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I'll try to keep this short and to the point.
Daedalus (5550)
+81 damage
25% chance to critical strike for 240% damage
In the basic case where there are no other sources of crit, we can call Daedalus +81 damage and +35% dps.
It should be noted that critical strike does not apply against buildings, and does benefit illusions. Illusions do not benefit from +81 added damage.
Desolator (4100)
+60 damage
-7 armor
Each point of armor is worth very close to 6% effective hit points (EHP). In the simple case that you remove all the armor from a hero with 7 armor (reducing from 7 armor to 0), this is basically +42% dps. If you reduced a level 16 unequipped Juggernaut from 10 armor to 3, this is like +36% dps.
There are some consequences to armor working like this. First, every point of additional armor is worth less and less. (Because you are getting less and less % increase in effective hitpoints. For example, going from 106 EHP to 112 EHP is not as good as going from 100 EHP to 106 EHP.) High armor agility heroes thus prefer evasion.
Inversely, each additional point of armor reduction is worth more and more! Consult the graphs here for further information: http://dota2.gamepedia.com/Armor
Thus desolator tends to have additional value on heroes that already have armor reduction, and against heroes that lack armor.
It should be noted that the desolator orb does apply to buildings, and fully stacks with other armor reduction. It also benefits other sources of physical damage. An exception is cleave, which ignores armor.
Monkey King Bar (5400)
+88 damage
+15 attack speed
35% chance to minibash for 100 damage.
True strike
Several things to note. First, attack speed (http://dota2.gamepedia.com/Attack_speed) in this game is not multiplicative. +15 attack speed is NOT the same as +15% dps, it is far inferior. Like armor, additional attack speed is worth less and less.
Minibash deals magical damage for melee carriers, and physical damage for ranged carriers (the bash is physical for melee and magical for ranged). Therefore gamepedia is incorrect and it is not the equivalent of adding 35 damage to every attack, as for melee carriers it is subject to magic resistance.
If a hero had no increased attack speed (IAS) (it would also have to have 0 agility, as each point of agility increases attack speed), then +15 attack speed would be equivalent to +15% dps. If this hero had only treads, this 15 IAS is now only worth 11.5% dps.
Now pretend a hero has 50% evasion and 1/2 incoming attacks miss. If you took that away, it's like a 100% dps increase! If a hero has 35% evasion from Butterly, the true strike is worth about +54% dps.
It should be noted that true strike benefits illusions, does not apply to attacks against buildings uphill. Attacks from cleave and flak cannon cannot be evaded.
Conclusion: MKB is a poor choice for a DPS item unless an opponent has evasion or a way to make you miss.
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Northern Ireland22208 Posts
On January 23 2015 13:32 aboxcar wrote:
Each point of armor is worth very close to 6% effective hit points (EHP). In the simple case that you remove all the armor from a hero with 7 armor (reducing from 7 armor to 0), this is basically +42% dps. If you reduced a level 16 unequipped Juggernaut from 10 armor to 3, this is like +36% dps.
There are some consequences to armor working like this. First, every point of additional armor is worth less and less. (Because you are getting less and less % increase in effective hitpoints. For example, going from 106 EHP to 112 EHP is not as good as going from 100 EHP to 106 EHP.) High armor agility heroes thus prefer evasion.
Armour does not stack with diminishing returns.
I understand your perspective, if you take a hero with 1000HP, the first 10 armour will give him 1600EHP (60% increase), but the next 10 armour will give him 2200EHP (120% increase from 0 armour, but only 37.5% increase from 10 armour). You're still getting +60% EHP for every 10 armour, because EHP should be calculated from your actual HP. You don't calculate your EHP by using EHP, if you understand what I mean.
You could say the same thing about stacking vit boosters. Each vit booster (like armour) gives you an absolute increase in the amount of HP, but they will give you decreasing relative increase.
If we take a situation where we have a medallion and we are against a Puck with 1000HP/7 armour, and a centaur with 2700HP/17 armour. If you medallion the puck you reduce her EHP by about 42%. If you medallion the centaur, you reduce his EHP by about 21%. However, in terms of actual damage, you're essentially nuking the centaur for over 1000 damage, whereas you're only nuking the puck for 400 damage. Naturally this only holds true if you outright kill both of them, and you only do so with physical damage (which is unlikely in a real game). Most people are still going to medallion the puck just to kill her faster, but if you have a team of expert mathematicians who can calculate the the most efficient way to kill, medallioning the centaur does more "effective damage"
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do heroes have or attain evasion in some way other than buying a butterfly or pa's passive?
like, does a lv25 antimage or mirana with no items have 12% evasion?
ie is it only worth getting an mkb when opponent makes butterfly or pa? (ignoring high ground miss) fuck macs holy fucking shit
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Northern Ireland22208 Posts
On January 23 2015 20:56 FFGenerations wrote:
do heroes have or attain evasion in some way other than buying a butterfly or pa's passive?
like, does a lv25 antimage or mirana with no items have 12% evasion?
ie is it only worth getting an mkb when opponent makes butterfly or pa? (ignoring high ground miss) fuck macs holy fucking shit
No you don't get evasion as part of any of the attributes.
You not only get mkb to deal with evasion, but when you're dealing with miss chances caused by blinds.
And yeah troll axes and blinding light are blinds and not evasion. There's a big difference between the two - evasion is a property of a hero, whereas blinds are debuffs placed on enemy heroes. If you have evasion, you can evade attacks from all enemy heroes, whereas if you apply a blind, it only affects that enemy hero.
Brewmaster being especially annoying and worth buying mkb for, since he has both evasion AND can apply blind.
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On January 23 2015 20:56 FFGenerations wrote:
do heroes have or attain evasion in some way other than buying a butterfly or pa's passive?
like, does a lv25 antimage or mirana with no items have 12% evasion?
ie is it only worth getting an mkb when opponent makes butterfly or pa? (ignoring high ground miss) fuck macs holy fucking shit
The posts above mentioned a few sources of miss chance. There are more like Tinker's laser and windrun (and halberd). It's usually worth getting MKB against these heroes. BKB won't even remove the haze from panda after he's already made you drunk!
I didn't explicitly point it out b/c I didn't want OP to get long and math-y, but if you have super low damage and low attack speed, like a support CM, MKB will give you more damage than Daedalus.
It's the same with phase boots vs treads. For most heroes, at the early levels, phase boots actually gives you more damage.
As you level and farm up, treads becomes the better item from a DPS point of view.
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Well if you try to put most stats into dps-terms, you might as well do so with any flat damage bonus.
Thus the 81 damage on daedalus is +81%dps if you are have 100 damage, but it's just +40,5% dps if you have 200 damage.
Comparing dps is fun if you like theorycraft, but for practical relevance in the game, one should always keep in mind that "+20% dps" rarely translates into "20% better" or "20% more useful", in dota even more so than in many other video games.
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"Armor has diminishing returns" arguments were more interesting when it was people going "omg 10 armor gives 40% reduction but 20 only increases that to 60% diminishing returns!!!11!" now I just feel like it's people who didn't want to admit they were wrong about the former argument so they're making up their own definition for diminishing returns to still be right.
Diminishing returns has a pretty simple definition: If you increase your input by a factor of n, and the output is increased by a factor less than n, you have diminishing returns. This is clearly not true for armor, since, as pointed out above, 10 armor increases EHP by 60%, while 20 increases by 120%. When the input and output have the same factor, we have a constant return.
The fact that HP becomes more valuable as our armor increases does not change the fact that armor has a constant return.
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But the question is: what is the most cost-efficient way to increase my EHP? Armor's value does change considering the amount of HP and armor you already have. Armor has diminishing returns from a cost-efficiency stance.
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On January 24 2015 19:16 Saechiis wrote:
But the question is: what is the most cost-efficient way to increase my EHP? Armor's value does change considering the amount of HP and armor you already have. Armor has diminishing returns from a cost-efficiency stance.
Well hp also have a diminishing return if you wanna look at it that way.
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On January 24 2015 19:37 vndestiny wrote:Show nested quote +On January 24 2015 19:16 Saechiis wrote:
But the question is: what is the most cost-efficient way to increase my EHP? Armor's value does change considering the amount of HP and armor you already have. Armor has diminishing returns from a cost-efficiency stance. Well hp also have a diminishing return if you wanna look at it that way.
Yes, that makes it intersting to figure out what's the best buy.
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I never used the term "diminishing returns" because it's confusing. You forget what the point you are talking about is. What is the return? and How is it diminishing?
The armor system is from WC3: http://classic.battle.net/war3/basics/armorandweapontypes.shtml
Damage Reduction or Increases for Armor
For positive Armor, damage reduction =((armor)*0.06)/(1+0.06*(armor))
For negative Armor, it is damage increase = 2-0.94^(-armor) since you take more damage for negative armor scores.
Consult this chart* for more information. A Positive Armor of 1 reduces damage by about 5.7%. A negative armor of 10 increases damage by 46.1%. A unit with 20 armor basically has 55% extra hitpoints -- 100 would become effectively 155.
Is EHP a "return" of armor, or is it just a tool to understand damage reduction? Is damage reduction the "return"?
If you gain 20 EHP, then 20 EHP, and then 20 more, are you returning less? What if equivalently your damage reduction increases less and less?
But what was the point again? To win an argument about "diminishing returns"?
The point is, if you have lots of armor, more armor does not mean a lot to you. If you have no armor, a little armor goes a long way.
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It's not like we haven't already dereailed the thread, so yes, I'm on the internet and I'd like to argue about diminishing returns.
We all agree, but let's argue about whether the definition is strictly correct.
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Northern Ireland22208 Posts
But that each point in armour gives you less and less is wrong, each point still gives you +6% of your HP as EHP. The question is, at what point is it a better use of money (and more importantly, inventory slots) to increase your HP.
This may help visualise it
![[image loading]](http://i.imgur.com/xUQz6sT.png)
That's purely physical EHP. There's no optimal hp to armour ratio, more you need to factor in gold and slots (and magical/pure sources of damage). Basically, you could spend 1400 gold to buy a platemail and get, say +300 more EHP, or you could spend 1100 on a vit booster and end up with +500 EHP
To put it another way, buying more armour doesn't make you gain less EHP, but you could be getting more EHP if you get HP items. Therefore, armour is not less effective the more you buy it, it's just that you could be getting more effective items.
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On January 24 2015 19:16 Saechiis wrote:
But the question is: what is the most cost-efficient way to increase my EHP? Armor's value does change considering the amount of HP and armor you already have. Armor has diminishing returns from a cost-efficiency stance.
That's not what diminishing returns mean, you're saying something that is true (having more armor increases the effectiveness of buying HP), and then trying to change the definition of a term because you don't understand it.
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HP and armor is not the whole story though. Evasion is another way to look at it.
0 to 9 armor (giving 35.1% damage reduction) is, all other things being equal, worth almost the same as evasion from butterfly. They will both give about 54% more effective hit points.
but 9 to 18 armor is not worth as much as 35% evasion from butterfly. Can you see that?
Or try thinking about it backwards. If you reduce someone from 25 armor to 20 armor, this is not as potent as reducing them from 5 armor to 0 armor. You can do the math to show it, but maybe this is intuitive based on game experience.. If you can accept this, then the inverse must be true too.
It's not just about the raw number of EHP, and it's certainly not about the definition of whatever terms you want to pull out. It just confuses people...
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That's because evasion gives more EHP the more armor you have. But armor remains equally eficient no matter how much armor you have. Diminishing returs implies that it drops in value, when it doesnt. The fact that other stats increase in value is meaningless to how armor works, armor doesn't get worse.
It's like saying damage has diminishing returns because at some point it's better to buy attack speed. It's dumb to treat armor that way because that's how evey single stat works. It's almost always better to not stack only a single stat, be it armor, evasion, damage, attack speed, magic reduction or whathever.
It's you who explained what you wanted to say poorly and keeps trying to defend it when it makes no sense.
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Evasion will give the same % increase no matter what the other variables are. Armor will not.
And actually, not all attributes work this way.
Magic resistance and, recently after icefrog added it, evasion, stack simply multiplicatively.
For example, if you have two instances of 20% evasion, your total evasion is 1 - .8 * .8 = 36%
I also agree that buying more attack speed at certain points is not worth it.
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If you have a lot of evasion, more evasion is worse than other stats.
If you have a lot of MR, more MR is worse than other stats.
If you have a lot of armor, armor is worse than other stats.
If you have a lot of HP, HP is worse than other stats.
If you have a lot of damage, damage is worse than other stats.
If you have a lot of attack speed, attack speed is worse than other stats.
Every single stat can be argued to have "diminishing returns" in the same way you argued armor does.
Armor gives the exact same amount of EHP for every point of armor. It's not about %s. Increasing the output by the same % is broken and that's why almost no stat actually does it. Evasion doesn't do it because it's multiplicative. If lets, say, every 100 damage you got always doubled your DPS damage would be a broken stat.
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ahswtini's view on HP/Armor is correct. The question isn't what level of armor you have but what level you have in relation to your HP.
I have never heard of the different minibash damage types depending on if the carrier is ranged or meele before. Do you have a source?
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On January 25 2015 15:49 Skyro wrote:
ahswtini's view on HP/Armor is correct. The question isn't what level of armor you have but what level you have in relation to your HP.
I have never heard of the different minibash damage types depending on if the carrier is ranged or meele before. Do you have a source?
The different damage depending on ranged vs melee was true in dota1, but in dota2 it's all the same regardless of ranged or melee, so he's wrong as far as dota2 goes.
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Northern Ireland22208 Posts
Yeah MKB in dota 2 always does magic damage and does not penetrate spell immunity
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While situational, the actual mini-bash (damage aside) from MKB can be worth a lot more than an extra 5-10% 'dps' difference. Not only it interrupts channeled abilities like black holes or tp scrolls, but also normal casts and autoattacks, which can make a huge difference in a variety of situations. Doesn't mean you should go buying MKB in every game on every hero, but it's something worth considering, especially since in late game scenarios the few extra %'s of pure damage are worth less and less than additional utility / control is.
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On January 25 2015 21:14 Unleashing wrote:Show nested quote +On January 25 2015 15:49 Skyro wrote:
ahswtini's view on HP/Armor is correct. The question isn't what level of armor you have but what level you have in relation to your HP.
I have never heard of the different minibash damage types depending on if the carrier is ranged or meele before. Do you have a source? The different damage depending on ranged vs melee was true in dota1, but in dota2 it's all the same regardless of ranged or melee, so he's wrong as far as dota2 goes.
I didn't know this, good to know.
I'm honestly very sad that I must not be good at explaining things...
the fact is, from both attacker and defender points of view, the % benefit from + armor or - armor does change depending on the actual value. I'm really sorry I failed you all but I don't know how else I can explain.. oh well
I guess I can try one last time..
If you go from 100 to 200 EHP, or from 200 to 300 EHP, both is a gain of 100 EHP so you can say that the "return" is the same, but in the first case you are doubling your EHP and in the second you are only gaining 50% more. The first case is better than the second.
Everything else is mathematically basically related to this.. from % damage reduction, to % amplification for negative armor...
I really don't know how else I can say..
Why does it matter? It matters b/c this is how you answer questions like, when is 25% chance to crit. for 240% damage better or worse than -7 armor, which was my original point. Critical strike is not always better or worse (from a dps/math perspective, not gameplay): it depends on armor.
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Northern Ireland22208 Posts
If you take the case of a puck with 1000HP and 7 armour, he has 1420EHP. If you remove the 7 armour, he loses 420 EHP which is a 30% EHP decrease.
Now compare with a centaur with 2000HP and 17 armour, who has 4040EHP. If you remove 7 armour, he loses 840 EHP, which is only a 21% EHP decrease. But the -7 armour does double the "damage" to him compared to what it would do to the puck. Obviously this comparison only holds true if you kill the heroes outright, and with physical damage only. So here, I don't think it's necessarily less effective to reduce the armour of centaur
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but first of all you are mistaken mathematically. it's not right to look at it as an EHP decrease:
it is a damage reduction decrease, or equivalently damage done increase.
EHP is not the real variable, it is only a tool to understand how armor was designed...
one way you can think of it is, at 0 armor. you do a base 1x HP damage to kill. if you have 7 armor, you have 42% more EHP.
if you reduce from 7 armor to 0, obviously it's like you're bringing it back to 1xHP to kill, so you can think of it as a 42% damage done increase (in order to deal the 1.42 EHP from 7 armor, which is not real) (in other words, if someone now has 1.42 times HP, I need to do 1.42 times damage)
or another way: 7 armor = 29.6% reduction = 70.4% damage taken
to bring it back to 100% damage taken: .704 * 1.42 = 1; or a 42% damage increase
or another way to look at it, where 1 = no reduction and .704 = reduction from 7 armor:
1 / .704 = .42 = 42% less value from your armor.
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evasion is the same. you guys are erroneously thinking HP value has anything to do with it. while it is TRUE, your EHP and the precise increase you get depends on the relationship between armor and HP and evasion,
the % benefit of evasion compared to armor has NOTHING to do with actual HP. it is only a function of armor.
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again, it's easy to become confused by math or term definitions or logic, but if you ask the relevant questions you will stay on the right path. questions such as:
is crit chance better or negative armor better?
is evasion better or more armor better?
is more attack speed better or some other form of dps increase better?
it's very hard to explain things via math to people who aren't doing the same math as you, or to explain things via definitions to people who aren't using the same definitions. but if you stay focused on the point, if you stay focused on the meaning, then it's harder to be led astray.
I mean I could do math all day but it doesn't convince anyone who isn't doing the same math. but can you answer those questions? do you really know how to arrive at the answer?
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EPT
