Shieldbreaker vs Savage Mace - Mathcraft

[yyr_]

================================================== ===========

Conclusion only applies for Armour>6 before debuff from shield breaker is applied.

Pure DPS throughout the game
http://wikiwiki.jp/hon/?plugin=ref&page=image&src=Savage-Mace.png

DPS:Cost.
http://wikiwiki.jp/hon/?plugin=ref&page=image&src=Duck-Boots.png


Yes duck boots kick the **** out of everything for DPS:cost, but out of the two you care about http://wikiwiki.jp/hon/?plugin=ref&page=image&src=Shieldbreaker.png

Formula used
a>6, (x+60)(1-((a-6)*0.06)/(1+0.06(a-6)))/(1-(a*0.06)/(1+0.06*a))=(x+123)*(1.05)

a= armour
x= damage before SB/SM
1.05 is an approximation of how attack speed from mace affects DPS

if you have over 200 agility+attackspeed this favours SM if not favours SB, for heroes with 100 agility+attackspeed it should be changed to 1.075 for more accurate readings.

If you're interested in the comparison keep reading :D

[MacroHard]

updated for v2.1.4. numbers used are for shieldbreaker level 3

Introduction:


The point of this post is to provide a comparative analysis between Savage Mace and Shieldbreaker WITHOUT MAKING ASSUMPTIONS.

For most posts I see where people try to use math to prove a point, something is missing. Some people neglect speed factors. Some people assume a specific armor value (normally 0). Nearly everyone failed to recognize that this game has an economy, so damage needs to be normalized by gold costs.

I will not make ANY assumptions. My calculations below factor in attack speed, armor of target, as well as the gold cost of the items (in this case 5400 vs 4300 is far from negligible).


The Acronyms and Variables:


SM = Savage Mace
SMd = Added damage output, including all factors, that SM adds
SMv = Value of SM = SMd / 5400
SB = Shieldbreaker
SBd = Added damage output, including all factors, that SB adds
SBv = Value of SB = SBd / 4300
D = Damage BEFORE purchasing any of the items or components
A = Armor value of enemy target
S = Attack speed bonus BEFORE purchasing any of the items or components
(includes everything... so if you have 80 agility and +30 attack speed worth of items, S = 110)


The Basics:


SMd = (88+.35*100)/(1+.06A)+[15/(100+S)]*[(D+88+.35*100)/(1+06A)]
SMv = {(88+.35*100)/(1+.06A)+[15/(100+S)]*[(D+88+.35*100)/(1+06A)]}/5400
SBd = 70/[1+.06(A-6)]+D/[1+.06(A-6)]-D/(1+.06A)
SBv = {70/[1+.06(A-6)]+D/[1+.06(A-6)]-D/(1+.06A)}/4300


The Method:


To solve the problem of which is better, we have to find the trend line where the values SMv and SBv are equal to each other. Since we have three variables (D, A, and S), we shall fix A at a given value then solve for S in terms of D. The method is repeated for varying values of A.

Basically it boiled down to this:
1) Set SMv = SBv
2) Solve for S in terms of D and A
3) Plot for fixed values of A


The Results:


v2.1.4
http://i52.tinypic.com/2ypc7dx.jpg

v2.0.38:
http://i56.tinypic.com/1zyhno3.jpg


The Conclusion:


As you can see from the graph, if your target has low armor, Shieldbreaker has greater effect. The numbers where damage, attack speed, and armor all come together are reasonable for in game scenarios.

Intangibles will also factor largely into your decision:

SM stops channeling and gives truestrike.
SB reduces armor so your allies also benefit and bypasses HotBL block.


Decision Tree:


I put this together for those who like cookie cutter builds. Obviously you can use your judgement to vary from this!

Instructions: Answer each question in order. If you answer yes, go with the item suggested. If the answer is no, go on to the next question!

Do you already have an attack modifier? -> Savage Mace
Does an allied hero already have Shieldbreaker? -> Savage Mace
Does the enemy team have more than one annoying channeling spell? -> Savage Mace
Do your or allied hero spells do mostly physical damage? -> Shieldbreaker
Do you or an allied hero have spells that reduce enemy armor? -> Shieldbreaker
Does an enemy hero have one annoying channeling spell? -> Savage Mace
Does the enemy carry have a form of evasion? -> Savage Mace
Is your current damage currently above 175? -> Shieldbreaker
Did you answer "no" to all of the above? -> Savage Mace

[WorstPlayer]

Your allies benefit from shieldbroken and its easier to build.

Now, since you like maths, intergrate x factorial dx

[yyr_]

Your allies benefit from shieldbroken and its easier to build.

Now, since you like maths, intergrate x factorial dx

As its a tad difficult to do i hope this approximation of the intergral about x=0 is suffice.

x - (gamma x^2)/2 + (1/36)*(6*gamma^2 + pi^2)*x^3 + (1/24)*(x^4)*( -gamma^3 - (gamma pi^2)/2 + psi^(2)(1)) + (1/120)*(x^5)*gamma^4 + gamma^2*pi^2 + (3 pi^4)/20 - 4*gamma*psi^(2)(1)) + (x^6*( -12 gamma^5 - 20 gamma^3*pi^2 - 9*gamma*pi^4 + 120*gamma^2*psi^(2)(1) + 20*pi^2*psi^(2)(1) + 12*psi^(4)(1)))/8640 + O(x^7) + constant

-Where gamma is the Euler-Mascheroni constant
-Where psi^(n)(x) is the nth derivative of the digamma function

:blac:

[procupine]

^ Great Odin's raven!

[dreamex]

Shieldbreaker vs Savagemace

(x+60)y=0.81*(x+123)*(1.15), 50<x<120, 1<y<1.30

X= Base damage
Y= Damage increase due to the -6 armour.
0.81 is the ratio of the cost of shield breaker to savage mace
123 as 88+35 as it has a 35% chance to deal 100 damage

Here is the question. As it gives +15 attack speed can i just multiply it with the rest of the damage on the right hand side as is the generation of attackspeed formed by attackspeed= 1.7*(agility increase + straight attackspeed increase) rather than 1.7*(agility increase)*(straight attackspeed increase).

If it is the former what modifications are needed?

Ignore the fact that shield breaker debuff affects teammates and lets assume it carries equal weight for purpose of this comparison.

Maybe savage mace will be the best damage : gold item in the game...

Note: Sorry mods if this isnt the correct forum, please shift if it nesc.

Shieldbreaker actually isn't easy to model in this linear term.

The reason being is that Shieldbreaker's effect doesn't increase your damage, it reduces your opponents effective HP by 36% of their Max HP, implicitly requiring you to do less damage to kill the same target.

To model it properly you need to consider attacking and defending hero stats.

For instance, on a hero with 1000 HP and 50 armor (giving him effectively 4000 HP, an attack that would normally strike a hero for 100 damage instead strikes him for 25, and what would've taken 10 attacks to kill a hero with 100 HP instead takes 40 attacks to kill him, resulting in him having survived the effective of 40 x 100 damage = 4000) Shieldbreaker's effect is equivalent to reducing his effective HP to 3636, meaning you would need only 36 attacks to kill the target, thereby increasing the value of each attack by the amount of effective health removed, thus reducing the time to kill this target by 4 attacks. In this case, it's as if you've done the equivalent of 4000 damage in 36 attacks, which is an increase of about 10 damage per attack equivalence.

On a target with 2944 hp and 6 armor (still giving him 4000 effective HP) the Shieldbreaker's effect is equivalent to reducing his effective HP to his Max HP of 2944. Were you still dealing 100 damage per hit this would reduce the amount of time to kill this target by 10.5 attacks, such that you've done the equivalent of 4000 damage in 29.5 attacks which is an increase of about 35.8 damage per attack equivalence.

For example's sake I mapped out a spreadsheet for Madman previously, take these hero stats:

Attacker (Madman)
Damage 135 BAT 1.7 Base AS 229 Modifier 1.28
Base AS is his attack speed from Agility along with his ultimate active
Modifier is to accomodate the increase in damage through his critical strike passive.

Defender (Arbitrary hero)
Target Max HP 2000 Target Armor X Target M. Armor 5.5
Assuming at end game most heroes have around 2000 HP (often this is higher, the lower this number the less favourable Shieldbreaker is)

With Shieldbreaker Madman attacks 1.94 times per second, with Savage Mace Madman attacks 2.02 times per second.

At X=5, eHP = 2600 (Shieldbreaker reduces this to 1880 / by 720)
Naked Madman takes 7.77 seconds to kill the target (uses 15 attacks @ 172.8 Damage per hit / 334.42 DPS)

Shieldbreaker Madman takes 3.89 seconds to kill the target (uses 7.5 attacks @ 249.6 Damage per hit / 483.05 DPS), an improvement of 49.94% (1.14% improvement per 100g)

Savage Mace Madman takes 4.02 seconds to kill the target (uses 8.1 attacks @ 320 Damage per hit / 647.53 DPS), an improvement of 48.35% (0.90% improvement per 100g)

At X=10, eHP = 3200 (Shieldbreaker reduces this to 2480 / by 720)
Naked Madman takes 9.57 seconds to kill the target (uses 18.5 attacks @ 172.8 Damage per hit / 334.42 DPS)

Shieldbreaker Madman takes 5.13 seconds to kill the target (uses 9.9 attacks @ 249.6 Damage per hit / 483.05 DPS), an improvement of 46.35% (1.05% improvement per 100g)

Savage Mace Madman takes 4.94 seconds to kill the target (uses 10 attacks @ 320 Damage per hit / 647.53 DPS), an improvement of 48.35% (0.90% improvement per 100g)

At X=15, eHP = 3800 (Shieldbreaker reduces this to 3080 / by 720)
Naked Madman takes 11.36 seconds to kill the target (uses 22 attacks @ 172.8 Damage per hit / 334.42 DPS)

Shieldbreaker Madman takes 6.38 seconds to kill the target (uses 11.9 attacks @ 249.6 Damage per hit / 483.05 DPS), an improvement of 43.89% (1.00% improvement per 100g)

Savage Mace Madman takes 5.84 seconds to kill the target (uses 12.3 attacks @ 320 Damage per hit / 647.53 DPS), an improvement of 48.35% (0.90% improvement per 100g)

At X=20, eHP = 4400 (Shieldbreaker reduces this to 3680 / by 720)
Naked Madman takes 13.16 seconds to kill the target (uses 25.5 attacks @ 172.8 Damage per hit / 334.42 DPS)

Shieldbreaker Madman takes 7.62 seconds to kill the target (uses 14.7 attacks @ 249.6 Damage per hit / 483.05 DPS), an improvement of 42.10% (0.96% improvement per 100g)

Savage Mace Madman takes 6.80 seconds to kill the target (uses 13.8 attacks @ 320 Damage per hit / 647.53 DPS), an improvement of 48.35% (0.90% improvement per 100g)

At X=25, eHP = 5000 (Shieldbreaker reduces this to 4280 / by 720)
Shieldbreaker gives an improvement of 40.74% (0.93% improvement per 100g)
Savage Mace gives an improvement of 48.35% (0.90% improvement per 100g)

At X=30, eHP = 5600 (Shieldbreaker reduces this to 4880 / by 720)
Shieldbreaker gives an improvement of 39.67% (0.90% improvement per 100g)
Savage Mace gives an improvement of 48.35% (0.90% improvement per 100g)

At X=35, eHP = 6200 (Shieldbreaker reduces this to 5480 / by 720)
Shieldbreaker gives an improvement of 38.81% (0.88% improvement per 100g)
Savage Mace gives an improvement of 48.35% (0.90% improvement per 100g)

So in short, Shieldbreaker's effect is a static 36% of the target's maxHP removed from their eHP, but as their eHP increases while maxHP stays the same the same (720 in this case) amount being removed becomes less and less significant.

Meanwhile the Savage Mace's DPS gain is consistent and linear regardless of what your target armor levels or HP levels are, it will always provide a consistent return.

[Urizen]

in the end, the shieldbreaker reduction of EHP applies for all enemies attacking a unit where the savage mace's effectiveness is only for that single hero

it is ALWAYS more beneficial to get a shieldbreaker over a savage mace for this reason

[GosuTurtle]

it is ALWAYS more beneficial to get a shieldbreaker over a savage mace for this reason

:arac:

[RogerDodger2]

Also consider that Savage Mace gives truestrike (good against Fayde, Night Hound, Wingbow) and a ministun (useful for heroes who are countered by TPs such as Arachna).

Plus it can stack with lifesteal.

[WorstPlayer]

As its a tad difficult to do i hope this approximation of the intergral about x=0 is suffice.

x - (gamma x^2)/2 + (1/36)*(6*gamma^2 + pi^2)*x^3 + (1/24)*(x^4)*( -gamma^3 - (gamma pi^2)/2 + psi^(2)(1)) + (1/120)*(x^5)*gamma^4 + gamma^2*pi^2 + (3 pi^4)/20 - 4*gamma*psi^(2)(1)) + (x^6*( -12 gamma^5 - 20 gamma^3*pi^2 - 9*gamma*pi^4 + 120*gamma^2*psi^(2)(1) + 20*pi^2*psi^(2)(1) + 12*psi^(4)(1)))/8640 + O(x^7) + constant

-Where gamma is the Euler-Mascheroni constant
-Where psi^(n)(x) is the nth derivative of the digamma function

:blac:

You just killed a kitten. I hope your happy.

[Easy_Lee]

So if I'm reading this right, savage mace is good for killing a wingbow carry because of ministun and truestrike, while shieldbreaker is better for other targets because your allies get the effect too.

[Czech0]

Also consider that Savage Mace gives truestrike (good against Fayde, Night Hound, Wingbow) and a ministun (useful for heroes who are countered by TPs such as Arachna).

Plus it can stack with lifesteal.

Good points. In these cases you would want to use Savage Mace.

Otherwise, Sheild breaker is better. There have been many other threads that analyzed this topic.

[sieneh]

This thread makes my brain hurt in places that don't exist.

[Autism_Prime]

wait there are smart people playing hon? I can do university calculas but I don't understand where those numbers are coming from lol i feel dumb

[Wickedsickk`]

this thread is why the servers imploded today

[NwGRich]

only get shieldbreaker on warbeast soulstealer pest and pred

[Yoda``]

wait there are smart people playing hon? I can do university calculas but I don't understand where those numbers are coming from lol i feel dumb

Well I know what a Gamma is, but I have no idea where he pulled that from.

[ElementUser]

I'm not that advanced in Mathematics, but I do recall that MKB vs. Buriza was done on the DA forums a lot. Can't find anyting that compares MKB vs. Desolator though.


The reason being is that Shieldbreaker's effect doesn't increase your damage, it reduces your opponents effective HP by 36% of their Max HP, implicitly requiring you to do less damage to kill the same target.This is true if the opponent's armor is positive, but if the armor is negative then this is not necessarily true.

For instance, assume the hero drops from 0 armor to -2 armor.

Generally, EHP = HP/Damage Reduction

EHP (0 Armor) = HP/(1-0) = HP (-0 is there because there is 0% damage reduction)

-2 Armor gives 0.94^-(-2) - 1 = 0.94^2 - 1 = -0.1164 damage reduction

EHP (-2 Armor) = HP/(1 - (-0.1164) = HP/(1.1164) = 0.89573629523468290935148692225009 ≈ 0.896 ≈ 89.6% EHP

100% - 89.6% = 10.4% drop in EHP when you go from 0 to -2 armor, not a 12% drop like you would expect it to.

(You can also use common sense and see that if the opponent has -17 armor, he would have 100 - 17*6 = -2% EHP, which would not make sense)

Anyway, you're right about Shieldbreaker's DPS not being so easy to represent as it is a function of the enemy's EHP, which can differ depending on what damage reduction sources they have. Not to mention Shieldbreaker's damage coefficient varies with the enemy armor (see this: http://forums.heroesofnewerth.com/showthread.php?t=61190), while Savage Mace adds a static amount of damage & True Strike (means that Savage Mace would generally be better if the opponent has Evasion).

[dreamex]

I'm not that advanced in Mathematics, but I do recall that MKB vs. Buriza was done on the DA forums a lot. Can't find anyting that compares MKB vs. Desolator though.

This is true if the opponent's armor is positive, but if the armor is negative then this is not necessarily true.

For instance, assume the hero drops from 0 armor to -2 armor.

Generally, EHP = HP/Damage Reduction

EHP (0 Armor) = HP/(1-0) = HP (-0 is there because there is 0% damage reduction)

-2 Armor gives 0.94^-(-2) - 1 = 0.94^2 - 1 = -0.1164 damage reduction

EHP (-2 Armor) = HP/(1 - (-0.1164) = HP/(1.1164) = 0.89573629523468290935148692225009 ≈ 0.896 ≈ 89.6% EHP

100% - 89.6% = 10.4% drop in EHP when you go from 0 to -2 armor, not a 12% drop like you would expect it to.

(You can also use common sense and see that if the opponent has -17 armor, he would have 100 - 17*6 = -2% EHP, which would not make sense)

Anyway, you're right about Shieldbreaker's DPS not being so easy to represent as it is a function of the enemy's EHP, which can differ depending on what damage reduction sources they have. Not to mention Shieldbreaker's damage coefficient varies with the enemy armor (see this: http://forums.heroesofnewerth.com/showthread.php?t=61190), while Savage Mace adds a static amount of damage & True Strike (means that Savage Mace would generally be better if the opponent has Evasion).

Aye this is a good amendment, negative armor values behave differently than positive ones and further alters how the shieldbreaker effect can be measured.

[Mutin]

As its a tad difficult to do i hope this approximation of the intergral about x=0 is suffice.

x - (gamma x^2)/2 + (1/36)*(6*gamma^2 + pi^2)*x^3 + (1/24)*(x^4)*( -gamma^3 - (gamma pi^2)/2 + psi^(2)(1)) + (1/120)*(x^5)*gamma^4 + gamma^2*pi^2 + (3 pi^4)/20 - 4*gamma*psi^(2)(1)) + (x^6*( -12 gamma^5 - 20 gamma^3*pi^2 - 9*gamma*pi^4 + 120*gamma^2*psi^(2)(1) + 20*pi^2*psi^(2)(1) + 12*psi^(4)(1)))/8640 + O(x^7) + constant

-Where gamma is the Euler-Mascheroni constant
-Where psi^(n)(x) is the nth derivative of the digamma function

:blac:

Dude knows how to google
:scou:

[AARP]

Illusions get the ministuns and full +100 damage from savage mace. Geometers babe + savage mace is completely ridiculous if the game lasts that long. The result is a ministun every second with insane dps.

[yyr_]

MATH!

Thanks for the indepth reply :D

Just want to note: using madman actually favours shieldbreaker as you had your ultimate on and you also used him as a lvl 25. Being lvl 25 increases his attack speed due to agility to further an advantage to shield breaker. This is because adding +15 attack speed increase you damage "less" relative to itself as your IAS increases. A hypothetical case where a hero has no +IAS and a Mace will gain a 15% bonus to their damage output because they +15 will be equate to 15%. Where as a hero with a large +IAS is only getting a small percentage increase. Picking madman who has a skill that furth increases his IAS by approx 50% is being favourable to shield breaker. Unmodified damage is also an important variable, the higher it is the more it favours shield breaker, as you picked a lvl 25 madman his base damage is fairly high favouring shield breaker, if you were to give it to a hero with 50 base damage savagemace>>>shieldbreaker in DPS and DPS/gold cost.

Also my formula wasnt linear but hyperbolic, the RHS was linear for savagemace for obvious reasons. The LHS however was hyperbolic because i had a compensating factor for armour, which i think you might see is a viable way to calculate this for all cases if i can find a way to approximate or add another compensating factor for the +15 attackspeed. Id assume a approximate increase would be more viable than a third variable :P

As you proved with your spreadsheet as armour increases, the damage dealt by shield breaker decresase.

[yyr_]

Dude knows how to google
:scou:

Wolframapha >>>>>>>>>>>> google

[Decency]

Ministun also interrupts enemy attacks (and forces them to restart, correct?). I feel that's definitely significant enough to require being calculated in.

[Jo]

On one hand your entire team makes more damage on the person you are focusing with a minus armor debuff

On the other hand the mini stun interupts attack animation, channeling spells and even walking animation.

Some other things to think about.

-orb effects, can't use desolator (-armor thingy) together with non-aura lifesteal, not sure which one cancels the other, probably you get no lifesteal.
-crit heroes, in theory, would benefit more from -armor thingy since harder hits scale with their ability while the +100 damage ministun doesen't.
-the +100 damage ministun doesen't help your lifesteal but you can still use lifesteal while using it.

Interesting dilemmas, just like it should be in a game with depth, there is no "right" answer, like everything else it's situational.

Still, getting a proper 1vs1 damage calculation of them both helps.

Personaly I tend to like -armor on the hard hitters (like soulstealer) and ministun on the fast hitters (chronos etc).

[yyr_]

Does anyone know the formula for damage reduction based on armour?

[ElementUser]

Does anyone know the formula for damage reduction based on armour?

It's in the Mechanics FAQ. :)

First place you look for formulas lol

http://img64.imageshack.us/img64/226/damagereduction.jpg

[yyr_]

...

Ta and sigh my bad :P

okay i will replace my Y variable with:
(1-((a-6)*0.06)/(1+0.06(a-6)))/(1-(a*0.06)/(1+0.06*a))
Which allows you to substiture armour right into the equation.

I took the attack speed damage increase to be approx 5% DPS giving me
(x+60)(1-((a-6)*0.06)/(1+0.06(a-6)))/(1-(a*0.06)/(1+0.06*a))=0.81*(x+123)*(1.05)

Do we believe 5% is an appropriate amount? i pulled a number out of my ass too be honest :P

EDIT: only works for a>6

[Porpoise_God]

Went into Excel and ran the math. Spreadsheet's attached if you care to look at it, just play with the first entry in Base Damage and Attack Speed (set for a level 1 hero with 50 damage, 120 AS at present).

At low stats, Savage Mace kicks the crap out of Shieldbreaker, Shieldbreaker makes up ground with heroes closer to tiered out (and this doesn't take into account that Broken Armor helps everyone hitting the target). However, Shieldbreaker works best on low-armor targets, Savage Mace tends to win when dealing with targets at 20+ armor, just because of the obscene +123 or so damage it's worth with procs factored in.

Too tired right now to figure out photobucket to post pretty graphs.

[Battle_Fury]

4351

Shieldbreaker is the better team item and for the extra dmg that mace gives it's 28. not a deal breaker. the 100 dmg crit doesn't scale with the game.

Usually you get a runed axe before the mace, and that means the extra dmg isn't part of the runed axe splash.

Basicly Shieldbreaker is a standard item for most heros. Mace is just a bonus item if you don't know what else to get. It all has to do with it lifesteal.

[Battle_Fury]

Went into Excel and ran the math. Spreadsheet's attached if you care to look at it, just play with the first entry in Base Damage and Attack Speed (set for a level 1 hero with 50 damage, 120 AS at present).

At low stats, Savage Mace kicks the crap out of Shieldbreaker, Shieldbreaker makes up ground with heroes closer to tiered out (and this doesn't take into account that Broken Armor helps everyone hitting the target). However, Shieldbreaker works best on low-armor targets, Savage Mace tends to win when dealing with targets at 20+ armor, just because of the obscene +123 or so damage it's worth with procs factored in.

Too tired right now to figure out photobucket to post pretty graphs.

but take into account soul stealers aura, shamans ulti, panda's flick, andro's aura, pesti's ulti, demonic breatplates, and that extra dmg that other people do is multiplied by them.

so if shieldbreaker and mace are close to being equal, breaker wins if it stacks with more neg armor OR if you attack the person with more then one hero. that extra dmg from neg reduction is then doubled triple or quadrupled...

and that's including some phyiscal spells too like pesti's ulti or war beasts pets, or the rockets from chipper, they get bonus dmg from the neg armor.

[Certa]

edit: pretty much what they said, except I'd use smaller words (and 150% less math). shieldbreaker > mace

[D_Pak]

not anymore because sb uses orb effect so no lifesteal for you

[yyr_]

Pretty much my conclusion is in any real game, DPS:Gold, Breaker>Mace for targets Armour>6. need to change my formula for when the armour goes negative. Real game is where you dont get it at lvl 8 or your opponents dont have 40+ armour

But if your just comparing damage Mace>Breaker for the entire duration of the game pretty much in all cases as well. This is still against targets with above 6 armour before they get shield broken, pretty much everything if your team isnt -armour stacking and they havent countered.

[MichaelBurge]

Shieldbreaker makes your attacks do more damage, but doesn't scale with attack speed. So for maximum effect you put it on someone who you don't plan on building attack speed on. It's the same way Pestilence can afford to get a Portal Key and defensive items like Shrunken because his main scaling ability allows anyone else to increase their damage as well. So you might as well have your "real" carry build better DPS items, and have Pestilence(or your Shieldbreaker) apply the debuff.

But unless you have a build where each item gives attack speed in some form, I don't recommend a Savage Mace unless there's a Night Hound or Wingbow in play.


Illusions get the ministuns and full +100 damage from savage mace. Geometers babe + savage mace is completely ridiculous if the game lasts that long. The result is a ministun every second with insane dps.

The best build for any carry is 5 Savage Maces, a Geometer's Bane, and a lucky Illusion rune. You have effectively 25 Savage Maces all of which can proc independently. I don't know if the extra damage is reduced on the illusions.


The reason being is that Shieldbreaker's effect doesn't increase your damage, it reduces your opponents effective HP by 36% of their Max HP, implicitly requiring you to do less damage to kill the same target.

No, Shieldbreaker's effect increases your damage. Damage reduces HP; "effective HP" is just some construct you made up to help understand the effect of armor. If the game stored effective HP and translated it to regular HP on display, you might have a point - but it doesn't do that. It stores "real" HP which damage reduces.

Unless you're willing to tell me that turning on my Elder Parasite doesn't make me take more damage - it just reduces my effective HP by 20%. (or some related value based off of it I'm too lazy to calculate).


As its a tad difficult to do i hope this approximation of the intergral about x=0 is suffice.

x - (gamma x^2)/2 + (1/36)*(6*gamma^2 + pi^2)*x^3 + (1/24)*(x^4)*( -gamma^3 - (gamma pi^2)/2 + psi^(2)(1)) + (1/120)*(x^5)*gamma^4 + gamma^2*pi^2 + (3 pi^4)/20 - 4*gamma*psi^(2)(1)) + (x^6*( -12 gamma^5 - 20 gamma^3*pi^2 - 9*gamma*pi^4 + 120*gamma^2*psi^(2)(1) + 20*pi^2*psi^(2)(1) + 12*psi^(4)(1)))/8640 + O(x^7) + constant

-Where gamma is the Euler-Mascheroni constant
-Where psi^(n)(x) is the nth derivative of the digamma function

:blac:

You can't integrate the factorial function in the standard way because it's only defined on the natural numbers. The Gamma function is a related extension to the Complex numbers, but the person you were quoting wasn't talking about the Gamma function - he said the factorial function.

So the only way to integrate such a function would be over the discrete distribution at each natural number. It simplifies to a sum over the factorial function the closed form of which is explained here: http://mathworld.wolfram.com/FactorialSums.html

noob


wait there are smart people playing hon? I can do university calculas but I don't understand where those numbers are coming from lol i feel dumb

He just punched it into a calculator. As long as I'm countering his post on a technicality to make myself look smart because I lack self-esteem yet want to appear to have a big ego, you mis-spelled "university calculas".

[ElementUser]

No, Shieldbreaker's effect increases your damage. Damage reduces HP; "effective HP" is just some construct you made up to help understand the effect of armor. If the game stored effective HP and translated it to regular HP on display, you might have a point - but it doesn't do that. It stores "real" HP which damage reduces.

Unless you're willing to tell me that turning on my Elder Parasite doesn't make me take more damage - it just reduces my effective HP by 20%. (or some related value based off of it I'm too lazy to calculate).
General Formula is EHP = HP/Damage Factors

If you don't believe the concept of EHP, you should read the thread in the DA forums about EHP: http://forums.dota-allstars.com/index.php?showtopic=67285 (requires DotA-Allstars forum account)


Effective hitpoint, or EHP is defined as the total amount of damage you can receive without factoring damage reduction before your hero dies.

Maximum hitpoint, or MHP, is the amount of hitpoint displayed on the unit.Actually, Elder Parasite does reduce your EHP, though not exactly by 20%.

Plugging it into the general EHP formula:

EHP = HP/(1 - (-0.2)) = HP/1.2 = 0.8333 ≈ 83.3%

So it only reduces your EHP by about 17.7%

[yyr_]

Shieldbreaker makes your attacks do more damage, but doesn't scale with attack speed. So for maximum effect you put it on someone who you don't plan on building attack speed on.

Basic dps output is hyperbolic paraboloid taking the form xy=z
X= damage per attack
Y= attacks per second
Z= damage per second
As any damage increasing effects will be multiplied to the LHS, and as it is commutative it doesnt matter if you plan on building attack speed OR damage.

Also due to the nature of the DPS equation going straight +damage is actually hindering your DPS as each additional +damage will be a small increase percentage wise, where as an installment to attackspeed would be a large increase by percentage. Not getting attackspeed when stacking damage is not the way to get the "maximum effect".

For those less math savvy check the drop down.

X*Y=Z, for example we will start with 10 for both values. So
10*10=100

If i increase my damage by say 40, so X=50 we now have
50*10=500.

Now if i could increase either X or Y by 50 which would be better, well if i add it to X i get:
100*10=1000
If i add it to Y
50*60=3000

As you can see stacking one stat isnt the best strat, you want a combination of the two.


The best build for any carry is 5 Savage Maces, a Geometer's Bane, and a lucky Illusion rune.

Yep, thats the best build for any carry.


No, Shieldbreaker's effect increases your damage. Damage reduces HP; "effective HP" is just some construct you made up to help understand the effect of armor.

If you don't believe the concept of EHP, you should read the thread in the DA forums about EHP: http://forums.dota-allstars.com/index.php?showtopic=67285 (http://forums.dota-allstars.com/index.php?showtopic=67285) (requires DotA-Allstars forum account)

http://wikiwiki.jp/hon/?plugin=ref&page=image&src=Legionnaire.png
ElementUser has spoken


You can't integrate the factorial function in the standard way because it's only defined on the natural numbers. The Gamma function is a related extension to the Complex numbers, but the person you were quoting wasn't talking about the Gamma function - he said the factorial function.

So the only way to integrate such a function would be over the discrete distribution at each natural number. It simplifies to a sum over the factorial function the closed form of which is explained here: http://mathworld.wolfram.com/FactorialSums.html

noob

Pretty sure he said
intergrate x factorial dx and what i did was this. (http://www.wolframalpha.com/input/?i=integrate+x%21) Its funny how much my answer looks exacly like a sum, and was generated by the same website you used. Maybe you should send them email saying their program is faulty. :blac:

[m00p]

Sorry guys but could you speak english? :/

[LightRain]

Sorry guys but could you speak english? :/

Shieldbreaker is more efficient (dps/gold) than Savage Mace, and also has the benefit of increasing the effectiveness of all physical damage from your team.

Savage Mace gives more dps to you (albeit for a greater cost), and also has the benefit of interrupting enemy heroes and defeating evasion/miss chance mechanics. It also stacks with all orbs.

The 'added benefits' are slightly harder to calculate than the simple 1v1 dps scenarios, so either one may be the proper purchase depending on how much gold you can spend (Savage Mace costs 1k more), whether the opponent is using evasion, whether you rely on another orb effect, and whether your build allows enough attacks/second for the ministun proc to translate into substantial survivability when standing against another hero via preventing him from attacking or casting effectively.

[m00p]

Thanks light rain :D
I'm personally a savage mace fan, which recently got buffed in a way with the orb change

[Lethe]

I expected savage mace to win actually :)

[yyr_]

I expected savage mace to win actually :)

What about duckboots! they are broken man.

[ShredderIV]

Savage mace is generally better if you have a higher attack speed... That is all.

[NullDragon]

Situations in which Savage Mace should be gotten first: Someone on the other team has innate evasion. Such as Chronos or Zephyr. Especially nighthound.

Situations in which Shieldbreakre should be gotten first: You are DPS, you have some other people who deal nice physical DPS on your team. This includes pandamonium and deadwood.

Everything else I think would really be preference. Ranged attackers MAY favor the savage mace more, being that you can ignore miss chance attacking up(I think miss chance is ignored by it?). It also has the 0.1 second ministun which interrupts attack animations, so in reality that's more of a 0.1-0.4 second stun depending on where in their animation you hit them. Plus the stun works a little like a slow in that it can help keep up to opponents for more attacks, plus attack speed is nice.

[yyr_]

Savage mace is generally better if you have a higher attack speed... That is all.

Not exacly true. The slower your attack speed the larger the DPS increase due to the nature of the +attackspeed formula. So heroes like :hell: get the biggest DPS increase from it. Because of this savage mace scales a little better early game than it does late game in terms of DPS increase.

On the other hand when talking about utility the faster your attack speed the more micro stuns you get.

Shieldbreakers DPS increase is unaffected by attackspeed.

[Shogun]

Also consider that Savage Mace gives truestrike (good against Fayde, Night Hound, Wingbow) and a ministun (useful for heroes who are countered by TPs such as Arachna).

Plus it can stack with lifesteal.

Yes

The ministun Savage Mace has can stop a channelling ultimate and turn a game around. As far as pure DPS, the math guys above can figure that out but I personally like SM better. The true-strike is really nice and coupling it with lifesteal (for high dps agil heroes) is important imho for lategame battles.

[ma5]

So how bout that Charged Hammer?

*runs and hides from shitstorm inc*

[yyr_]

So how bout that Charged Hammer?

*runs and hides from shitstorm inc*

I guess i have alot of spare time... but the formula for that would be so disgusting due to the attackspeed formula...

[ma5]

I guess i have alot of spare time... but the formula for that would be so disgusting due to the attackspeed formula...
Well, it's a static increase, no?

[Cawk]

Well, it's a static increase, no?

Nope, diminishing.

[yyr_]

Nope, diminishing.

What he said, but as agility also gives +attackspeed it gets ugly because you need to take what hero your playing and level into account. Also the other items in your inventory.

[peekachew1]

So, where are the proc calculations?
I love those.

18 hours of maths for one Irekei Assassin toon on Shadowbane, then realising that my previous build dealt more dps.

[ElementUser]

Nope, diminishing.

+Attackspeed is not diminishing because it stacks directly.

It is the attacks/second you get as a result of +attackspeed that is diminishing. Perhaps this is a minor point, but it's still important to distinguish between what diminishes and what does not.

As Virot2 said, we consider things in DotA/HoN "diminishing" if it's a diminishing absolute amount and not a diminishing ratio.

http://forums.heroesofnewerth.com/showthread.php?t=106459

:)

[Maraxus]

Yep, it's official, math geeks are playing hon.

Just kidding keep doing what you are doing, you are doing it well.

Also I knew most of that without the math but solid numbers keep the evil witch of the guess at bay.

[Lethe]

Some quick minor calculations, plz correct me if I am wrong anywhere.

Shieldbreaker costs 73.3 gold/point of damage, with the added benefit of -6 armor.

The components of shieldbreaker are warhammers, each costing 66.67 gold/point of damage.

Comparing to Savage Mace, which on average does 5400 gold/ (88+35 dmg) for 43.9 gold/point of damage.

The components of Savage Mace are Slayer, which costs 52.2 gold/point of damage, and Halberd, which costs 1500 g/ (21+6 dmg) for 55.56 gold/point of damage for the first halberd, 1500 g/((.85*40*.15)+21) for 57.47 gold/point of damage for the second halberd.

Just by looking at this, it becomes clear that savage mace outdoes Shieldbreaker by alot. This doesn't even take into account the +15 AS boost from Savage Mace.

The damage before armor reduction from savage mace is effectively double that of shieldbreaker (123 vs. 60). Which means for shieldbreaker to be better, it has destroy enough armor that the damage inflicted is double. With a -6 armor/attack attribute, at no point will this happen.

Yes, allies can take advantage of the -armor, but the truth is most heroes in a lineup are still going to be casters. Desolator is somewhat unpopular in dota for this very reason, and even in HoN things aren't much different, especially after the last couple of patches.

The way I see it, if you can farm the extra 1k g, savage mace >> shieldbreaker by a long shot. Exceptions could (and would) probably apply to heroes like soulstealer and Pestilence, but I'll leave that for someone else to figure out.

[TLSHadow]

Savage Mace > Shieldbreaker in most situations I find myself in, so 90% of the time I opt for MKB. It's a much more flexible item and has little hidden benefits most people don't realize! ;)

[Lethe]

Honestly the only time I could see shieldbreaker > savage mace would be if you were SS/Pestilence and the math worked in your favor. It's not likely though, and savage mace aren't exactly bad items on SS/Pestilence.

+ Illusions can actually ministun and deal the bonus damage, something that dota's illusions could not.


MKB 4 life.

[yyr_]

+Attackspeed is not diminishing because it stacks directly.

It is the attacks/second you get as a result of +attackspeed that is diminishing. Perhaps this is a minor point, but it's still important to distinguish between what diminishes and what does not.

As Virot2 said, we consider things in DotA/HoN "diminishing" if it's a diminishing absolute amount and not an absolute ratio.

http://forums.heroesofnewerth.com/showthread.php?t=106459

:)

I have to consider myself outside the HoN community on this one :P. Absolute ratio matters more to me :D

[ElementUser]

Sorry, diminishing ratio** roar blasted typo

[Shoutenkou]

I will join this discussion to look smart. Too bad I have bad math grades.
Also guys:
a^2+b^2=c^2
Remember !

[Stokkolm]

The only conclusion this calculations can reach is that both items are somewhat tied in damage/cost, and the choice depends a lot on situation. Shieldbreaker can increase the damage of :dead:'s ulti, :swif: ulti, and :arma: spine burst, and of course the damage done by your teams autoattacks. Savage mace's proc damage affects illusions, but it's not improved by criticals. Also shieldbreaker doesn't stack with lifesteal and slow orbs, and that limits the choices even further.

[Squallz]

only get shieldbreaker on warbeast soulstealer pest and pred

...........
fail

only get sb on heros who have decent ms and some slow/stun or your team have decent slow/cc

no sense of getting sb , when you have to run after the target all the time and only hit it once all 4-5 sec

for example
if you get it on wb , you are worthless once ulti is over
if you get skadi ( i get it all the time ) , i can kill someone solo and run away with ulti or i can kill someone with ulti so fast ( since he is so mega slowed ) that his team cant make it in time
same with sb .... the target will come much much futher towards his own team

i only get sb , when i know i never have to chase or the enemies will come to me cuz either they need to push or they have good initiator , who will start the fight or my team is full of cc but lack pure dmg ( like elec+andro+ws+polly+hb+demented+slith and so on )

[Johnson]

Note:
http://forums.heroesofnewerth.com/showthread.php?t=115053

this thread compares savage mace and riftshards, fyi
and I believe that riftshards wins...

[yyr_]

Riftshard > Savage

If you have over 177 damage pre-purchase. Other wise reversed.

[MacroHard]

Savage > Riftshards, and I posted my mathcraft on that thread to prove it.

I will do one of Savage vs Shieldbreaker as well, and as always, make no assumptions. Stay tuned.

[yyr_]

Savage > Riftshards, and I posted my mathcraft on that thread to prove it.

I will do one of Savage vs Shieldbreaker as well, and as always, make no assumptions. Stay tuned.


As you can see from the graph, there are very few instances where Riftshards will provide more damage per gold spent. You'd have to hit for 190 at 100% increased attack speed BEFORE purchasing your item. This is a rare situation.

Well ill going to have to disagree with your mathcraft for savage > crit.

100% IAS is pretty much a given on every agi hero, pretty much every single agi carry has over 100 agility basic at lvl 25 making this situation far from rare. 1 agility = +1IAS so getting +100 is piss easy. So the only issue is getting above 190 base damage. Also your calculations include DPS/gold they actually dont prove which is definitively better but rather which is better value.

In a nutshell: Do you have above 180 or so damage?
Yes -> Get crit
No -> Get mace

[Tape]

Wrong section.

Belongs in the Guides subforums.

[ElementUser]

Did you miss the other thread again? ._.

Merged.

Oh and both threads are now in Guides & Lists

[MacroHard]

Did you miss the other thread again? ._.

Merged

No, I figured this deserved it's own since I factored in attack speed, armor, damage, and gold cost. Either way I hope you guys like it.

[ElementUser]

I'll link your post in the first post of both threads as well so users don't have to sift through these pages

[MacroHard]

Yes duck boots kick the **** out of everything for DPS:cost

Assuming 100 base ias, 100 base damage, 10 enemy armor...

Duck Boots
3 damage
3 attack speed
150 gold
dps/gold = [3 + 3/(100+100)*(100+3)]/[1+.06(10)]/150 = .0189

Shieldbreaker
60 damage
-6 armor
4400 gold
dps/gold = [60/(1+.06(10-6))+100/(1+.06(10-6))-100/(1+.06(10))]/4400 = .0151

Doombringer
250 damage
6200 gold
dps/gold = (250)/[1+.06(10)]/6200 = .0252

Doombringer is actually the winner when it comes to efficiency.

:)

[yyr_]

...

(x+250)/6200<(x+3)*(a+3)/150a

Didnt check the price of doombringer just stole it from your formula, assuming its right though.

This is the equation for when duckboots is better than doombringer. We will find an upper bound for the value assuming that a=3397, or +3297 IAS which brings total IAS to 3400 or +3300 IAS, which is the highest possible attackspeed the engine allows (one attack per frame, or 1 attack every 0.05 seconds).

(x+250)/6200<(x+3)*(3400)/(510000)

For this to hold true x>328/121, or approximately 3.1. Thus holds true for all values of a for x>3. As x has the given limit x>30 as every agi hero has above 30 base damage at lvl 1. This holds for all cases.

(x+250)/6200<(x+3)/150. Even without the attackspeed bonus it still wins with an x>3 value. (always).

Doombringer is never better DPS:Cost then Duckboots on Agi heroes.

[MacroHard]

(x+250)/6200<(x+3)*(a+3)/150a

Didnt check the price of doombringer just stole it from your formula, assuming its right though.

This is the equation for when duckboots is better than doombringer. We will find an upper bound for the value assuming that a=3397, or +3297 IAS which brings total IAS to 3400 or +3300 IAS, which is the highest possible attackspeed the engine allows (one attack per frame, or 1 attack every 0.05 seconds).

(x+250)/6200<(x+3)*(3400)/(510000)

For this to hold true x>328/121, or approximately 3.1. Thus holds true for all values of a for x>3. As x has the given limit x>30 as every agi hero has above 30 base damage at lvl 1. This holds for all cases.

(x+250)/6200<(x+3)/150. Even without the attackspeed bonus it still wins with an x>3 value. (always).

Doombringer is never better DPS:Cost then Duckboots on Agi heroes.

Dude. You're calculated total DPS/cost. What really matters is ADDED DPS/cost.

Which is 250/6200 > 3/150

Using your logic and formula, buying no items at all is better than everything...

x/0 > anything

If total dps/cost mattered you'd see heroes running around naked.

Sorry, my analysis stands.

[yyr_]

Well i believe, regardless of others, that relative increase is more important than static increase.

What we are comparing is just two methods.

Yours is looking at what the item contributes as a stand alone piece, where as i look at how it fits into the entire puzzle. Each piece in the puzzle alters the outcome, so i take the puzzle into account when choosing my pieces.

I dislike your method because it may lead to the assumption that 6 doombringers is the best DPS:Cost build as its composed of the best DPS:Cost item stacked 6 times. When in fact 5 Doombringers and a Charged hammer will actually output higher DPS and will be cheaper, making it a better DPS:Cost combination although it is composed of an "inferior piece" in the form of a charged hammer. (this is just a hypothetical and is by no-means viable but proves my point).

Your math is correct for what your trying to calculate, i just dont agree that what your calculating is as important

[edxs]

Neither of you is incorrect. It's important when making comparisons to take all input variables into consideration. On a hero dealing 900 damage per attack, items that provide attack speed or reduce enemy armor naturally become more influential. On a level 1 hero, items that provide bonus damage generally win.

If a Doombringer is the best purchase on a 100 damage/100 AS hero, it doesn't mean it's the best on a hero with 5 Doombringers.

[MacroHard]

Neither of you is incorrect. It's important when making comparisons to take all input variables into consideration. On a hero dealing 900 damage per attack, items that provide attack speed or reduce enemy armor naturally become more influential. On a level 1 hero, items that provide bonus damage generally win.

If a Doombringer is the best purchase on a 100 damage/100 AS hero, it doesn't mean it's the best on a hero with 5 Doombringers.

That's it. I'm going to start a new thread on Doombringer.

[Falcon213]

Pretty much my conclusion is in any real game, DPS:Gold, Breaker>Mace for targets Armour>6.

Do you mean less than or equal to 6? From my understanding of armor, Shieldbreaker would do its max damage when the opponent has 6 armor before applying SB debuff but after applying any other +/- armor effects. (Meaning a total of 0 armor with everything including SB.) The further you deviate from this (both above and below) the less effective Shieldbreaker becomes.

[ElementUser]

Do you mean less than or equal to 6? From my understanding of armor, Shieldbreaker would do its max damage when the opponent has 6 armor before applying SB debuff but after applying any other +/- armor effects. (Meaning a total of 0 armor with everything including SB.) The further you deviate from this (both above and below) the less effective Shieldbreaker becomes.

It's actually ~4 armor.

http://hon.mikaelsunde.se/mechanics-damagecoefficients-1.62.0-zoom.png

[mindspank]

Shieldbreaker makes your attacks do more damage

True. EHP is just a helpful tool for understanding how armor relates to damage. It seems however that people like ElementUser get lost.



You can't integrate the factorial function in the standard way because it's only defined on the natural numbers. The Gamma function is a related extension to the Complex numbers, but the person you were quoting wasn't talking about the Gamma function - he said the factorial function.

So the only way to integrate such a function would be over the discrete distribution at each natural number. It simplifies to a sum over the factorial function the closed form of which is explained here: http://mathworld.wolfram.com/FactorialSums.html (http://mathworld.wolfram.com/FactorialSums.html)

noob

When you talk about the factorial function you very often mean the gamma function implicitly, especially in number theory, where you quite often write x! for simplicity over \Gamma(x). It's not ambiguous as they latter is just the analytic continuation of the former.

As for the second paragraph. It doesn't make mathematical sense to integrate a function over a distribution. What you probably meant was to use a discrete point measure which would reduce the integral into a countable sub.

Noob.


Pretty sure he said and what i did was this. (http://www.wolframalpha.com/input/?i=integrate+x%21) Its funny how much my answer looks exacly like a sum, and was generated by the same website you used. Maybe you should send them email saying their program is faulty. :blac:
MichaelBurge is correct in a non-nitpicking sense that the factorial (gamma) function is not elementary and as such does not have an easy expression of its integral in terms of functions one would consider elementary.

What Wolfram Alpha shows is a series representation of the integral based on the Laurent series of \Gamma around 0

\Gamma(x) = \sum_{k=0}^\infty \Gamma^{(k)}(1)/k! z^{k-1}

which you can then differentiate/integrate term-wise (remember that it was analytic). You can then use

\Gamma(x)' = \Gamma(x) \psi(x)

repeatedly to gain a series expansion with arbitrary many number of terms. In your case they only showed 6.

[TheVeronicas]

BUY BOTH

[MiniDon]

so i try to understand all of this..and wow... yeah id rather just try it out in some pubs loled..... sooo ima make mental notes, damage over 180 buy shards instead of savage.... channeling we all know that savage, shield = better dps than savage kkkkk

[Ntrain]

Damn, my head hurts.

Thanks for the info guys.

[Twiggie]

savage also makes it a lot easier to solo kong.

[rhinostopper]

As its a tad difficult to do i hope this approximation of the intergral about x=0 is suffice.

x - (gamma x^2)/2 + (1/36)*(6*gamma^2 + pi^2)*x^3 + (1/24)*(x^4)*( -gamma^3 - (gamma pi^2)/2 + psi^(2)(1)) + (1/120)*(x^5)*gamma^4 + gamma^2*pi^2 + (3 pi^4)/20 - 4*gamma*psi^(2)(1)) + (x^6*( -12 gamma^5 - 20 gamma^3*pi^2 - 9*gamma*pi^4 + 120*gamma^2*psi^(2)(1) + 20*pi^2*psi^(2)(1) + 12*psi^(4)(1)))/8640 + O(x^7) + constant

-Where gamma is the Euler-Mascheroni constant
-Where psi^(n)(x) is the nth derivative of the digamma function






^ Great Odin's raven!

I agree. Odin should shun him for learning math in the first place.

[Theburned]

I really think the ministun from savage mace really just sells the item so much easier while giving 88 damage + 35 with proc and another 15 AS (well 35% for a 100 damage hit.)
but really the ministun does wonders.

[Hikary`]

i want both on preda or scout O:!

[MacroHard]

stuff

I updated my post for version 2.0.38 using level 3 ShieldBreaker. Unfortunately, even the recent gold cost reduction buff wasn't enough to make it a better value than Savage Mace.

However, it is now an easier buildup, so who knows what the future holds.

[MacroHard]

I updated my graphs for the recent SB buff in v2.1.4. Shieldbreaker is now viable for targets with less than 20 armor.

http://forums.heroesofnewerth.com/showthread.php?p=1583797#post1583797