armor, Attack type (melee, range or AOE), # dies, and trait's. In my mind the level and school is of minor importance because you will pick an appropriate mage for the creatures you use most of the time and the actual level is rarely considered while playing (few exceptions like Graveyard). Sub type is more tricky...

What we (read you Lettucemode  ) can do is to look for two creatures that only have one ability / trait that they have in common, or three creatures that share two of the same abilities. Like Skeletal Sentry and Skeletal Minion and ...well there might not be one more... In that case we can eliminate further parameters in your equation (still linear though).

[fas723]

Maybe we can do some progress with the combination of Asyran Cleric and Acolyte of the bog queen? Is it possible to approximate there abilities as equal you think?

[fas723]

There is one more thing we have to consider in this and that is that AW most likely think ahead of us and places sub types and traits (like Frost -2) on creatures that doesn't have an effect today, but in the future will. That will show up in the mana cost in creature already today.

[DaveW]

But as Aylin says, you need at least one creature for each unknown properties you what to have in your evaluation (as long as all of them have a linear behavior).

I doubt that Armor will be a linear function. Two armor is a little less valuable than twice the value of one armor, as both will stop a single point of non-critical damage if only one is rolled. Four armor is less valuable than four times the value of one armor, or two times the value of two armor. Ultimately, there will come a point (somewhere around 20 armor, perhaps?) where additional armor is no more valuable than the next lower number of armor as all possible non-critical damage is absorbed by either amount of armor.

[Sailor Vulcan]

There is one more thing we have to consider in this and that is that AW most likely think ahead of us and places sub types and traits (like Frost -2) on creatures that doesn't have an effect today, but in the future will. That will show up in the mana cost in creature already today.

I think we should keep in mind that the value of cards is relative to the value of other cards and that their value will change as new cards are released.

That being said, I do still think an accurate formula could be possible. Even though the value of all the cards is related to the value of other cards, there are some cards that are so valuable that the value of an extremely large number of cards is based on them: Mages.

However, I think we'll need a computer program to determine the formula though, since each and every individual mage values cards differently, both within and between schools. I think the only way we could determine the formula by hand is if every single mage had at least one or two no-trait creatures or conjurations, and even then it would be very difficult and time consuming.

Of course, it's entirely possible that Arcane Wonders is already doing something like that, creating proxy generic no-trait cards that they don't plan on ever releasing as real cards, in order to figure out how to cost other cards that they do end up releasing.

I'm not too worried about seeing the wizard behind the curtain, since it's doubtful that I'll understand everything he's saying anyway. Mage Wars is such a complex game that you need to play it to learn it piece by piece.

Even IF you found the universal formula for Mage Wars Card Value, you have to update it with every new expansion. As the card pool and the number of mages grows, it will likely become harder to calculate because of the sheer number of variables to keep track of. It's probably faster and more efficient to just play and develop from experience our own approximations of this formula, those approximations of course being our intuition. It will cause us to make mistakes every now and then, but in the long run it's easier.

If we want to determine different approximations of a universal card value formula that are more precise than our own intuitions, that should be possible, but I doubt that it will work just as well for every card. Sort of like how a flat map never completely matches the accuracy of a globe in terms of the area and shapes of the land masses--if it's more accurate in shape it's less accurate in size, and vice versa.

Of course a lot of this is probably just my opinion...

[Wiz-Pig]

This is a pretty cool way of looking at things. I like how you've laid out your ideas. I think though that there is probably a lot more variability of the value of an ability based on context. And I don't think that Armor and Health are equivalent in value.

My point being which would you say is a better more survivable creature?

A creature with 12 health, or a creature with 10 health and 2 armor? I think it's pretty clear that the 10 health and 2 armor is more survivable to most damage scenarios (piercing +2 being the obvious exception).

Also, I should think that certain traits have greater value in combination than separately. A creature with Intercept is of course much better if it has high armor, a defense, or both. Intercept on a creature with 5 health could still be useful but not nearly so much. Perhaps certain traits could have value thresholds relating to other traits.

I do think that the observation of higher level creatures being more Mana efficient is an interesting one, they do cost more to put in your spell book, so there is a certain trade off there, but they are also more action efficient in the sense that you can get more on the board with a single full action... perhaps the trade off comes in the number of actions you can take and the number of places you can be in at one time with smaller creatures.

As a final note: I would think certain abilities might have a multiply effect on the thing that they modify instead of an inherent value. The one that comes to mind as the most clear cut example is Resilient. This trait functions effectively as infinite armor (except for the case of corrode), but what is that worth? Clearly it's not worth infinite points. What it does do is almost effectively double the number of attack dice that it takes to kill a creature. Although they can theoretically get lucky and roll a lot of criticals taking a creature with 7hp and resilient down much faster than one with 14 hps (A single 4 die attack could potentially one shot kill vs. minimum of 7 dice for 14 hp).