Most efficient creature 3

[sIKE]

@Aylinis

The OP said he was not going to repeat what he had previously said. He then linked to the two previous posts  he made on this topic for reference to his methodology.

Perchance did you read those? I haven't in a while but do recall that there was reasoning and logic for his power rankings. If you haven't, please take the time and I think things will make more sense to you then.

[Aylin]

@Aylinis

The OP said he was not going to repeat what he had previously said. He then linked to the two previous posts  he made on this topic for reference to his methodology.

Perchance did you read those? I haven't in a while but do recall that there was reasoning and logic for his power rankings. If you haven't, please take the time and I think things will make more sense to you then.

I read the links he posted. They did not answer my questions.

Basically all it had was what his formula was and the values he had given to traits. How those were arrived at was not given.

[jacksmack]

Well... it aint possible to make this list.

You can make a list of how much bang for the buck (read average damage per hit) vs X armor


And on the other way around, you can make a list of each creature's survivability vs X dice rolled per hit.

Thats IT - Everything else is nonsense.
Do those 2 lists and let people calculate the value of various of traits depending on the scenario they are in when they have the option to summon creatures - THEN we have something worth of value.

Or hell... do the dice math for us, and we have something of value.  (the dice role results are not as intuitive as 1 might think.)



Hydras are very strong vs swarm.
Hydras are much weaker vs Few bigs (high armor)

Hydras a decent vs high armored targets.
Hydras are godlike vs targets without armor

How does your list take this into account?



I cant be bothered reading what your list is based on, because just looking at it tills me that its 70%+ wrong.


Edit:
Your list gives traits values... we dont need that.
Sometimes traits will be useless... so we need a clean list of pure HP / Damage / armor /resilient / incorporal
(its not use summoning another unit with defense if the enemy has falcon strike on everything)

[fas723]

@Aylinis

The OP said he was not going to repeat what he had previously said. He then linked to the two previous posts  he made on this topic for reference to his methodology.

Perchance did you read those? I haven't in a while but do recall that there was reasoning and logic for his power rankings. If you haven't, please take the time and I think things will make more sense to you then.

I read the links he posted. They did not answer my questions.

Basically all it had was what his formula was and the values he had given to traits. How those were arrived at was not given.

Okay, I will give it one more try (since it apparently was hard to follow the first time).

The objective is to create a curve that in the best possible way describe all creature "performance". Out of this you/we can see how valuable each creature is and compare them to each other.

First approach:
We know the stats for each creature (Attack, Armor & Health). We also know which Traits they have. If we add this together it should represent the cost for the creature. Thus:

Attack + Armor + Health + Trait = Calculated Cost => which squared difference should be minimized towards the true Cost

In order to evaluate how much each term gives or represents a coefficient is used (this is what is calculated later on):

x1 * Attack + x2 * Health + x3 * Health + x4 * Trait = Calc cost

However, each term isn't strictly linear. Therefore the following apply to each component:

Attack:

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

Attack1 = #dice * attack type ^y1 * (attack1_trait +1) same for Attack2

attack1_trait = (attack_trait1 +...+ attack_trait_n) / max(all_attack_traits) same for Attack2

y1 is the first exponent I have used which determine the value between melee, range and AOE attacks. As you can see every set value one each creature is represented and multiplied. The importance of the attack type is also corrected. The +1 is to give creature without an attack_trait a coefficient which is not 0, since it is a multiplayer. As you can see the trait component is just one third of the overall attack part in the general equation.

Armor:
Armor is set to have a square root behavior. x2 * Armor^(1/2). This because the first point of armor is better than the second and so on. Armor is not a linear.

Health:
The most simple one. 1 health is half as good as 2 health, and 4 health is twice as good as 2 health. Health is strictly linear. x3 * Health.

Trait:
The generate traits have similar model as the ones for attacks, but without the +1 (no trait, no gain).
trait = (trait1 +...+ trait_n) / max(all_attack_traits) which gives an normalized function. To make the evaluation even better an exponent has be assigned even here. x4 * trait^y2

Summary:
The final equation will then look like:

x1 * Attack + x2 * Health + x3 * Healt + x4 * Trait^y2 = Calc cost

where

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

Attack1 = #dice * attack type ^y1 * (attack1_trait +1) same for Attack2

attack1_trait = (attack_trait1 +...+ attack_trait_n) / max(all_attack_traits) same for Attack2

and

trait = (trait1 +...+ trait_n) / max(all_attack_traits)

Now we have a equation purely based on the behavior of all input data each creature have. This without guessing anything or to make assumptions regarding any values/traits. The only thing to do now is to calculate the parameters: x1, y1, x2, x3, x4 and y2 to make the best fit possible.

Calculation:
To find these best values of the parameters. I have used the common: "least square method":

(Calc_Cost(x1, y1, x2, x3, x4, y2)_n - True_cost_n)^2 => 0. For all n.

This will give the best curve fit.
I used a Mote Carlo sampling to generate starting points and to track the directions of the values for the parameters.

Up until here is what I have done prior to this post / version.
In the first version of this calculation I had set trait values. As I wrote in the first post I have now done a similar calculation as the one described above, but now for traits instead. Basically I have used the calculated parameters out from what I just described as fixed values and instead tracked the trait values. By doing these two calculations back and forth a few times the optimum curve (both for traits and other inputs) could be achieved.


I hope this gives you a better understanding of what is done. If it doesn't I think you have to read some book about math first and I will gladly discuss further with you.




 

[fas723]

Hydras are very strong vs swarm.
Hydras are much weaker vs Few bigs (high armor)

Hydras a decent vs high armored targets.
Hydras are godlike vs targets without armor

How does your list take this into account?

It doesn't. You are right about that no list can accommodate for this. However mine never intended to do that anyway.

I cant be bothered reading what your list is based on, because just looking at it tills me that its 70%+ wrong.

Well, then you need to express yourself a little bit more than just your gut feeling...

Your list gives traits values... we dont need that.

An calculated estimate used in the equation to give the calculated cost, yes. That is not what the list is for.

Sometimes traits will be useless... so we need a clean list of pure HP / Damage / armor /resilient / incorporal

Here you apparently want to bring in traits anyhow (Resilient and Incorporeal)..?... As I said before: If you want to do a good calculation you can not just skip things just because they are hard to figure out. It is much better to make your best guess, and even better if you do your evaluation with good reasoning and research .

[Zuberi]

I am not a mathematician so I can't tell you where you went wrong. It is clear that you have put a lot of thought and consideration into your formulas. However, you say the purpose is so that we can "see how valuable each creature is and compare them to each other." If that is the case, then just looking at the results we can, and ARE telling you that they are wrong! Anybody who has played the game knows that a lot of the creatures you have listed as being top notch simply aren't worth your time.

When your results and reality don't line up, it is insanity to claim that reality is mistaken. Your results are mistaken. You need to reevaluate.

[fas723]

What is the miss match to you? I could be wrong but to me it looks quite good...

Take the Adramelech, Lord of Fire  for example. He is numer 74 on the list, but you get 92% efficency rate for him. Not bad at all for a creature at 24 mana. But compared to others he isn't as efficent. In the right situation he is the best play though...

[MrSaucy]

I hope I am not doing something that has already been done, but if I were to calculate raw creature efficiency I would keep it simple and do something like this:

Adramelech, Lord of Fire:
Mana: 24
Armor: 3
Life: 14
Average attack: 5 (one attack does 4 damage, the other does 6)
Armor per mana = 3/24 = 0.125
Life per mana: 14/24 = 0.583
Attack per mana: 5/24 = 0.208
Efficiency rating = (1/3) (0.125 + 0.583 + 0.208) ~ 0.3

Bitterwood Fox:
Mana: 5
Armor: 0
Life: 5
Average attack: 3
Armor per mana: 0
Life per mana: 5/5 = 1
Attack per mana: 3/5 = 0.6
Efficiency rating = (1/3) (0 + 1 + 0.6) ~ 0.5

Blue Gremlin:
Mana: 7
Armor: 1
Life: 7
Average attack: 3
Armor per mana: 1/7 = 0.143
Life per mana: 7/7 = 1
Attack per mana: 3/7 = 0.423
Efficiency rating = (1/3) (0.143 + 1 + 0.423) ~ 0.5

Brogan Bloodstone:
Mana: 15
Armor: 4
Life: 11
Average attack: 4
Armor per mana: 4/15 = 0.267
Life per mana: 11/15 = 0.733
Attack per mana: 4/15 = 0.267
Efficiency rating ~ 0.4

With this way, efficiency ranges from 0.0 to 1.0
I can't imagine a creature having an efficiency > 1 without being broken.
I predict that most creatures would be within the [0.3, 0.6] range.

[Aylin]

Okay, I will give it one more try (since it apparently was hard to follow the first time).

All you did before was state what your formula was. In what world exactly does that constitute explaining?

The objective is to create a curve that in the best possible way describe all creature "performance". Out of this you/we can see how valuable each creature is and compare them to each other.

If your objective was to create a curve, where is it? You have yet to present a curve. (Hint: a curve is also known as the graph of a continuous function!)

First approach:
We know the stats for each creature (Attack, Armor & Health). We also know which Traits they have. If we add this together it should represent the cost for the creature. Thus:

Attack + Armor + Health + Trait = Calculated Cost => which squared difference should be minimized towards the true Cost

In order to evaluate how much each term gives or represents a coefficient is used (this is what is calculated later on):

x1 * Attack + x2 * Health + x3 * Health + x4 * Trait = Calc cost

And what exactly makes you so sure that these should just be added together? How do you know you that there aren't mixed terms?

However, each term isn't strictly linear. Therefore the following apply to each component:

Attack:

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

Attack1 = #dice * attack type ^y1 * (attack1_trait +1) same for Attack2

attack1_trait = (attack_trait1 +...+ attack_trait_n) / max(all_attack_traits) same for Attack2

y1 is the first exponent I have used which determine the value between melee, range and AOE attacks. As you can see every set value one each creature is represented and multiplied. The importance of the attack type is also corrected. The +1 is to give creature without an attack_trait a coefficient which is not 0, since it is a multiplayer. As you can see the trait component is just one third of the overall attack part in the general equation.

*Sigh.* Multiplier, not multiplayer.

Right off the bat you've failed to consider when secondary attacks are never worth using. The best example of this is Vine Snapper where the 4-dice attack is never worth using. You're increasing the value of archers based on their melee attacks even though if your archers are using their melee attacks something is terribly wrong.

And how did you come up with these equations? Your final equation is especially bizarre: you're saying that an attack that only has Doublestrike and an attack that only has Triplestrike are the same! Did you forget that x/x=1?

Your equations for "attack1_trait" and "Attack1" also have you doubling the value of an attack if it has any traits. Your own equation says that you're valuing a 3-dice piercing +1 attack over a 4-dice attack! Even worse it would give the same value for a 2-dice piercing +1 attack as it would for a 4-dice attack with no traits! That is inexcusable.

Armor:
Armor is set to have a square root behavior. x2 * Armor^(1/2). This because the first point of armor is better than the second and so on. Armor is not a linear.

You are aware that sqrt(x) isn't the only nonlinear function, right? How did you determine that it was a square root, and not a cubed root or a log function?

Also your assumption here is false (again), because you fail to take into account the prevalence of Piercing +1 in the meta. Because of it the second point of armour is as good, if not a little better, than the first.

Health:
The most simple one. 1 health is half as good as 2 health, and 4 health is twice as good as 2 health. Health is strictly linear. x3 * Health.

Is it strictly linear? Not in the slightest. Huginn at 5 health is considered extremely squishy, while Blue Gremlin at 7 is considered pretty durable. The difference is that Huginn dies to a single unavoidable attack or spell much more often than a Blue Gremlin does. You failed to take into account that any health value 5 is pretty much the same (because of the ease of dying to a Flameblast), and values over ~12 don't matter as much either (because now we're getting into "Too Big to Kill" territory).

Trait:
The generate traits have similar model as the ones for attacks, but without the +1 (no trait, no gain).
trait = (trait1 +...+ trait_n) / max(all_attack_traits) which gives an normalized function. To make the evaluation even better an exponent has be assigned even here. x4 * trait^y2

Same problem as above, except here it's even worse! With this equation you're having Dark Pact Slayer's Flame -2 and Knight of Westlock's Lightning +2 both add 1 to their values!


I took out some useless junk here.

Now we have a equation purely based on the behavior of all input data each creature have. This without guessing anything or to make assumptions regarding any values/traits. The only thing to do now is to calculate the parameters: x1, y1, x2, x3, x4 and y2 to make the best fit possible.

Calculation:
To find these best values of the parameters. I have used the common: "least square method":

(Calc_Cost(x1, y1, x2, x3, x4, y2)_n - True_cost_n)^2 => 0. For all n.

This will give the best curve fit.
I used a Mote Carlo sampling to generate starting points and to track the directions of the values for the parameters.

Up until here is what I have done prior to this post / version.
In the first version of this calculation I had set trait values. As I wrote in the first post I have now done a similar calculation as the one described above, but now for traits instead. Basically I have used the calculated parameters out from what I just described as fixed values and instead tracked the trait values. By doing these two calculations back and forth a few times the optimum curve (both for traits and other inputs) could be achieved.

I'm not familiar with Monte Carlo (with an 'n'!) methods, but I can definitely say that if your initial equations are wrong (and they fail at almost everything) then you won't get anything close to accurate.

I hope this gives you a better understanding of what is done. If it doesn't I think you have to read some book about math first and I will gladly discuss further with you.

Considering how poorly this was done, I would never suggest that anyone take math lessons from you. Ever.

Your assumptions from the very beginning were wrong, your equations were wrong... And in the end your final list is wrong. You should have been able to tell when your list had ridiculously bad creatures in the top 10. You can call me a hater or insult me if it'll make you feel better, but at the end of the day you still made mistakes and got called out on them. Learn from it and move on.

[Zuberi]

I'm not going to bother going through your whole list as the mistakes are legion. If you can't see them, then you need to spend more time actually playing rather than messing with your calculator. Everybody who has commented has stated the list is in error, yet you still defend it. I will give a single example for your pleasure.

Asyran Cleric is listed as the 12th most efficient creature. Comparing that to the list to see how valuable it is relative to the others, as you state the list is intended to do, we get the impression that it is a better deal than over 85% of the other creatures. Yet it is pure garbage!

By itself, nobody would ever in their life cast the asyran cleric. The only time you ever see somebody try using it is in combination with other cards, such as Temple of Asyra and Holy Avenger. Even in those cases, most people agree it is a sub-optimal play. There is not a single instance I can think of where casting this guy is definitively better than 85% of the other creatures you could be casting, as I have trouble thinking of times when I would ever want to cast it.

[fas723]

MrSaucy:
I tried that approach in the beginning. Problem is when you divide with the total mana it contains everything, including the part coming form the traits. I would really like this method to work, but I don't really see that at the moment.

[fas723]

*Sigh.* Multiplier, not multiplayer.

I'm sorry, but English isn't my native language. We can have this discussion in Swedish or your third language if you like?

You have yet to present a curve. (Hint: a curve is also known as the graph of a continuous function!)

The curve is stated in my last post and the parameters are in the excel this time (as the curve). As you know it is impossible to draw a curve with more than three degrees of freedoms.

And what exactly makes you so sure that these should just be added together? How do you know you that there aren't mixed terms?

I'm not. Help me out if have a better suggestion. The curve fit quite good however.

Right off the bat you've failed to consider when secondary attacks are never worth using.

THe second attack is only given a 30% portion of the attack term. This I have also tested to give a good fit.

Your final equation is especially bizarre: you're saying that an attack that only has Doublestrike and an attack that only has Triplestrike are the same!

No, I defiantly don't. I have always stated that Triplestrike is better than Doublestrike, both in the calcualtions and in my posts. Thinkagain.

Your equations for "attack1_trait" and "Attack1" also have you doubling the value of an attack if it has any traits. Your own equation says that you're valuing a 3-dice piercing +1 attack over a 4-dice attack! Even worse it would give the same value for a 2-dice piercing +1 attack as it would for a 4-dice attack with no traits! That is inexcusable

Wrong again. I don't know how much I should explain? It seems like you don't want or can understand.

Because of it the second point of armor is as good, if not a little better, than the first.

It is much easier to roll one perfect die with three dice than two. Thus: the first point of armor is better then the second and so on. You are correct though, that it might not be a square function.

Same problem as above, except here it's even worse! With this equation you're having Dark Pact Slayer's Flame -2 and Knight of Westlock's Lightning +2 both add 1 to their values!

Same problem as above, you have read it wrong again. These two does not give the same value.

I'm not familiar with Monte Carlo (with an 'n'!) methods, but I can definitely say that if your initial equations are wrong (and they fail at almost everything) then you won't get anything close to accurate.

https://en.wikipedia.org/wiki/Monte_Carlo_method

Considering how poorly this was done, I would never suggest that anyone take math lessons from you. Ever.

I think this was the worsted tone I have ever heard in forum. I haven't done anything to you except trying to explain what I have done. If this table doesn't match up with your favorite creatures it is not my fault. Do take it so personal; it is bad for your reputation.
I don't want to insult you, but give some hints how to behave.

[ACG]

If I understand correctly, you are trying to find a model for the value of traits and stats by weighting them according to other traits and stats with which they appear on specific creatures, and then comparing the actual mana cost of the creature to your theoretical mana cost based on the values of traits and stats that your model predicts. I am having trouble seeing your specific methodology, but this is the general idea, yes? So the value of, for instance, the fast trait would be based on the mana costs of creatures with the fast trait compared with the stats and other traits of those creatures?

I like the idea of crunching the numbers to arrive at a model that assigns values to traits based on existing cards, not because I think that it would necessarily give an accurate representation of the values of different creatures (as others have mentioned, there are too many other factors) but because it would make it much easier to give crude estimates of the value at which a newly designed creature could be initially priced, before playtesting narrows in on the exact value.

That said, due to the complexity of Mage Wars I would agree that iterative playtesting is the best way to compute the value of a creature. It is definitely not possible to arrive at a good model through analysis of creature spells alone, since the game has other types of spells relevant to the performance of creatures as well. I also find it odd that (unless I am missed something) you do not take into account the schools and subclasses of the various creatures, since these can be quite relevant when determining their values. Might be something to consider.

I think what you should be aiming for, rather than interpreting calculated cost vs. actual cost as efficiency, is trying to reduce the residuals between your calculated cost and the actual cost. If you can come up with a model that accurately predicts the mana cost of every creature to within a small margin of error, that will be both extremely impressive and extremely useful for card designers. As your indices show, your model still has some distance to go. I encourage you to try to refine it. I don't know whether it is possible to mathematically model Mage Wars cards, and given the number and complexity of the variables, it is likely to be an extraordinarily difficult task. If you can find a model that accurately predicts the values of even 75% the cards, that will be an achievement. As it is, it looks like your model only predicts about 1/8 cards, depending on how much precision we require.

Edit: Also, there probably isn't enough data yet to do this.

[fas723]

I'm not going to bother going through your whole list as the mistakes are legion. If you can't see them, then you need to spend more time actually playing rather than messing with your calculator. Everybody who has commented has stated the list is in error, yet you still defend it. I will give a single example for your pleasure.

Asyran Cleric is listed as the 12th most efficient creature. Comparing that to the list to see how valuable it is relative to the others, as you state the list is intended to do, we get the impression that it is a better deal than over 85% of the other creatures. Yet it is pure garbage!

By itself, nobody would ever in their life cast the asyran cleric. The only time you ever see somebody try using it is in combination with other cards, such as Temple of Asyra and Holy Avenger. Even in those cases, most people agree it is a sub-optimal play. There is not a single instance I can think of where casting this guy is definitively better than 85% of the other creatures you could be casting, as I have trouble thinking of times when I would ever want to cast it.

Well what can I say? The model is not by far perfect. It is even so that it might never be. As long there is a "real" difference in the cards the least square method will always show a none perfect fit.

Yes, I defend the model and method. I have not yet seen anyone with real complains about it. However, it is very easy to mix the method with your feeling for the game and cards. I also play cards on the lower end of the scale, and they are very good in these situations, even if the efficiency isn't that high. You sse I play the game a lot as well, not just number crunching.

If I can just respond to your Asyrian Cleric example:
The Asyrian Cleric got a 2 die quick attack, 1 armor, 6 health, plus an ability. All for 5 mana
Compare that to something with the same cost:
Darkfenne Bat: 2 die quick attack with effect, 0 armor, 4 health, plus one ability.
Firebrand Imp: 2 die quick attack with effect, 0 armor, 6 health, plus one ability.

As you can see, quite hard to determine if one is better than the other. The table show this in one way. That the difference is approximately 0,7 mana. If that mistake is legion I will rest my case.

[fas723]

Thank you ACG for good feedback.
Yes you are correct. That is the target for this exercise. I do it for my own purposes and I just wanted to share it with all of you. I will consider your thought and see what I can do. Problem is to include all cards. They are so different in it nature.