Mana Efficient Attackers

[Drac]

I have been inspired by the analysis done by fas723 and lettucemode to create my own analysis.  With the rise of spawnpoints lately, this analysis focuses entirely on the mana efficiency of attacking creatures and conjurations.  Please read the Limitations section before attempting to make any sense of the results.

Methods:
I first started by separating each relevant attack from the creature or conjuration and perform simplistic statistically averaged attack against a set of hypothetical defenders to calculate the expected damage.  There were 8 defender configurations that were chosen... 0 Armor, 2 Armor, 4 Armor, and Resilient, 0 Armor Aegis 1, 2 Armor Aegis 1, 4 Armor Aegis 1, Resilient Aegis 1.  In this calculation, resilient means the same thing as arbitrarily large armor.  Once the attacks were computed, the average of the attacks were calculated and stored for the rest of the calculations.  The efficiency score of the is then computed by dividing the average projected damage by the mana cost of the creature or conjuration.

To calculate best general attack efficiency, the highest scoring attack for each creature or conjuration is selected and ranked according to it's score.  Similarly, the best general weakest attack efficiency is the lowest scoring attack for each creature or conjuration ranked according to it's score.  These two scores should provide upper and lower bounds to the true score of a creature.

Equations Used:
1:  Dice Rolled = Attack Dice - Aegis Value
2:  Expected Crit Damage = 1/2 Dice rolled
3:  Expected Damage = Number of Strikes * MAX( Dice Rolled - MAX( Armor - Piercing : 0 ) : Average Crit )
4:  Average Damage = ( Expected Damage for 0 Armor + Expected Damage for 2 Armor ... ) / Sample Count
5:  Cost Efficiency = Mana Cost / Average Damage

Limitations:
Attacks that have a trait that directly affects the number of dice rolled or damage dealt vs armor were applied where applicable.  The traits included in the calculation include charge +X, piercing +X, +X vs Type(+2 vs flying), critical damage, bloodthirsty +X, doublestrike, triplestrike, sweeping, and zone attacks(calculated vs at most 3 defenders).  Many other traits are left out of the calculation such as burn, corrode, unavoidable, ethereal, and so on because they represent more tactical lines of play, which is outside the scope of this analysis.

There is no way to know how likely a given attack is usable in the general case (if even at all).  As such, the best I can do is provide a maximum and minimum score from the best attack and the worst attack and let you guys figure out for yourselves where the true value actually lies.

Finally, before taking note about about the efficiency of Ballista, remember that this calculation does not factor in tactical play, and that includes the fact that it can only attack every other turn at most.  It was calculated the same way that other creatures were.  That said, an argument could be made that no creature is guaranteed to attack every turn in all cases(except possibly Grimson).

Top 50 Results:

Best General Attack Efficiency			Best General “Weakest” Attack Efficiency
Rank	Name	Score	Rank	Name	Score
1	Ballista	0.461	1	Ballista	0.461
2	Vine Snapper	0.446	2	Goblin Grunt	0.391
3	Feral Bobcat	0.438	3	Akiro's Hammer	0.391
4	Akiro's Hammer	0.427	4	Raptor Vine	0.319
5	Dwarf Kriegsbiel	0.398	5	Bitterwood Fox	0.313
6	Goblin Grunt	0.391	6	Skeletal Minion	0.313
7	Zombie Crawler	0.391	7	Vine Snapper	0.313
8	Ludwig Boltstorm	0.361	8	Iron Golem	0.279
9	Shaggoth-Zora	0.359	9	Orc Butcher	0.273
10	Oscuda	0.346	10	Shaggoth-Zora	0.273
11	Zombie Brute	0.330	11	Skeletal Sentry	0.273
12	Temple High Guard	0.323	12	Thunderift Falcon	0.260
13	Raptor Vine	0.319	13	Timber Wolf	0.243
14	Bitterwood Fox	0.313	14	Zombie Crawler	0.234
15	Skeletal Minion	0.313	15	Blue Gremlin	0.232
16	Zombie Minion	0.313	16	Thornlasher	0.223
17	Darkfenne Hydra	0.293	17	Zombie Minion	0.223
18	Unstable Zombie	0.292	18	Nightshade Lotus	0.223
19	Iron Golem	0.279	19	Bridge Troll	0.221
20	Steelclaw Grizzly	0.276	20	Devouring Jelly	0.221
21	Mountain Gorilla	0.273	21	Knight of Westlock	0.221
22	Orc Butcher	0.273	22	Skeletal Knight	0.221
23	Sir Corazin	0.273	23	Earth Elemental	0.219
24	Skeletal Sentry	0.273	24	Deathfang	0.203
25	Thunderift Falcon	0.260	25	Darkpackt Slayer	0.202
26	Goran, Werewolf Pet	0.250	26	Dwarf Kriegsbiel	0.199
27	Timber Wolf	0.243	27	Zombie Brute	0.199
28	Bloodcrag Minotaur	0.242	28	Temple High Guard	0.198
29	Grimson, Deadeye Sniper	0.242	29	Asyran Defender	0.195
30	Dire Wolf	0.240	30	Invisible Stalker	0.192
31	Tarrok, The Skyhunter	0.240	31	Accolyte of the Bog Queen	0.188
32	Earth Elemental	0.234	32	Asyran Cleric	0.188
33	Blue Gremlin	0.232	33	Brogan Bloodstone	0.188
34	Kralathor, the Devourer	0.227	34	Darkfenne Bat	0.188
35	Goblin Slinger	0.223	35	Feral Bobcat	0.188
36	Thornlasher	0.223	36	Firebrand Imp	0.188
37	Venomous Zombie	0.223	37	Goblin Builder	0.188
38	Nightshade Lotus	0.223	38	Psylok	0.188
39	Bridge Troll	0.221	39	Steelclaw Grizzly	0.184
40	Devouring Jelly	0.221	40	Oscuda	0.183
41	Highland Unicorn	0.221	41	Ravenous Ghoul	0.183
42	Knight of Westlock	0.221	42	Grey Angel	0.182
43	Skeletal Knight	0.221	43	Whirling Spirit	0.182
44	Spitting Raptor	0.216	44	Ichthellid	0.181
45	Selesius, The East Wind	0.208	45	Necropian Vampiress	0.180
46	Deathfang	0.203	46	Redclaw, Alpha Male	0.180
47	Darkpackt Slayer	0.202	47	Emerald Tegu	0.174
48	Skeletal Archer	0.199	48	Unstable Zombie	0.174
49	Royal Archer	0.198	49	Togoroh, Forest Sentinel	0.173
50	Asyran Defender	0.195	50	Thorg, Chief Bodyguard	0.169

I have probably forgotten to include important information on my methods.  Please ask you you have any questions or feedback, enjoy the data, and remember that it is only a guide.

[fas723]

Interesting!
I have a couple of comments, but no time to write them now. Can you upload you calculation somehow (is it in MS Excel? ) , that would eliminate some of the questions.

[Drac]

My calculation was performed in openoffice calc, the free equivalent of excel.  I could try to export it as a .xls file, but I cannot verify that the export actually worked from excel.  Let me know which you think would be more useful.

[Aylin]

You need to publish any equations or whatever asap. Another thing to consider is that currently there is no way for a creature to have both Resilient and Aegis. Why did you ignore odd armour values and only go up to 4 armour as well?

Also you separate the attacks based on type (quick melee, slow melee, quick ranged, and slow ranged).

[Drac]

You need to publish any equations or whatever asap. Another thing to consider is that currently there is no way for a creature to have both Resilient and Aegis. Why did you ignore odd armour values and only go up to 4 armour as well?

Also you separate the attacks based on type (quick melee, slow melee, quick ranged, and slow ranged).

I agree on publishing the equations, but I think I am about to redo the same list as a simulation instead... to eliminate any inaccuracies in statistical equations.  I will have to gather the equations and will post them again later.

As to the question on resilient and aegis, I specify that resilient only means arbitrarily large armor( to the point that even with a creature's built in piercing, a creature will, on average rely solely on crits for damage ).  The main reason this configuration is present is to simulate attacks against an armor stacked mage with aegis.  I agree that this is a bit oversimplified at times, which is why I want this list to proceed as a application based simulation(which shouldn't take too long if enough interest is present).

Why I only did even armor was mostly to reduce work in this draft while still representing what I feel are reasonable target configurations(unarmored, light armor, heavy armor, and obscene armor/resilient).

As to your last sentance, are you asking me to separate them in this manner?  Or just seeking a clarification on how the attacks were separated?

[Drac]

Ok, I added an equations section to the table.  I concede that equation number 3 could be improved upon.  It is the primary reason I would like to redo this as a simulation... to properly account for the chance of burst damage and whiffs more appropriately.

[Aylin]

As far as I know, the absolute highest armour a mage could have would be:

2 (elemental armour/demonhide) + 1 (elemental cloak) + 2 (leather gloves/boots) + 2 (Rhino Hide) + 2 (Barkskin) +2 (Fortified Position) + 1 (Hand of Bim-Shalla) + 1 (Standard Bearer) = 13, which is only possible for a Druid in a team game, with a Warlord as the ally.

In a 1v1 game against a non-Druid non-Warlord the highest armour possibly is 10 (-2 Barkskin -1 Standard Bearer).

Equating that with Resilient would be incorrect for two reasons:
1. Steelclaw Grizzly's unbuffed "Heavy Claw Strike" has a 1/279936 chance to roll all normal 2s. Against resilient the damage would be 0 but against the hypothetical 13 armour above it would hit for 2. This skews the results. Also against 10 armour there are several creatures that could still deal damage without relying on only critical damage (Grizzly, Earth Elemental, Brogan, Iron Golem, Grimson, Temple High Guard [while guarding], Tarok [against Flying], etc)
2. In most games a mage's armour is not going to reach 10 (or higher). I don't think I've ever played a game where armour went above 6. You've implied that you're giving this scenario equal weight to the others, which is not even close to accurate. This is probably my biggest issue overall.

Because of the above issue, it might be better to show which gives you the most damage per mana in a given situation, since accurately weighting the scenarios would be impossible (even if you were able to accurately determine the frequency of each given scenario, once you publish your work players are likely to take that into account...which would of course change the frequencies and make your work inaccurate).

Also you're defining "attack efficiency" as damage per mana spent, though that might not be accurate...


And I am asking you to separate the attacks based on their type. You can't say that a slow melee attack is more efficient than a slow melee attack without taking into account the position of the board...something that is impossible to do here. By separating them

[Drac]

Equating that with Resilient would be incorrect for two reasons:
1. Steelclaw Grizzly's unbuffed "Heavy Claw Strike" has a 1/279936 chance to roll all normal 2s. Against resilient the damage would be 0 but against the hypothetical 13 armour above it would hit for 2. This skews the results. Also against 10 armour there are several creatures that could still deal damage without relying on only critical damage (Grizzly, Earth Elemental, Brogan, Iron Golem, Grimson, Temple High Guard [while guarding], Tarok [against Flying], etc)

You are right about that.  In practice though, the average expected damage should vary by only a small(but still significant) amount from the way it is currently calculated.

2. In most games a mage's armour is not going to reach 10 (or higher). I don't think I've ever played a game where armour went above 6. You've implied that you're giving this scenario equal weight to the others, which is not even close to accurate. This is probably my biggest issue overall.

I'd have to agree there as well.  I could however easily envision an 8 armor, aegis 1 brogan or thorg though,  but that's not addressing your point.  Weighting these as I have done was a judgment call I had to make.  It is not backed up by mathematics, and the sample points will undoubtedly change the results.  I see no other way to making a general ranking here without making a judgment call somewhere.  But feel free to criticize my judgment calls as you see fit.

Also you're defining "attack efficiency" as damage per mana spent, though that might not be accurate...

I don't see the problem with that as long as...
a) Tactical analysis is deliberately left out.
b) The assumption that an attacker can repeatedly utilize it's attack(while keeping with point a), unless dealt with by the opponent, holds.
c) Longevity of the attacker is ignored. (I plan to do a separate analysis on longevity following similar principles in the future)

If these three points hold, then this type of analysis should hold merit.

And I am asking you to separate the attacks based on their type. You can't say that a slow melee attack is more efficient than a slow melee attack without taking into account the position of the board...something that is impossible to do here. By separating them

I understand your point.  When I complete the simulator, I will be able to more easily modify the rankings data to show that.  Understand that I am much better at programming with C# and Java than I am at working with spreadsheet formulas, I posted this as more of a rough draft to get opinions on how best to proceed.  (Plus, the spreadsheet is already a mess)

[Kharhaz]

As far as I know, the absolute highest armour a mage could have would be:

2 (elemental armour/demonhide) + 1 (elemental cloak) + 2 (leather gloves/boots) + 2 (Rhino Hide) + 2 (Barkskin) +2 (Fortified Position) + 1 (Hand of Bim-Shalla) + 1 (Standard Bearer) = 13, which is only possible for a Druid in a team game, with a Warlord as the ally.

In a 1v1 game against a non-Druid non-Warlord the highest armour possibly is 10 (-2 Barkskin -1 Standard Bearer).

Beastmaster

+2 (armour) +1 (cloak) +2 (leather gloves / boots) +2 (Rhino Hide) +2 (Fortified position) +1( Hand) +4 (Animal kinship x4) +1 (standard) = 15 (14 solo match)

With the warlord ally bonus. Each kinship provides the beastmaster with +1 armor. Beastmaster also has the highest melee attack potential last I checked.

[aquestrion]

Hey aylin I would love to see your compleated model.

[Aylin]

As far as I know, the absolute highest armour a mage could have would be:

2 (elemental armour/demonhide) + 1 (elemental cloak) + 2 (leather gloves/boots) + 2 (Rhino Hide) + 2 (Barkskin) +2 (Fortified Position) + 1 (Hand of Bim-Shalla) + 1 (Standard Bearer) = 13, which is only possible for a Druid in a team game, with a Warlord as the ally.

In a 1v1 game against a non-Druid non-Warlord the highest armour possibly is 10 (-2 Barkskin -1 Standard Bearer).

Beastmaster

+2 (armour) +1 (cloak) +2 (leather gloves / boots) +2 (Rhino Hide) +2 (Fortified position) +1( Hand) +4 (Animal kinship x4) +1 (standard) = 15 (14 solo match)

With the warlord ally bonus. Each kinship provides the beastmaster with +1 armor. Beastmaster also has the highest melee attack potential last I checked.

I can't believe I forgot about Animal Kinship. X_X