Shieldbreaker - An in depth look

[Ubuntu]

This is an in depth look at shieldbreaker,

The first column is how much armor they had, the second is their original damage reduction %. The next two columns are the reduced armor and % reduction wheras the last column is the increase in damage.


Armor Reduction After Reduction +% From Shieldbreaker
-11 -49.4 -17 -65.1 10.51
-10 -46.1 -16 -62.8 11.43
-9 -42.7 -15 -60.5 12.45
-8 -39.0 -14 -57.9 13.60
-7 -35.2 -13 -55.3 14.88
-6 -31.0 -12 -52.4 16.33
-5 -26.6 -11 -49.4 17.98
-4 -21.9 -10 -46.1 19.86
-3 -16.9 -9 -42.7 22.03
-2 -11.6 -8 -39.0 24.55
-1 -6.0 -7 -35.2 27.50
0 0.0 -6 -31.0 31.01
1 5.7 -5 -26.6 34.21
2 10.7 -4 -21.9 36.56
3 15.3 -3 -16.9 37.99
4 19.4 -2 -11.6 38.43
5 23.1 -1 -6.0 37.80
6 26.5 0 0.0 36.00
7 29.6 1 5.7 33.96
8 32.4 2 10.7 32.14
9 35.1 3 15.3 30.51
10 37.5 4 19.4 29.03
11 39.8 5 23.1 27.69
12 41.9 6 26.5 26.47
13 43.8 7 29.6 25.35
14 45.7 8 32.4 24.32
15 47.4 9 35.1 23.38
16 49.0 10 37.5 22.50
17 50.5 11 39.8 21.69
18 51.9 12 41.9 20.93
19 53.3 13 43.8 20.22
20 54.5 14 45.7 19.57
21 55.8 15 47.4 18.95
22 56.9 16 49.0 18.37
23 58.0 17 50.5 17.82
24 59.0 18 51.9 17.31
25 60.0 19 53.3 16.82

As we can see, shieldbreaker's effectiveness is lessened with each point of armor the target gains.

EDIT: took out information about Riftshards > Shieldbreaker

That is only true when enemy -4< armor < 20, after spells like pestilence's ulti or Soulstealer's passive.


I hope my guide/info post contained some useful information.

[dreamex]

This is an in depth look at shieldbreaker,

The first column is how much armor they had, the second is their original damage reduction %. The next two columns are the reduced armor and % reduction wheras the last column is the increase in damage.


Armor Reduction After Reduction Difference
1 5.7 -5 -36.3 41.9
2 10.7 -4 -28.1 38.8
3 15.3 -3 -20.4 35.7
4 19.4 -2 -13.2 32.5
5 23.1 -1 -6.4 29.5
6 26.5 0 0.0 26.5
7 29.6 1 5.7 23.9
8 32.4 2 10.7 21.7
9 35.1 3 15.3 19.8
10 37.5 4 19.4 18.1
11 39.8 5 23.1 16.7
12 41.9 6 26.5 15.4
13 43.8 7 29.6 14.2
14 45.7 8 32.4 13.2
15 47.4 9 35.1 12.3
16 49.0 10 37.5 11.5
17 50.5 11 39.8 10.7
18 51.9 12 41.9 10.1
19 53.3 13 43.8 9.5
20 54.5 14 45.7 8.9
21 55.8 15 47.4 8.4
22 56.9 16 49.0 7.9
23 58.0 17 50.5 7.5
24 59.0 18 51.9 7.1
25 60.0 19 53.3 6.7As we can see, shieldbreaker's effectiveness is lessened with each point of armor the target gains.

Lets compare this to riftshards (level 4)

20% chance for 2.4 critical strike

2.4/20% = average of 28% increase in damage. Therefore riftshards > Shieldbreaker whenever the target has >6 armor. Since everyone should have more than 6 armor by the time you can get this item, it is effectivly useless.

This shows that Riftshards > Shieldbreaker for any carry that doesn't already have a built in crit (Warbeast, Madman Swiftblade).

Of course, this doesn't completely close the book for this item. Any hero that already has an armor debuff, the effective range of shieldbreaker is larger. For example, predator with his ultimate (-6 armor) increases the range to 12 armor. Another use is heroes that have other physical damage moves. Such as Deadwood and arachna. In this case the damage is going to be increased for both sources, and may make it more worthwhile.

The final example is heroes that already have crit, aka madman, swiftblade and warbeast. Since crits don't stack, shieldbreaker may be a better option.



I hope my guide/info post contained some useful information.

Your guide is flawed because Shieldbreaker is 1100g cheaper than Riftshards.

[Ubuntu]

Your guide is flawed because Shieldbreaker is 1100g cheaper than Riftshards.

Good point. I will factor that in.

EDIT: I did

Shieldbreaker is still only a better option for heroes with >8 armor, which almost every hero will have, through the various support buffs (Plated greaves, nomes, astro etc..)

[Lambchop]

I'll get you one day, Charlie Horse, one day...

[Arkillion]

Riftshards level 4 is the cost of (2650 + 950 + 950 + 950) which accumulates to the total amount of 5500 whereas Shieldbreaker is 4400), the damage from level 4 Shards is +15 and there's a 24% or 20%? Chance of hitting 2.8x Damage which estimated target has 200 damage is equivalent to 560 which is way better overall than hitting more with less armour imo.

Do you think Level 4 Shards is more viable on a Pestilence than a shieldbreaker when Swarm + Shield = -21 Armour?

[Shiri]

Also shieldbreaker increases the damage of the rest of your team, right?

[ZeroHonor]

well you forget the fact that shildbreaker also increases teammebers/pets damage, and you need to calc in price too.. Else fine overview...

[dreamex]

Here's a silly spreadsheet I made to validate the value of Shieldbreaker on Madman as a cost to benefit ratio:

edit: The calculation for Riftshards there is inflated actually, since Madman has a built in crit that would reduce the effectiveness of additional crit, but you sort of get the picture anyways.

[Ubuntu]

Here's a silly spreadsheet I made to validate the value of Shieldbreaker on Madman as a cost to benefit ratio:

Shieldbreaker makes sense on madman because he has built in crit, thus riftshards is less effective on him.

[dreamex]

Shieldbreaker makes sense on madman because he has built in crit, thus riftshards is less effective on him.

The spreadsheet can be modified for any hero, just take out the column where I put in madman's stats.

Also, at extremely high armor levels riftshards would still be better than shieldbreaker on madman, and were you to ignore cost completely then Savage mace would be better than shieldbreaker.

[HONYoda]

Shieldbreaker > Riftshards for the simple fact that it buffs anyone on your team who is attacking your target. I always go Shieldbreaker over Riftshards.

Also, if Madman has Riftshards (level 4 - 20% chance for crit?), and say his crit% from skills is 20%, then he effectively has a 20% + 16% = 36% chance to critical strike. While the Riftshards can't proc at the same time as his crit skill, they can proc 20% of the other 80% of the time that his skill doesn't proc, which gives him a 16% extra chance to crit. So it's still not a bad item...especially if he has a Shieldbreaker TOO!

[NotDan]

Could you add some negative values, for pestilence / demented shaman players?

[awayish`]

you have to remember that people get shieldbreaker usually on heroes with -armor skills or synergize well with -armor.

[Ubuntu]

Could you add some negative values, for pestilence / demented shaman players?

I did. Also i had the formula for negative armor slightly wrong, was showing shieldbreaker to be more powerful than it actually is.


To everyone that is complaining:

Shieldbreaker does increase the damage of everyone else attacking the target, so depending on your line-up the item may or may not be worth it.

I also stated in my original post that for heroes like arachna, it is a better item because it will increase the damage of her ulti.

[Ubuntu]

Do you think Level 4 Shards is more viable on a Pestilence than a shieldbreaker when Swarm + Shield = -21 Armour?

Depends where the -15 armor debuff puts them.

Basically, look at the graph. If you want to fight someone with 20 armor than shieldbreaker will add another 31% damage. However if they only have 10 armor, then shieldbreaker only adds 22%.

Basically Riftshards > Shieldbreaker on pest IF

Enemy armor (before pest ulti) Is less than 8 or greater than 24.

So shieldbreaker is a good item on pest unless the enemy is stacking armor or is mainly composed of weak Ints.

[dreamex]

Depends where the -15 armor debuff puts them.

Basically, look at the graph. If you want to fight someone with 20 armor than shieldbreaker will add another 31% damage. However if they only have 10 armor, then shieldbreaker only adds 22%.

Basically Riftshards > Shieldbreaker on pest IF

Enemy armor (before pest ulti) Is less than 8 or greater than 24.

So shieldbreaker is a good item on pest unless the enemy is stacking armor or is mainly composed of weak Ints.

uhm, you are doing your math wrong.

[Ubuntu]

uhm, you are doing your math wrong.

Level 3 riftshards adds 19.2% damage on average

An enemy with 8 armor, pest ulti --> -7 armor

Shieldbreaker makes that -13, which gives a 18% boost over -7

Enemy with 24 armor pest ulti --> 9 armor

Shieldbreaker makes it 3 armor for a difference of 19.8%

So actually 24 armor shield breaker still stronger, however at 25 it breaks.

[dreamex]

Level 3 riftshards adds 19.2% damage on average

An enemy with 8 armor, pest ulti --> -7 armor

Shieldbreaker makes that -13, which gives a 18% boost over -7

Enemy with 24 armor pest ulti --> 9 armor

Shieldbreaker makes it 3 armor for a difference of 19.8%

So actually 24 armor shield breaker still stronger, however at 25 it breaks.

This is the same fallacy that people who don't understand armor perpetrate.

To evaluate Shieldbreaker you are not looking at only target armor, but also an evaluation of target damage taken which is a function of your initial damage.

Shieldbreaker is essentially something that reduces your targets effective HP by 36% at all times regardless of armor level or base hp or damage. What this means is that heroes with high EHP through armor will be penalized less than heroes with high EHP through health.

Take your example:

At 8 armor, an enemy has 32% Damage Reduction

With Pestilence Ultimate, the enemy has 1 armor, and 5.7% Damage Reduction.

Were you to strike the original target with 100 damage he would have taken only 68, striking the now modified target would result in you striking for 94.3.

That is an improvement in damage of 38.6% just for the ultimate.

With Level 3 Riftshards your initial damage (100) is increased by 19.2, now you deal 119.2 damage. Against the original target you would've done 81.05 Damage, with Pestilence's ultimate up you would've done 112.4 damage.

The same 38.6% benefit increase is tendered by Pestilence's Ulti.

The difference in damage is evaluated as the changes between both values:

With Pestilence Ulti:

Base - 94.3
Riftshards - 112.4

Improvement: 19.2%

Now to model Shieldbreaker effect what you do is you're taking the target to -5 armor, meaning a damage reduction of -36.2% or rather, a damage increase of 36.2%.

So with Pestilence Ulti and Shieldbreaker you would deal 100 * 1.362 * 0.943 damage, or 128.4 damage

94.3 to 128.4 damage is an increase of 36.1%

Significantly better than Riftshards at these armor levels.

Edit:

The effect value of Shieldbreaker with respects to damage done is dynamic depending on 3 variables your damage, target armor, target HP, this makes it difficult to model linearly with respects to the other items. The static effect of Shieldbreaker is that in essence, it reduces your targets EHP by 36%.

For instance, the effect value of Riftshards is static, in that it is always a 28% damage done increase, irregardless of target armor or your damage.

[a_cloth]

This thread is retarded, sheildbreaker increases your entire teams dps on the enemy not just yours. Your argument is invalid









/thread

[Ubuntu]

This is the same fallacy that people who don't understand armor perpetrate.

To evaluate Shieldbreaker you are not looking at only target armor, but also an evaluation of target damage taken which is a function of your initial damage.

Shieldbreaker is essentially something that reduces your targets effective HP by 36% at all times regardless of armor level or base hp or damage. What this means is that heroes with high EHP through armor will be penalized less than heroes with high EHP through health.

Take your example:

At 8 armor, an enemy has 32% Damage Reduction

With Pestilence Ultimate, the enemy has 1 armor, and 5.7% Damage Reduction.

Were you to strike the original target with 100 damage he would have taken only 68, striking the now modified target would result in you striking for 94.3.

That is an improvement in damage of 38.6% just for the ultimate.

With Level 3 Riftshards your initial damage (100) is increased by 19.2, now you deal 119.2 damage. Against the original target you would've done 81.05 Damage, with Pestilence's ultimate up you would've done 112.4 damage.

The same 38.6% benefit increase is tendered by Pestilence's Ulti.

The difference in damage is evaluated as the changes between both values:

With Pestilence Ulti:

Base - 94.3
Riftshards - 112.4

Improvement: 19.2%

Now to model Shieldbreaker effect what you do is you're taking the target to -5 armor, meaning a damage reduction of -36.2% or rather, a damage increase of 36.2%.

So with Pestilence Ulti and Shieldbreaker you would deal 100 * 1.362 * 0.943 damage, or 128.4 damage

94.3 to 128.4 damage is an increase of 36.1%

Significantly better than Riftshards at these armor levels.


This is wrong because armor does not scale linearly.

And pestilence ulti is -5,-10-,15 armor, Not -7 as you showed.

[Meowshi]

Just because you're a carry does not mean you're a one-man-army.

Shieldbreaker increases the damage of the other four people on your team.

[Ubuntu]

Unless you have another carry or someone like deadwood, giving your team mates a 20% damage increase is not going to help.

[LegoPirate]

This is an in depth look at shieldbreaker,

The first column is how much armor they had, the second is their original damage reduction %. The next two columns are the reduced armor and % reduction wheras the last column is the increase in damage.


Armor Reduction After Reduction Difference
-11 -49 -17 -65.1 15.7
-10 -46 -16 -62.8 16.7
-9 -43 -15 -60.5 17.8
-8 -39 -14 -57.9 18.9
-7 -35 -13 -55.3 20.1
-6 -31 -12 -52.4 21.4
-5 -27 -11 -49.4 22.8
-4 -22 -10 -46.1 24.2
-3 -17 -9 -42.7 25.8
-2 -12 -8 -39.0 27.4
-1 -6 -7 -35.2 29.2
0 0 -6 -31.0 31.0
1 5.7 -5 -26.6 32.3
2 10.7 -4 -21.9 32.6
3 15.3 -3 -16.9 32.2
4 19.4 -2 -11.6 31.0
5 23.1 -1 -6.0 29.1
6 26.5 0 0.0 26.5
7 29.6 1 5.7 23.9
8 32.4 2 10.7 21.7
9 35.1 3 15.3 19.8
10 37.5 4 19.4 18.1
11 39.8 5 23.1 16.7
12 41.9 6 26.5 15.4
13 43.8 7 29.6 14.2
14 45.7 8 32.4 13.2
15 47.4 9 35.1 12.3
16 49.0 10 37.5 11.5
17 50.5 11 39.8 10.7
18 51.9 12 41.9 10.1
19 53.3 13 43.8 9.5
20 54.5 14 45.7 8.9
21 55.8 15 47.4 8.4
22 56.9 16 49.0 7.9
23 58.0 17 50.5 7.5
24 59.0 18 51.9 7.1
25 60.0 19 53.3 6.7

As we can see, shieldbreaker's effectiveness is lessened with each point of armor the target gains.

Lets compare this to riftshards (level 3) - similar cost to shieldbreaker - only about 200g more

16% chance for 2.2 critical strike

2.2/16% = average of 19.2% increase in damage. Therefore riftshards > Shieldbreaker whenever the target has >8 armor. Since everyone should have more than 8 armor by the time you can get this item, it is effectively useless.

This shows that Riftshards > Shieldbreaker for any carry that doesn't already have a built in crit (Warbeast, Madman Swiftblade).

Of course, this doesn't completely close the book for this item. Any hero that already has an armor debuff, the effective range of shieldbreaker is larger. For example, predator with his ultimate (-6 armor) increases the range to 14 armor. Another use is heroes that have other physical damage moves. Such as Deadwood and arachna. In this case the damage is going to be increased for both sources, and may make it more worthwhile.

The final example is heroes that already have crit, aka madman, swiftblade and warbeast. Since crits don't stack, shieldbreaker may be a better option.



I hope my guide/info post contained some useful information.

your chart makes about 0 sense.

granted rift is a bit better then flayer, iirc flayer is = to sheildbreakers effectiveness at about 14 armor, ill find the D-A thread later when im not tired.

[Ubuntu]

your chart makes about 0 sense.

granted rift is a bit better then flayer, iirc flayer is = to sheildbreakers effectiveness at about 14 armor, ill find the D-A thread later when im not tired.

My chart shows the amount of damage shieldbreaker adds based on the target's armor.

The last column is how much % your damage is increased by. For example at the bottom of the chart, if your enemy has 25 armor shieldbreaker increases your damage by 6.7%.

The first column shows that your enemy originally had 60% resistance, but was reduced to 53.3%, thus giving you a net gain 6.7% damage.

[dreamex]

This is wrong because armor does not scale linearly.

And pestilence ulti is -5,-10-,15 armor, Not -7 as you showed.

I didn't scale armor linearly, so I don't know where your first point is coming from.

I took the -7 because that was in the example you gave me...

Anyways to model this is easy.

Not counting Pestilence's ultimate as it's a static that would increase the upperbound.

The value of Shieldbreaker with respects to base damage done is easily modeled.

Flayer3 if you'd like to use for cost comparison is a static 19.2% increase to DPS

At 100 base damage you would do 119.2
At 200 base damage you would do 238.4
At 300 base damage you would do 357.6

To be able to come out ahead with shieldbreaker you must satisfy the following equation:

For positive Armor:
DamageReduction = Armor * 0.06 / (1 + Armor * 0.06)

For negative Armor:

DamageReduction = 0.94 ^ (-Armor)

Since for negative Armor values shieldbreaker is wildly better than Flayer, we'll model the positive armor value half.

119.2 * (Armor * 0.06) / (1 + Armor * 0.06) = 100 * ((Armor - 6) * 0.06) / (1 + (Armor - 6) * 0.06)

The intersection point for 100 Base damage is at ~22 armor

Extrapolated and in a general statement you could say:

At 100 base damage, shieldbreaker is more effective against targets up to ~22 Armor
At 200 base damage, shieldbreaker is more effective against targets up to ~21 Armor
At 300 base damage, shieldbreaker is more effective against targets up to ~20 Armor

Pestilence Ultimate would add +5/10/15 armor to these numbers, with Pest Ulti3 you would be better off with Shieldbreaker against a target of armor 37 then you would with Riftshards.

[LegoPirate]

My chart shows the amount of damage shieldbreaker adds based on the target's armor.

The last column is how much % your damage is increased by. For example at the bottom of the chart, if your enemy has 25 armor shieldbreaker increases your damage by 6.7%.

The first column shows that your enemy originally had 60% resistance, but was reduced to 53.3%, thus giving you a net gain 6.7% damage.

problem is, sheildbreaker reduces EHP, which makes it more then it seems. plug in some numbers (like that one guy did), and ull see that riftshard lvl 4 is = to sheildbreaker at more like 13-ish armor (after reduction i think, so like 20ish), but sheildbreaker is 1100 cheaper, which effectively makes it the best dps item in the game.

[dreamex]

Here's what I'm gonna do for you.

In any given fight, the amount of damage you do is only relevant up to the point that your target dies.

A target dies when their effective Health drops to ZERO.

EHP = BaseHP * (1 + 0.06Armor)

Thus a Hero with 1000 BaseHP and 10 Armor has 1600 EHP and you would have to do 1600 damage to kill it.

What Shieldbreaker's effect does is it reduces their EHP by 36% of their BaseHP, so now that hero that you needed to do 1600 damage to only needs to receive 1240 damage to die. An improvement of 360 damage that you didn't need to deal.

What this does is it means that shieldbreaker is more valuable against targets with High BaseHP but low armor.

[Ubuntu]

100 dmg base for the whole math equation:
Damage equation
Base Damage X (1-Armor rating)

25 Armor = 60% reduction
10 Armor = 37.5% reduction
4 Armor = 19.4% Reduction

Therefore

25 Armor with nothing affecting him:

100*(1-0.60) = 40 damage

25 Armor with pest ulti - 10 Armor total
100*(1-0.375) = 62.5 damage

25 Armor with shieldbreaker and Pest Ulti
100*(1-0.194) = 80.6 damage

Pest ulti added 56% damage
Shield Breaker added 28% damage


I see your point..... oops.

I was looking at the fact that

10 Armor = 37.5% reduction
4 Armor = 19.4% Reduction

And then subtracting to come to the conclusion that 37.5%-19.4% = amount of damage that shieldbreaker added, which is wrong.

[HONYoda]

Here's what I'm gonna do for you.

In any given fight, the amount of damage you do is only relevant up to the point that your target dies.

A target dies when their effective Health drops to ZERO.

EHP = BaseHP * (1 + 0.06Armor)

Thus a Hero with 1000 BaseHP and 10 Armor has 1600 EHP and you would have to do 1600 damage to kill it.

What Shieldbreaker's effect does is it reduces their EHP by 36% of their BaseHP, so now that hero that you needed to do 1240 damage to only needs to receive 1024 damage to die. An improvement of 360 damage that you didn't need to deal.

What this does is it means that shieldbreaker is more valuable against targets with High BaseHP but low armor.

Yase.

[Ubuntu]

Updated chart with new formula to follow what I have learned. With this information I have discovered that shieldbreaker > Shards when -4 < armor < 20

[Lethe]

Haha I've known this for like 3 years.

Nice work anyhow :)

[LegoPirate]

Haha I've known this for like 3 years.

Nice work anyhow :)

GOOD INFORMATION, THANKS FOR CONTRIUBTING.

seriously tho, wdf XD

[dreamex]

GOOD INFORMATION, THANKS FOR CONTRIUBTING.

seriously tho, wdf XD

ღ

:mage::witc::elec::souls::phar::arac:

[ElementUser]

Thread should be in Mechanics...

[Kros]

Thread should be in Mechanics...
Done.

To OP: Good job.

[ElementUser]

Well, it's been done before.

http://forums.dota-allstars.com/index.php?showtopic=140913

http://img.photobucket.com/albums/v646/Blaow/dota/damagegraph.png

(The red part is Shieldbreaker; the rest of the stuff is a bit outdated)

[Malle1]

And it was discussed in this thread (http://forums.heroesofnewerth.com/showthread.php?t=61190) just a week ago.


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

[CallofDuty5]

they are some very nice charts, but thats only the damage increase factor from the special effect, it doesnt include the bonus damage provided by the item

i.e increase/decrease items by a vertical amount to compensate for damage increases

[Malle1]

No, you cannot just increase or decrease them by a set amount to factor that in. If you take the set damage bonus from the items into account then the damage factor would be dependant on the attacker's damage range and we'd need a three dimensional graph to plot it properly (e.g. say the target has armor such that Shieldbreaker's armor reduction adds 25% damage. A unit with 40 initial damage would with Shieldbreaker have 100 damage before the armor reduction effect and 125 after, while a unit with 340 initial damage would have 400 damage before armor reduction and 500 after. Going from 40 to 125 is obviously a much higher damage factor than going from 340 to 500). You could do intersections to plot selected choices to see how the factors trends with increased damage, which might shed some extra light on the effectiveness of the items as a whole as opposed to the result of their secondary effects.