Most efficient creature 3

[Aylin]

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.

Not actually true.

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.

Doesn't address the point.

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.

*Sigh.*  Really?

Here are your equations:
attack1_trait = (attack_trait1 +...+ attack_trait_n) / max(all_attack_traits)
Attack1 = #dice * attack type ^y1 * (attack1_trait +1)

Let's run these for the Darfenne Hydra's Triple Bite and Goran's Feral Claws. Let's let T be the value of Triplestrike, and D be the value of Doublestrike.

attack1_trait = (sum_n=1^1 attack_trait_n)/(max over n attack_trait_n) = T/T (since T is the only trait and T is also the largest trait). But T/T = 1
Let's try for D:
attack1_trait = (sum_n=1^1 attack_trait_n)/(max over n attack_trait_n) = D/D = 1. Oh, they're the same because anything over itself is 1. It doesn't matter what values you assign them (as long as they aren't 0) if you just divide it by itself every time an attack only has one trait.

Since everything else about their respective attacks are the same, I trust you can see the issues with your equations now. But because I'm thorough, I'll show you the other issue.

Let's consider a hypothetical creature with a quick melee attack of 2 dice that has pierce 1. We'll be comparing that to Shaggoth-Zora's Mangling Claws attack. We'll let A stand in for attack type ^ y1

Shaggoth-Zora:
4 * A * (0+1) = 4A

As previously shown, the hypothetical creatures attack1_trait will equal 1, so
2 * A * (1+1) = 2A * 2 = 4A

According to your equations, those two attacks are equal. You keep defending them, even though everyone who plays this game will tell you they're wrong. Stop trying to fight against reality.

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.

Um...do you know how armour works in this game? It doesn't matter how much critical damage you roll, up to n of your normal damage is still blocked, where n=max{0,armour of target - piercing of attacker}

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.[/quote]

Actually, they do, for the same reason as above: your equation has a major flaw in it.

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

Is wikipedia where you learned the rest of your math "skills"?

[Zuberi]

I believe I have realized where we might have our disagreement on efficiency. Your chart only considers the efficiency of their mana cost, while my observational analysis of game play is skewed by action efficiency as well. A creature that costs 15 mana doesn't have to be strictly 3x better than a creature that costs 5 mana to be more efficient, because it only takes 1/3 the actions to summon compared to 3 of the 5 mana creature.

I think if you somehow factored in action efficiency into your calculations, your chart would align much better with people's concepts

[fas723]

First I must apologies that I saw a typo in my post here at the forum regarding the trait part in the function. Both the attack trait and general trait should be multiplied with 2 like this (which I have always used in the calc):

attack1_trait = 2 * (attack_trait1 +...+ attack_trait_n) / max(all_attack_traits)

Sorry, my bad.

It doesn't matter what values you assign them (as long as they aren't 0) if you just divide it by itself every time an attack only has one trait.

It is apparent that you don't understand the normalization of the traits.

the max(all_traits_x) applies for all traits not just the ones you use for the particular creature. That is how you normalize your function.

So, to bounce back your example:

Darfenne Hydra's second attack:
3 * A * (2*T/T +1) = 3A * 3

Bite and Goran's Feral Claws:
3 * A * (2*D/T +1) = 3A * (2*D/T + 1)

Extra example:
Bitterwood Fox:
3 * A_quick * (2*Nothing + 1) = 3A_quick * 1

As you can see all of them are different, but what do they actually give? (you find this at the first tab in the excel)
D/T = 0,89

Bite and Goran's Feral Claws:
3 * A * (2*D/T +1) = 3A + (2*D/T + 1) = 3A * 2,78

So what we are looking at is a triple strike value which gives 22% more mana cost than double strike. And a triple strike which gives 200% more than nothing (which is very naturally since it is two more attacks), but that creature has a quick attack instead.

The difference between a full attack and a quick attack is 1^0,67 / 2^0,67, which is 0,63.

Darfenne Hydra's second attack:
3 * 1 * 3 = 9

Bite and Goran's Feral Claws:
3 * 1 * 2,78 = 8,34

Bitterwood Fox:
3 * 2^0,67 * 1 = 4,77

There you have your real diff.

You did the same error for the other traits example as well.

Is wikipedia where you learned the rest of your math "skills"?

What's the matter with you? You didn't know what it was so I helped you get info about it. And no, I did not learn from Wiki, but apparently you did have the book about it so sent you the link. I can't buy the books for you.

[fas723]

I believe I have realized where we might have our disagreement on efficiency. Your chart only considers the efficiency of their mana cost, while my observational analysis of game play is skewed by action efficiency as well. A creature that costs 15 mana doesn't have to be strictly 3x better than a creature that costs 5 mana to be more efficient, because it only takes 1/3 the actions to summon compared to 3 of the 5 mana creature.

I think if you somehow factored in action efficiency into your calculations, your chart would align much better with people's concepts

You are correct. I have not considered this in my evaluation. It is only looking at invested / calc mana vs. actual mana cost.

However this is a quite interesting idea. Have you thought of how this could be implemented? I can look into it for future exercises.

Thanks for good feedback.

[Aylin]

This is getting sad.

It doesn't matter what values you assign them (as long as they aren't 0) if you just divide it by itself every time an attack only has one trait.

It is apparent that you don't understand the normalization of the traits.

the max(all_traits_x) applies for all traits not just the ones you use for the particular creature. That is how you normalize your function.

Don't blame me if your notation implied that's what you were doing. Even conceding that, it doesn't address any of the other issues, namely all of the assumptions you made without any proof. Instead of seeing if your assumptions made sense (which you should clearly be able to see that they don't by the ridiculous order your list is in), you've instead been arguing that reality is wrong and your list is correct. I mean hell, you've got Tataree as the third most efficient creature, despite the fact that is often survives 2 turns (3 at most) against any sort of competent player which is a net loss of 4 or 5 mana for you (since it dies to a single AoE attack/damage ability). You've got Earth Elemental as the ninth most efficient creature when summoning one will most often cause you to lose your match, Asyran Cleric as the twelfth most efficient creature despite the fact that it's terrible at everything, Ludwig Boltstorm as the eighth even though a 1-1 ranged attack is nearly worthless, psylok as the tenth despite the fact that it's pretty squishy and its only attack doesn't even do anything to 21% of the creatures currently in the game (and even against the 79% that it does work against a full action 0-0 ranged attack is pretty bad due to positional issues)... I could go on and on. Your list is wrong, and the reason is because your assumptions are wrong.

Any half-way decent Mathematician needs to be able to admit when her or his model is not accurate, and why. That is what leads to better models. None of us are served by this ridiculousness, especially you. Think about it; you've spent how long on something is utterly useless to everybody? I get that you want to make a mathematical model of the creatures in the game, but the truth of it is that there just isn't enough data yet to make one that has any hope of accuracy. Just admit it so we can all stop wasting our collective time.

[fas723]

Aylin,
You are amazing man. I have never ever said my model is perfect in any way, rather the opposite. Here I have start a topic where I publish what I have done and ask for a nice discussion. Then you jump into it and keep on nagging on about your unproved theories and gut feelings about the model with no mathematical or scientific explanation at all. You have even clearly proven over and over again that you don't understand model despite me trying to explain it for you (no I have not written a scientific repot about it explaining everything, since it is quite basic.). The only thing you have contributed with is your bad attitude.

As you probably know this is the third time I post this calc. Why is that? Because it’s been improved each time, due to the discussion we have had about it in here. Completely the opposite of what you are claiming.

I was also surprised how the result came out. But instead of crying like a baby I tried to understand the result and why it became like it did, and not just the approach "the table is wrong because my favorite creature isn't on top".

So please stop posting in here if you don't have any constructive to come with or redeem yourself with explain to me (in a scientific way) your statement: "the truth of it is that there just isn't enough data yet to make one that has any hope of accuracy". If you can't I ask you nicely to just keep it for yourself.

[Aylin]

Aylin,
You are amazing man. I have never ever said my model is perfect in any way, rather the opposite. Here I have start a topic where I publish what I have done and ask for a nice discussion. Then you jump into it and keep on nagging on about your unproved theories and gut feelings about the model with no mathematical or scientific explanation at all. You have even clearly proven over and over again that you don't understand model despite me trying to explain it for you (no I have not written a scientific repot about it explaining everything, since it is quite basic.). The only thing you have contributed with is your bad attitude.

Pointing out that your initial assumptions are flawed isn't displaying a "bad attitude", it's pointing out a fact. I began by asking for your equations because I noticed serious problems with your list. Instead of providing it, you've taken every opportunity to insult me, such as the above. Don't be surprised if people don't treat you like a king if you act like a spoiled man-child.

As you probably know this is the third time I post this calc. Why is that? Because it’s been improved each time, due to the discussion we have had about it in here. Completely the opposite of what you are claiming.

And each time your results have been wrong. In your second thread you even claim that because it's "similar" to your first that they both must be accurate! You've stated over and over that you're defending your model and your method...despite it not actually giving any useful information to anybody.

I was also surprised how the result came out. But instead of crying like a baby I tried to understand the result and why it became like it did, and not just the approach "the table is wrong because my favorite creature isn't on top".

You've used this particular strawman a few times, but until now I never thought you were serious. No one is "crying because a favourite creature isn't on top", people are pointing out that your list doesn't match reality. Your list has some of the worst creatures in the game in the top 20, some of which can literally make you lose for casting them.

So please stop posting in here if you don't have any constructive to come with or redeem yourself with explain to me (in a scientific way) your statement: "the truth of it is that there just isn't enough data yet to make one that has any hope of accuracy". If you can't I ask you nicely to just keep it for yourself.

*Sigh.* Do you really need this explained to you?

Things that affect how effective a creature is once you summon it:
Armour
Health
Attack Type
Attack Traits
Special Abilities
Traits
Level
Subtypes
Restrictions (such as Epic, Legendary, [Mage Type] Only, etc.)

Including Promo cards, there have been 91 creatures currently released. There are not enough creatures currently released to determine, with accuracy, what affects any of those may or may not have on mana cost. Out of those 91, there are only three creatures that have no Traits and Attack Traits...except you can't use those to determine anything except as functions of the other variables. There aren't enough creatures with certain traits either. Just traits (ignoring special abilities or familiar rules), we have:
Aegis X
Bloodthirsty +X
Burnproof
Charge +X
Climbing
Corporeal
Elusive
Familiar
Fast
Finite Life
Flying
Immunity to Y
Incorporeal
Living
Nonliving
Pest
Poison Immunity
Psychic Immunity
Rage +X
Regenerate X
Slow
Tough -X
Uncontainable
Unmovable
Vampiric
Intercept
Lumbering
Resilient
Rooted
Uproot X
Vigilant
Damage Type +/- X

That's thirty two traits currently in the game, several of which only appear on a single creature. When you expand it to include attack traits, special abilities, familiar rules, subtypes, etc. you quickly realise that for many of the things, the only data point available is a single creature, and the most that can do would be to tell you that it's worth whatever mana to make that creature cost what it costs (in other words, it's useless). Once you remove every single creature with something unique about them (this would be the part where you control your unknown variables) you end up with...a pool too small to determine anything conclusively. And, contrary to what you apparently think making shit up doesn't fix the problem[/b].

The only way any of us would be able to determine things like "how much mana would this cost if it was a soldier instead of an animal" would be if they eventually released enough creatures to make such an analysis possible.

And that's not even getting into the area of "efficiency", which in Mage Wars, is how much this creature helps you win vs. your investment in said creature (which, contrary to what you apparently think, isn't just based on mana cost). The only way to determine that would be to analyze each creature in the current meta. The reason for that is because creatures that can cause Bleed 50% of the time during an attack and/or are Bloodthirsty are strong when the meta is filled with living creatures, but extremely weak when nonliving creatures dominate. This kind of analysis can and has been done on the forums, but it involves analyzing card synergies, counters, vulnerabilities, etc. only part of which can be done with mathematics.

As an example, the reason Iron Golem Wizard builds have dominated the meta for months is because they're hard to kill (5 armour, 13 HP, immunity to psychic/burning, unmovable) with their only major weakness (Slow) being removed by Teleport (most builds do not have the Lightning damage to make the Lightning +2 much of a problem). Their efficiency is undeniable, and mathematics certainly played a part in making that determination (such as illustrating how hard to kill they are), but it could not have determined things like how effective Psychic Immunity is (because this is based on the meta you play in) any more effectively than realising that your opponents often cast Sleep on your creatures and Psychic Immunity prevents them from doing that.

All that said, mathematics definitely has a place analyzing Mage Wars, it's just that that place doesn't involve making up data that cannot currently be known.

[fas723]

Aylin:
This is the kind of post I was looking for initially for this thread (at least the last part). Now you have some good arguments that makes sense, and some thing for me/us to discuss around. My whole idea here was to get good input how to improve the evaluation.

I don't see the point us arguing the way we have done up until now. It is clear I believe the model is a good start and quite close to good result, you think it needs more tuning. I never wanted anyone to treat me like a king, therefore I will suggest us gain from each other rather than any of us acting like this man-child as you call it. To be honest I think none of us can be proud of how this turned out. So, instead of you pointing at all the flaws, I would really appreciate if you could help me out instead and improve the model.

Whit this said I hope we can bury the fight and keep on with a good meaningful discussion instead.

*Sigh.* Do you really need this explained to you?

I'm not going to pick on your comment. I just want to say that I am well aware of the needed statistical requirements. I was just going to see if you had anything solid, which you have. I also became aware of this issue when I made the analysis. So what I did was that I grouped the similar traits together. Example:

Triplestrike
Doublestrike
Sweeping
Counterstrike
Doublestrike or Sweeping

Now there was 8 creatures that shared the same group in the above example. Then I made this for all traits and placed a guess as my starting difference between the traits in each group. Basically I said that Triplestrike must be 50% better than Doublestrike and so on. Now I could vary the groups value instead of each trait, which prevented the effect you and I see in this. After the groups had find a steady state level I went into the groups again started to see if the relation within the groups had to be changed. I published the table when I saw that I couldn't change much without losing reality (as you use to say) between the perceived values in the traits. (Like double strike being higher evaluated than Triplestrike)

What do you say about this approach? Maybe you could suggest which trait should go into which group?

[Aylin]

I also became aware of this issue when I made the analysis. So what I did was that I grouped the similar traits together. Example:

Triplestrike
Doublestrike
Sweeping
Counterstrike
Doublestrike or Sweeping

Now there was 8 creatures that shared the same group in the above example. Then I made this for all traits and placed a guess as my starting difference between the traits in each group. Basically I said that Triplestrike must be 50% better than Doublestrike and so on. Now I could vary the groups value instead of each trait, which prevented the effect you and I see in this. After the groups had find a steady state level I went into the groups again started to see if the relation within the groups had to be changed. I published the table when I saw that I couldn't change much without losing reality (as you use to say) between the perceived values in the traits. (Like double strike being higher evaluated than Triplestrike)

What do you say about this approach? Maybe you could suggest which trait should go into which group?

I'm not big on that approach either.

Triplestrike isn't 50% better than Doublestrike because Melee +X (or Bloodthirsty +X or Charge +X, etc.) only take effect on the first swing. If both Hydra and Goran have Bear Strength, for example, then Triplestrike is only 37.5% better (against 0 armour). Or if neither are enchanted but Goran gets Bloodthirsty then it's only 14% better (assuming Goran is in the same zone as its controller).

Likewise, the relationship between Doublestrike and Sweeping is a bit complicated as well. Which is better: hitting the same creature twice or being able to break through a guard and still hit your target? How much better is it? How much better is having the option to do either?

Also some traits scale with how big the creature is. Psychic Immunity doesn't really matter on Zombie Crawler or Skeletal Minion, but it's a big part of what makes Iron Golem so powerful.

The second largest problem is that there are so many traits that can't be quantified currently. Grey Angel can kill itself to heal another creature for 6 dice, though the usefulness of this ability is hard to judge in a vacuum since it depends on how much damage is on Grey Angel and a potential healing target. Malacoda's AoE damage of 2 every upkeep is very nice if you and your creatures are immune to poison and your opponent has several small to medium-sized creatures, but in almost every other situation it isn't that great.

Probably the third largest problem is that some traits amplify the effects of others. A simple example involves Rajan's Fury; due to being hindered, Bitterwood Foxes cannot leave and reenter a square to gain Charge while Thunderift Falcons and Cervere, the Forest Shadow can do that since they have Flying and Elusive, respectively. While I'm sure finding all such cases of amplification are possible, finding how much mana that having both is compared to one or the other would be difficult and time consuming (if not impossible).

And of course, the absolute largest problem would be the changing meta. The value of traits and abilities changes every time the meta does, so in order to keep everything accurate you'd have to redo it every time a new set came out after the meta calmed down (and it likely wouldn't be accurate for smaller groups).



In my opinion, any solution would need to remove the need to factor in the meta (because mathematicians are lazy). Honestly the best solution would probably be to make a chart that shows the minimum, maximum, average, and one standard deviation of damage from 1-12 dice vs. 0-6 armour and incorporeal and resilient. That would let players figure out how much damage (or how many actions for certain creatures) they can expect from their creatures before they die, how worthwhile Rhino Hide vs. Divine Protection will be for them, how useful Power Strike is vs. Piercing Strike, etc. in addition to removing the need for recalculating everything every time the meta changes. A formula could be provided that would let players plug 'n' chug to find out how many attacks of a given number of dice, armour, and health it would take for the creature to have a greater than 50% chance of dying, and effects from Corrode, Burn, regeneration, vampirism, damage during upkeep effects, multistrike, etc. could probably be added in if you wanted to get fancy. It would additionally remove complications like how much more valuable Triplestrike is than Doublestrike, at the same time as making it easier for players to understand.

You could also analyze the survivability vs. effectiveness for familiars, or show when it's better to focus on killing a creature vs. the enemy mage, or compare the usefulness of Banish vs. Quicksand vs. Sleep vs. Tangle/Stranglevine, analyze the mana/actions one gains from playing spawnpoints and when they receive those benefits (and possibly the best spots to place to place them for various strategies), etc.

If you wanted to compare creatures to each other directly, consider just comparing creatures that fill a specific role together, like ones that can be Bloodreapers or Pets to show which ones are better in which situations, or Valshalla vs. Samandriel for example.

I know that probably isn't what you want to hear, though to be honest I'm not sure how useful finding out how much mana various things are worth would be. So far Arcane Wonders has released new mechanics every set, and some of the new mechanics only appear on a single creature. They're likely to continue this trend, so the only thing you could say about those would be that they're worth whatever mana is required to make the creature cost what it costs. Plus it would never be able to take into account supporting cards.

Though as a side benefit it would also help players know how much damage they get out of their mana for attack spells.

[fas723]

I'm not big on that approach either.

Triplestrike isn't 50% better than Doublestrike because Melee +X (or Bloodthirsty +X or Charge +X, etc.) only take effect on the first swing. If both Hydra and Goran have Bear Strength, for example, then Triplestrike is only 37.5% better (against 0 armour). Or if neither are enchanted but Goran gets Bloodthirsty then it's only 14% better (assuming Goran is in the same zone as its controller).

Likewise, the relationship between Doublestrike and Sweeping is a bit complicated as well. Which is better: hitting the same creature twice or being able to break through a guard and still hit your target? How much better is it? How much better is having the option to do either?

I think I did express myself a bit bad here. The 50% was just a staring guess in this loop. As you could see in my reply the 14th the calc ended up saying triple strike is 22% more valuable than doubles tike. But I get your point.

Also some traits scale with how big the creature is. Psychic Immunity doesn't really matter on Zombie Crawler or Skeletal Minion, but it's a big part of what makes Iron Golem so powerful.

The second largest problem is that there are so many traits that can't be quantified currently. Grey Angel can kill itself to heal another creature for 6 dice, though the usefulness of this ability is hard to judge in a vacuum since it depends on how much damage is on Grey Angel and a potential healing target. Malacoda's AoE damage of 2 every upkeep is very nice if you and your creatures are immune to poison and your opponent has several small to medium-sized creatures, but in almost every other situation it isn't that great.

I think I start to realize where our view upon this differs. You are considering how good or bad certain abilities are in different situations. It is correct and I understand way you bring this up since it is an important part of the game, especially while you play it and in the given situations. However that is not how I have done it. My approach is rather the same a AW have when they make a creature. AW can never know the specific situations or design the creatures for that. AW have to put a fixed mana cost for each creature prior to any game play situation, thus AW must decide a value for each property upfront. I would claim that the meta is for sure very important to consider when you select which creatures to play, but not when you have to decide how much mana it is going to cost. As you say; when we try to bring in the meta in this this calculation will always change and never be stable.

In my opinion, any solution would need to remove the need to factor in the meta (because mathematicians are lazy). Honestly the best solution would probably be to make a chart that shows the minimum, maximum, average, and one standard deviation of damage from 1-12 dice vs. 0-6 armour and incorporeal and resilient.

I actually did that table a while ago, but I never compleatly finished it...


Ok, here is my next thought.
Why not use the enchantments as our basis for traits. By just quickly looking at all enchantments I can see that about 50% of all traits are represented, and the best part is that they are evaluated by its mana cost from AW already. For example:

Eagle wings - flying - 6 mana
Regrowth - Reg 2 - 5 mana
Vampirism Vampiric - 6 mana
Enfeeble - slow - 6 mana
...and so on...

I'm not saying it will be exactly this amount, but here is a good start. And when all the represented traits at enchantments are done we have been able to reduce the number of "unknown" traits substantially.

Just to check so that we are in the neighborhood we can look at Bull endurance and Rhino Hide. They represent Armor and Health only, which I have selected as individual parameters for each creature.

Health got a coeffient of 0.40 mana/health. -> Bull Endurance is 1.25 mana / health. Diff is 68%.
Armor got a coeffient of 2.28 mana/armor^(1/2) -> In this case 1,53 mana / armor (with armor 2). -> Rhino Hide is 2 mana / armor. Diff is 24%

So enchantments give a bit less per mana compared to build in values in creatures. Let's use this info.

Comments?

[DrunkenSaint]

Wow a lot of negativity in here. Just wanted to get in my 2 cents!
First I just want to say that I work as an analytical mathematician. My firm deals with market trends.
It is impossible to predict with 100% accuracy anything in the real world. One of the things that makes this game more enjoyable for me than any other strategy game I have ever played; Is that it too has a truly intense number of variables to consider. 
I think that Given the currently available data this is a great collection of data! I think that most peoples problem lies not so much in the math, but in its presentation. they seem to think that just because an item appears higher on the list, it is better (or that the creator is claiming that it is). It is simply a cost/benefit analysis. One with  high margin of error but one that is more than acceptable given the lack of data.

If you grouped them by true cost (most to least expensive) and then arranged them with the calculated cost (again greatest to least) you might get a decent idea of how they would match up  in an "ideal world". I use "decent idea" and "ideal world" because this will in many cases not be true but in general the guy at the top of each true cost list should match up favorably with the next one down. and the guy at the bottom of each  true cost list should, in general lose to the ones above it. It does not take into account everything, and certainly does not compare direct synergy. It is however a place to start! and I think that that is all it ever claimed to be!

[fas723]

Wow a lot of negativity in here. Just wanted to get in my 2 cents!
First I just want to say that I work as an analytical mathematician. My firm deals with market trends.
It is impossible to predict with 100% accuracy anything in the real world. One of the things that makes this game more enjoyable for me than any other strategy game I have ever played; Is that it too has a truly intense number of variables to consider. 
I think that Given the currently available data this is a great collection of data! I think that most peoples problem lies not so much in the math, but in its presentation. they seem to think that just because an item appears higher on the list, it is better (or that the creator is claiming that it is). It is simply a cost/benefit analysis. One with  high margin of error but one that is more than acceptable given the lack of data.

If you grouped them by true cost (most to least expensive) and then arranged them with the calculated cost (again greatest to least) you might get a decent idea of how they would match up  in an "ideal world". I use "decent idea" and "ideal world" because this will in many cases not be true but in general the guy at the top of each true cost list should match up favorably with the next one down. and the guy at the bottom of each  true cost list should, in general lose to the ones above it. It does not take into account everything, and certainly does not compare direct synergy. It is however a place to start! and I think that that is all it ever claimed to be!

Thanks for trying to explain this better than I could. 
As I have tried to point out throughout this thread is that this method is only optimizing towards a minimum point where the curve have its best fit towards all creature. It is not in any way saying it is the perfect fit (it should have been if the errors were zero). Thanks again!

It is/was apparent that my presentation wasn't received that well. So when I read how you would have done it it caught my attention. You say that you would group them by true cost first and then arrange them with the calculated cost within the groups? So all with, let’s say, true mana cost of 10 in one group arranges according the evaluation. And all these goes below the 11 mana cost creatures who also are arranged in its group. Correct?

This won't show my first intent to display how much you would get out of your invested mana though, but maybe this is the way to present it to get buy in at the forum.
My conclusion from this last thread is, as Zuberi said somewhere, that there are disagreements of the trait evaluation. I think to get this all this to work we/I have to find a way to evaluate the traits people understand and agrees with together with a final result that somewhat looks like what people have expected.

Personally I believe we have enough amounts of data to make these types of analysis. It sound like you belive this too?

[DrunkenSaint]

Indeed you have nowhere near enough data to make an even near accurate predictive curve.
that said even an inaccurate model is often of some use! often the best results we come up with in market analysis wind up just being the average result of thousands of independently made, individually inaccurate models.

I personally track how often I summon each creature in a game, and tend to give it a simple 1,2,3 star rating on how well it managed what I wanted it to in that game. That way I can see what I am actually using after a few games, and how well it is serving me. If we could get these results from every player in every game played for a year; We could make a fairly simple and accurate practical application table.  I think this is what most of the people complaining about your list seem to actually want. We of course don't have that data. We don't have any way to actually get that data. And even with it.... there would be complaints, as everyone plays this game so differently!