Armor Misconceptions

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    • Armor Misconceptions

      Im Prinzip könnt ihr euch alles schenken und ganz runter scrollen und dass was nicht im quote ist lesen und ihr wisst auch alles, dass Zeug dazwischen kann aber nützlich sein:)

      Since you will most likely ask yourself "why should I bother to read this text-wall?", here is the answer: it will help you understand how armor/physical EHP (effective hit points) works and thus improve your ability to purchase the correct items and to properly react to items purchased by the opponent. Calculations can be partly skipped if you want to, but I have made sure to only do the most necessary calculations.

      Armor Misconceptions

      From a pure subjective and unreflected point of view people have always claimed or had the feeling that stacking armor becomes gradually less effective. Even today it's nothing unusual to meet people who feel this way and this feeling found it's expression on the mechanics pages of PlayDota, which I will quote later on. Already a long time ago however it was established that each additional piece of armor provides the same protection as the previous one. As a consequence the idea of armor stacking becoming less and less effective has been shelved, considered to not be true. Unfortunatelly this is partly a fallacy.

      - Armor stacking always provides the same extra protection when it comes to number of attacks required to kill a target -> this is true! (given we talk about the same amounts of armor obviously)
      - Armor stacking becomes less and less effective the more you have -> this is true aswell!

      How can both be true? How can purchasing multiple Plate Mails become less and less effective when, at the same time, each platemail provides the same protection from numbers of attacks? Well, it depends on what you compare it to/meassure it with, but answering this question and explaining why this matters and how it is expressed in gameplay is the aim of this article.

      1. Proof that stacking armor becomes less and less effective
      2. Why it matters
      3. Evasion compared to armor, supportive argument

      1. Proof that stacking armor becomes less and less effective

      It looks like people have taken a specific piece of information and repeated it like a mantra. Unfortunately that piece of information is incomplete and people frequently oversimplify what it means. Quoting from playdota:

      It is generally conceived that armor gets less and less effective the more you have (since the extra damage reduction gets less and less). That a Plate Mail gives you less extra protection from attacks if you already have 20 armor than if you would have only 5. This is false. If one Plate Mail makes the hero survive 3 extra attacks, then 4 Plate Mails will make the hero survive a total of 12 extra attacks before dying. Each Plate Mail gives the same amount of extra protection, which is in this case 3 more attacks before dying.

      Every armor point adds an additional 6% of your maximum HP to your EHP.

      In order to demonstrate my point I am going to always use the same examples, a hero with 0 armor and 1000 maximum hp which stacks platemails (10 armor each).

      Formulas and terminology
      - EHP: Effective Hit Points, refers to the amount of damage it takes to set your HP to zero.
      - pEHP: phycisal Effective Hit Points, In this article I exclusively refer to physical damage and thus use the term pEHP. pEHP is calculated by: maximum HP * (0.06 * armor value). Example: a 1000 hp hero with 10 armor is 1000 * (0.06*10) = 1600 pEHP
      - Initial pEHP = maximum HP combined with the armor the unit already has before we add an additional source of armor
      Display Spoiler

      I) A hero with 1000 HP, 0 armor
      Initial pEHP: 1000*1 = 1000
      pEHP after platemail: 1000*(1+0.6) = 1600 pEHP, an equivalent of 600 hit points added
      % of pEHP added = 1600/1000 = 1.6 = 60% EHP added

      II) The same hero with 1000 HP, 10 armor from the first Plate Mail
      Initial pEHP: 1000*[1 + (0.06*10)] = 1600
      pEHP after another platemail: 1000*[1 + (0.06*20)] = 2200 pEHP, an equivalent of 600 hit points added
      % of pEHP added = 2200/1600 = 1.375 = 37.5% EHP added

      The first Plate Mail adds 600 pEHP to the initial 1000 hit points, this is a 60% increase of your initial EHP. The second platemail adds another 600 pEHP to the previous 1600 intial pEHP. But at the same time this is only a 37.5% increase in pEHP when calculated from the previous pEHP value with 10 armor.

      One frequent misconception is that 1 point of armor does increase your EHP by 6%. As shown above that is NOT the case (unless you have 0 armor). Just like written on playdota, 1 armor does not increase your EHP by 6% (since EHP would be hp + armor), it only increases your EHP by 6% of your maximum HP. This is a significant difference.

      Generally speaking EHP is the only thing that matters, all damage calculations only take EHP into consideration. From the calculations above we can establish, and what PlayDota does not mention, that the more you stack armor, the less cost-efficient it becomes because we add a smaller proportion of armor to what we already have.

      Who cares? Why does it matter that the percentual increase in pEHP when stacking armor/Platemails is lower when it still provides the same number of effective hitpoints? It still increases the number of hits required to kill you just as much as the previous Platemail so it must be just as effective, right? Wrong.

      2. Why it matters

      In Dota being able to kill a hero, taking someone out of the fight is unbelieveably important because you remove those heroes abilities from the fight, preventing them from dealing damage, preventing them from regenerating or making narrow escapes, focusing down a target before a fight really starts can win you the battle already. A simple example to highlight how the importance/significance of burst to remove a target from the battlefield is expressed in gameplay & balance:

      Queen of Pain's Sonic Wave deals 350/475 (530)/600 (725) damage (Aghanims). It has a 135 seconds cooldown, 100/70/40 with Aghanims.
      Death Prophet's Crypt Swarm deals 300 damage. It ultimately has a 4 seconds cooldown.

      After 8 seconds Crypt Swarm as an ability deals 175 more magical dmg than Sonic Wave with Aghanims and will be up again in 4 more seconds. Even a lvl 3 Sonic Wave without aghanims, which you can only unlock on lvl 16, deals twice the damage of Crypt Swarm but has 135 seconds cd compared to 4 seconds cd once witchcraft is maxed too (around lvl 10). Yet Sonic Wave without a doubt is a much more powerful/impactful ability because bursting something down, setting the pace of a fight, getting an edge over your enemies is one of the most important things to do in battles.
      This principle also applies to single target spells or physical damage, if you can remove a target from the equation with little effort, time spent or abilities used then you can much more quickly focus on other targets. Efficiency.

      When playing the game it turns out that surviving 6 attacks instead of 3 is significantly better, more effective and more powerful than surviving 10 instead of 7 attacks. Surviving 8 instead of 4 attacks by far eclipses surviving 20 instead of 16 hits because the amount of time you gain to react and thus regenerate/reposition/use abilities again and consequently disrupt the enemy more is all you need to further extend the amount of time you will be alive and capable of contributing. This is where the extra damage reduction becoming less and less is expressed in gameplay.

      At the end of the day it's all about cost-efficiency and effectiveness of using your ressources (time, abilities, attacks) in general. Here are a couple of examples of item efficiency or from DotA's history:
      Display Spoiler

      - A Desolater, contrary to popular belief, is more effective when attacking targets with low armor compared to attacking targets with high armor. Why? Because the damage multiplier is bigger against low armor targets:…wA4c/s1600/armor+dota.jpg…-dota-allstars-guide.html
      note: Buriza amplifier in the image is outdated

      - It also means that Daedalus/Buriza is more effective against high armor targets compared to Desolater/armor reduction because the multiplier of Daedalus (37.5%) is higher than the multiplier after armor reductions.

      - Butterfly has evasion for a reason, the item is geared towards agility heroes and evasion works very well with naturally high armor heroes. It's a subtle item synergy which will make Butterfly in the majority of cases the superior choice compared to an Assault Cuirass on agi heroes:

      - Vanguard ist most effective against many low damage sources but extremely inefficient against high damage sources. If you have low armor purchasing a platemail is more effective in the long run than purchasing Vanguard.

      - Once we reach a certain amount of armor (13.5) a simple talisman of evasion becomes more slot-efficient than a platemail does. So unless the enemy has true strike, hex or armor reduction, which pulls back armor into regions where getting armor becomes more effective again, a DK with Heaven's Halberd is tougher to kill, has a higher pEHP value, than a DK with an AC due to his naturally high armor. The more armor you have the more effective evasion becomes compared to armor.

      - Low cost armor sources are incredibly efficient, subtle maybe, but efficient. Ring of Basilius armor aura for instance got nerfed to +2 from +3.

      - Vladmirs adds 30% of each heroes max hp to their pEHP which in case we assume an average of 1k hp per hero equals 1500 physical effective hit points added to the heroes. (screwed up by magic dmg of course^^)

      - The old Phase Boots with armor from 59d were a powerful comibation of utility and surviveability and consequently that was one of the reasons why the carry/damage dealer heroes in 59d turned out to be Necrolyte, Kunkka (pure dmg cleave and nukes) and Zeus, frequently paired up with Undying's damage amplification aura or WD's Maledict (spell dmg scaling). Or classic radi Spectre.
      That's also partly the reason why Death Prophet, despite being enabled to maximise her physical damage potential from Exorcism with phase boots herself, slowly degraded from "the" top pick/ban hero to a hero which wasn't picked at all anymore towards the end of 59d.

      3. Evasion compared to armor, supportive argument

      This section is here purely to show how armor becomes less effective when stacked.

      From Benchbreaker's EHP guide:
      Evasion scales exponentially

      It means 30% evasion is more than twice as good as 15% evasion

      15% evasion = 1/0.85 = 1.18 -> 18% increase in EHP
      30% evasion = 1/0.7 = 1.43 -> 43% increase in EHP

      Evasion is a multiplier of your initial pEHP (maximum hp+armor). 25% evasion will simply multiply your pEHP by 33.33% no matter what your pEHP currently is. Let's compare a talisman of evasion (25% evasion) to our previous examples with Plate Mails on a hero with 1000 hp and 0 and 10armor.
      Display Spoiler

      I) A hero with 1000 HP, 0 armor
      Initial pEHP: 1000*1 = 1000
      pEHP after Talisman of Evasion: 1000*(1+0.333) = 1333, 333 effective hit points added
      % of pEHP added = 1333/1000 = 1.333 = 33.33% pEHP added

      II) The same hero with 1000 HP, 10 armor
      Initial pEHP: 1000*[1 + (0.06*10)] = 1600 1840 mit 14 armor 2452,
      pEHP after Talisman of Evasion: 1600*(1+0.333) = 2133.33, 533,33 effective hit points added
      % of pEHP added = 2133.33/1600 = 1.333 = 33.33% pEHP added

      What we can observe here is that a Talisman of Evasion is weak compared to one simple Plate Mail in I), 267 effective hit points less. However the exact same amount of evasion as in I) suddenly provides almost the same pEHP increase the additional Plate Mails provides in II), the difference now is only 66.67 effective hit points.

      Being a flat multiplier, evasion catches up to stacking armor and at a certain point (13.5 armor) is going to surpasses armor stacking in increasing your EHP. Unlike armor, which scales linearly, evasion scales exponentionally.
      It's the same old story really, balance of armor and hp is most important, stacking just 1, either hp or armor, is not overly effective. Simply remember the following 2 things:
      - 1 armor does not increase your EHP by 6%
      - stacking armor does become less and less efficient indeed after all (cause other things in comparison become more effective)

      The post was edited 1 time, last by Chairraider ().

      Happiness, more or less, it's just a change in me, something in my liberty.
    • Chairraider wrote:

      - stacking armor does become less and less efficient indeed after all (cause other things in comparison become more effective)
      Das ist halt wieder so ein irreführender Satz. Genau so gut kannst du nämlich auch schreiben "stacking HP does become less and less efficient indeed after all (cause other things in comparison become more effective)".
      So wie es jetzt da steht denken die Leute wieder, sie kaufen einfach anfangs ein bisschen Armor und später stacken sie die Hearts, schließlich bringt Armor dann nicht mehr viel. Und das ist einfach Schwachsinn, in der einen Tabelle sieht man ja, dass ein 3k HP Held bespielsweise im Optimalfall ~40 Armor haben sollte.

      In dem Artikel, den du unter dem Punkt Evasion verlinkt hast, steht es imo recht schön in einem Satz zusammengefasst:
      Hp and Armor scales linearly, while Evasion scales exponentially
    • Dann lass ich des (cause other things...) weg.

      Anmerkung zur Tabelle: die ist natürlich pEHP. Deshalb ist Armor im Verhältnis zu HP so extrem hoch, Evasion sowie magic damage reduction ist bei so viel HP schon sehr viel effektiver wenn's um rein EHP geht..
      Happiness, more or less, it's just a change in me, something in my liberty.
    • bei "formulas and terminology" hast du bei der formel das "1+..." vergessen.

      ^ bei hp musst du aber auch beachten, dass es auch vor magic-dmg schützt und von dem her immer eine gute wahl ist.

      der artikel zeigt aber auch, dass evasion mass underrated ist.
    • Das hat der Ersteller der Tabelle schon berücksichtigt, er geht ja davon aus, dass 10 Armor so viel kosten wie 500 HP obwohl Ersteres eigentlich deutlich billiger ist.

      Was die Evasion angeht geb ich dir recht, dabei muss man allerdings bedenken, dass es lange Zeit außer Butterfly (und Radiance ;)) überhaupt kein Evasion Item gab, und die Tatsache schon allein deswegen noch nicht so in den Köpfen drin ist.
    • echte EHP kann man sowieso nicht sinnvoll betrachten weil der anteil an schaden der physical/magical ist von spiel zu spiel (eigentlich von kampf zu kampf) variiert. von daher passt das mit der beschränkung auf EHP gegen phys.dmg schon.
      €: evasion ist halt nur auf bfly, talisman und halberd drauf. bfly ist eins der teuersten items, halberd sehr situativ und für nen reinen talisman is vielen oft der slot zu schade, deshalb holt sich kaum jemand evasion.
    • Honclock :d

      Gut gemacht Chair !
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    • elephantTalk wrote:

      vllt ist halberd ja gar nicht mal so situativ und sollte viel öfter auf tanks gebaut werden.
      auf wem denn z.B.?
      also auf welchem helden ist halberd nicht nur in speziellen situationen (ein einzelner gegnerischer carry ist hart am ownen und muss disabled werden) sinnvoller als andere items?
      welche helden werden überhaupt auf tank gespielt? krobelus? undying?
    • ...Axe, Cent, Bristle, Shredder, Pudge, etc.

      Gibt schon ne Menge Helden auf denen das Item häufig sinnvoll ist. Spiele, in denen der Gegner überhaupt keinen Physical Damage Carry besitzt, sind ja jetzt auch nicht gerade die Regel, also wird auch das Active im Normalfall immer seinen Nutzen haben.

      ReWahn wrote:

      das sind helden die von natur aus viel aushalten, nicht helden auf denen man mit equip auf teufel komm raus mehr survivability kaufen will oder?

      Naja, Helden die zwangsweise immer inmitten der Gegner stehen brauchen definitiv gute Survivability, und die Evasion ist ja auch nur ein Teil von dem Nutzen, den man aus der Halberd zieht.
    • ReWahn wrote:

      das sind helden die von natur aus viel aushalten, nicht helden auf denen man mit equip auf teufel komm raus mehr survivability kaufen will oder?

      auf allen von mir genannten heroes wird gerne mal ac/heart gebaut.
      frage ist ob halberd da nicht genauso oder vllt sogar mehr bringt.
    • bleibt die problematik dass die helden eigentlich alle viel dringender andere items brauchen. (scheiss auf inb4 faggotry)
      axe sein vanguard und dagger (oldschool) oder irgendwas für mana (bh axe)
      cent seinen dagger
      shredder seinen bloodstone (oder sonstwas für 200000 mana)
      halberd bleibt halt das teil, was man dann bei manchen gegnern als drittes oder viertes item einpackt wenn man wider erwarten nach dem core noch viel cash stackt. die evasion ist zwar ok, aber der disarm ist schon sehr speziell und mit puren hp fährt man halt defensiv insgesamt oft besser weil halt in den meisten games bis ins tiefe lategame magical dmg mehr vorhanden ist als physical dmg.
    • ^ wer redet denn davon die core-items zu verschieben...
      es geht darum, die meiste survivability für sein geld zu bekommen, also die entscheidung ob man jetzt ac, heart oder eben halberd kauft.

      ck kann sichs kaufen nachdem er pt, drums, armlet hat z.b.
      dk kann sichs kaufen nachdem er pt, bkb, hotd hat z.b.
    • du hast natürlich recht - als 3. oder 4. item geht halberd schon klar auf diesen heroes ;)
      halberd bleibt halt das teil, was man dann bei manchen gegnern als
      drittes oder viertes item einpackt wenn man wider erwarten nach dem core
      noch viel cash stackt.
    • ich hole mir eigl immer ne halberd wenn ich mal melee str spiele und schon meine core items je nach hero habe.
      der maim ist nur ziemlich oft wasted, aber str+evasion ist unglaublich effektiv wenn man als str hero sowieso schon seine 2k hp und 10+ rüstung hat.
      und das active kann man wirklich immer gebrauchen, kein team spielt ganz ohne physical dps hero, auch wenn die meisten bkb holen.
    • Sange ist quasi n offensiver Vanguard, HP sind ziemlich gleich. Gibt eben Damage statt Block und kann sinnvoll weiterverarbeitet werden, auf Balanar oder DK imo >Vanguard.
      Kann man Disarm auf den Syllbear-Bear casten? Wäre dann, ähnlich wie RoA ne Möglichkeit das zu nutzen, wenn der mit AC rumrennt und deinen BKB-Carry mit Entangles zernichtet.
      we do not sow
    • rod of atos kontert den level 4 rabid/synergy + phaseboots bären schon gewaltig aus, da braucht man den disarm garnicht mehr.
      habe ganz vergessen wie gut das item doch ist, ab jetzt ein echter pflichtkauf.