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Author Topic: Mana Efficient Attackers  (Read 5349 times)

Drac

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Mana Efficient Attackers
« on: December 16, 2013, 11:18:54 PM »
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 EfficiencyBest General “Weakest” Attack Efficiency
RankNameScoreRankNameScore
1Ballista0.4611Ballista0.461
2Vine Snapper0.4462Goblin Grunt0.391
3Feral Bobcat0.4383Akiro's Hammer0.391
4Akiro's Hammer0.4274Raptor Vine0.319
5Dwarf Kriegsbiel0.3985Bitterwood Fox0.313
6Goblin Grunt0.3916Skeletal Minion0.313
7Zombie Crawler0.3917Vine Snapper0.313
8Ludwig Boltstorm0.3618Iron Golem0.279
9Shaggoth-Zora0.3599Orc Butcher0.273
10Oscuda0.34610Shaggoth-Zora0.273
11Zombie Brute0.33011Skeletal Sentry0.273
12Temple High Guard0.32312Thunderift Falcon0.260
13Raptor Vine0.31913Timber Wolf0.243
14Bitterwood Fox0.31314Zombie Crawler0.234
15Skeletal Minion0.31315Blue Gremlin0.232
16Zombie Minion0.31316Thornlasher0.223
17Darkfenne Hydra0.29317Zombie Minion0.223
18Unstable Zombie0.29218Nightshade Lotus0.223
19Iron Golem0.27919Bridge Troll0.221
20Steelclaw Grizzly0.27620Devouring Jelly0.221
21Mountain Gorilla0.27321Knight of Westlock0.221
22Orc Butcher0.27322Skeletal Knight0.221
23Sir Corazin0.27323Earth Elemental0.219
24Skeletal Sentry0.27324Deathfang0.203
25Thunderift Falcon0.26025Darkpackt Slayer0.202
26Goran, Werewolf Pet0.25026Dwarf Kriegsbiel0.199
27Timber Wolf0.24327Zombie Brute0.199
28Bloodcrag Minotaur0.24228Temple High Guard0.198
29Grimson, Deadeye Sniper0.24229Asyran Defender0.195
30Dire Wolf0.24030Invisible Stalker0.192
31Tarrok, The Skyhunter0.24031Accolyte of the Bog Queen0.188
32Earth Elemental0.23432Asyran Cleric0.188
33Blue Gremlin0.23233Brogan Bloodstone0.188
34Kralathor, the Devourer0.22734Darkfenne Bat0.188
35Goblin Slinger0.22335Feral Bobcat0.188
36Thornlasher0.22336Firebrand Imp0.188
37Venomous Zombie0.22337Goblin Builder0.188
38Nightshade Lotus0.22338Psylok0.188
39Bridge Troll0.22139Steelclaw Grizzly0.184
40Devouring Jelly0.22140Oscuda0.183
41Highland Unicorn0.22141Ravenous Ghoul0.183
42Knight of Westlock0.22142Grey Angel0.182
43Skeletal Knight0.22143Whirling Spirit0.182
44Spitting Raptor0.21644Ichthellid0.181
45Selesius, The East Wind0.20845Necropian Vampiress0.180
46Deathfang0.20346Redclaw, Alpha Male0.180
47Darkpackt Slayer0.20247Emerald Tegu0.174
48Skeletal Archer0.19948Unstable Zombie0.174
49Royal Archer0.19849Togoroh, Forest Sentinel0.173
50Asyran Defender0.19550Thorg, Chief Bodyguard0.169

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.
« Last Edit: December 17, 2013, 11:46:55 PM by Drac »

fas723

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Re: Mana Efficient Attackers
« Reply #1 on: December 17, 2013, 02:46:01 PM »
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

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Re: Mana Efficient Attackers
« Reply #2 on: December 17, 2013, 03:52:59 PM »
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

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Re: Mana Efficient Attackers
« Reply #3 on: December 17, 2013, 10:43:10 PM »
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

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Re: Mana Efficient Attackers
« Reply #4 on: December 17, 2013, 11:00:50 PM »
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

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Re: Mana Efficient Attackers
« Reply #5 on: December 17, 2013, 11:49:07 PM »
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

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Re: Mana Efficient Attackers
« Reply #6 on: December 18, 2013, 12:06:36 AM »
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

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Re: Mana Efficient Attackers
« Reply #7 on: December 18, 2013, 12:56:13 AM »
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

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Re: Mana Efficient Attackers
« Reply #8 on: December 18, 2013, 01:06:48 PM »
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.
« Last Edit: December 18, 2013, 01:31:15 PM by Kharhaz »

aquestrion

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Re: Mana Efficient Attackers
« Reply #9 on: December 18, 2013, 01:46:28 PM »
Hey aylin I would love to see your compleated model.

Aylin

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Re: Mana Efficient Attackers
« Reply #10 on: December 18, 2013, 07:35:28 PM »
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