Most efficient creature

[piousflea]

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.

[jhsjhs]

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.

[fas723]

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.

[piousflea]

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.

[fas723]

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...

[fas723]

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...