Rune Theorycrafting - Defense, Health and Damage Reduction

FoozleFoozle Member
edited September 2016 in Rune Discussion and Strategy
TLDR Summary: Bulwark (Defense) and Life (Health) runes are fairly well balanced, but Bulwark, for most heroes will be slightly more beneficial than Life in mitigating damage from direct attacks. However, rather than stacking all Bulwark or all Life, usually a combination of both provides the best benefit, again, depending on the hero. When determining whether Bulwark or Life is better, check to see which will increase the stat they affect by a greater percentage. Aegis (Damage Reduction) is generally less beneficial than both Bulwark and Life in terms of reducing direct damage from attacks, except at extremely high existing defense and life levels. Damage Reduction, however, reduces “damage over time” damage such as poison and burn, where Defense does not.

In a previous write up, I compared Damage Reduction, Dodge and Resist. Resist is the least beneficial in terms of mitigating direct damage and either Damage Reduction or Dodge, depending on the circumstances, could be better than the other. For purposes of this post, I’m going to compare Defense, Life and Damage Reduction. Dodge is very circumstance specific, so I won’t address again in this post.
For purposes of my comparison, I used the stats on Greater, 3 Star, Rare runes – where the runes had the same attribute on both the primary and one of the secondary stats. For Bulwark runes, on average, this type of rune will give you 278 defense (185 primary and 93 secondary). Life runes of the same type give 627 health (414 primary and 213 secondary). Aegis runes of the same type give 6.69% damage reduction (4.54% primary and 2.15% secondary).

Damage received by a hero is calculated as follows: base damage of attacker * attack rating of attacker / defense rating of defender. There are other modifiers such as armor adjustment, magical resistance, elemental advantage/disadvantage and others. However, my comparison will just be using the generic formula above and you can adjust, as necessary, for any other hero or situation specific modifiers.

The following chart shows a comparison for two heroes (Icebloom and Yokozuna), showing the extremes of low and high defense. I’m using the defense amount of 278 on Bulwark runes as a baseline and then showing what the Life rune and Aegis rune would need to be to give equivalent benefit. I used Black Diamond's attack rating at around level 63, but the attack rating doesn't really matter in comparing value of these runes - changing it will cause total damage to kill to go up or down, but it does so in relative amounts so doesn't impact which runes are better. In the case of Icebloom, because she has very low base defense she benefits more from added defense. It would take a Life rune of 741 health or an Aegis rune of 15.12% damage reduction to give the same benefit as the Bulwark rune. Since at the Greater, 3 Star, Rare rune level, Life runes only provide around 627 health and Aegis runes only 6.69% damage reduction, the Bulwark rune is better. Note that the “Damage required to kill hero” assumes no healing taking place. Healing complicates matters and is discussed at the end of this post.

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For Yokozuna, I used the assumption that he already had three very high level Bulwark runes equipped, which boosted his defense to 3,880. So the question is whether using the fourth rune slot for a Bulwark, Life or Aegis is better. Because of his extremely high defense level, you can see that the Life rune is actually better to place in the fourth slot than more defense. It would only take a Life rune of 454 health to be equivalent to the extra 278 defense, and since Life runes of that type provide 627 health, the Life rune provides more benefit. An Aegis rune, in this case, would provide the exact same benefit as a Bulwark rune because Aegis runes of that type give 6.69% damage reduction, which is what it would require to be equivalent to the Bulwark rune benefit. I didn’t do a third scenario, but if you did one where base health and defense were both high enough, than the Aegis rune would be better than both the Bulwark and Life runes. This would require defense of about 3,880 and health of about 8,800.

This can get fairly complicated, but an easy way to see which is a better upgrade is to calculate the percentage that a rune will increase the stat of interest and compare that percentage to what the other rune type will provide. In the chart above, for Icebloom, her base defense is 1,561 and base life is 4,158. A Bulwark rune will provide 278 defense, so that is 17.8% of base defense. A Life rune will provide 627 health, so that is 15.1% of base health. So between those two, adding more defense is better. Damage reduction is a bit trickier. To compare a Bulwark to an Aegis rune, take the percentage benefit from Bulwark and plug into this formula: 1 – (1/(1+defense percentage increase)). Then compare that result to the damage reduction on the Aegis rune. So in the Icebloom example it would be : 1-(1/(1+.178)) or 15.1%. Since Aegis runes of that type only provide 6.69% damage reduction, Bulwark would be better than Aegis. If you wanted to compare Life to Aegis, you’d do the same thing, except substitute “health percentage increase” into the formula instead of “defense percentage increase.”

So those are the basics. It gets more complicated when dealing with heroes with individual and team passive buffs. The undead are a good example. Zomm gets a 25% boost to health for being a slow hero and also gets a 25% boost to health because he is Zomm. The boosts are applied after including the rune benefits, so if you were comparing the benefits of Life runes to Bulwark runes, you’d have to adjust for this effect. In this case, Life runes have added benefit and in many cases this will shift the equation in their favor. However, Zomm is often run on a team with Yorick, so Yorick would give Zomm a 30% defense boost. In that case it might swing things a bit in favor of Bulwark runes (although I can’t confirm whether the 30% team defense boost is applied before or after rune benefits, like they are for individual passives).

Another factor is that even though Aegis runes are generally inferior to Bulwark and Life runes, except at very high defense and health levels, damage reduction has the benefit of reducing damage related to effects like burning and poison, where defense provides no benefit. I did some testing of this and proved it to be true. So, it is hard to quantify because it is situational, at least in comparing Bulwark to Aegis runes, it is relevant.
One more complication is when healing starts to be involved. All the above computations assume no healing happening. Once you start introducing healing, things get more complicated. The previous discussion will still generally apply, but there are concepts such as “over healing” and others that need to be factored in. Since this post is already pretty long, maybe good to discuss in another post sometime.

As always, happy to hear different opinions. This topic is fairly complex, so I wouldn’t be surprised if I’m not thinking about all the factors involved.
Post edited by Foozle on

Comments

  • FoozleFoozle Member
    edited September 2016
    Reserved for Healing discussion. Hoping to do a few simulations showing effect of defense, healing and damage reduction over a longer battle that involves healing.
  • FoozleFoozle Member
    edited September 2016
    Reserved for other. Possibly use this for discussing how to factor in team passive buffs and other factors.
  • How did you determine the attacker's attack rating?
  • MysteriosX wrote: »
    How did you determine the attacker's attack rating?

    Good question. I just used Black Diamond, I think. But the result is the same regardless of the attack value used. The total damage required to kill can go up or down, but it does so in relative amounts, not affecting the outcome of determining which runes are best.
  • ItchytorturepoxItchytorturepox Member, Dungeon Boss Guru, Volunteer Moderator
    Some thoughts, based on your observations:
    • Health runes may better suit self-healing heroes (and/or those equipped with life steal runes). Where total health for the session can be maximized
    • Bulwark could be better suited to those heroes that might not receive any healing, or infrequent/targetting healing. Best for Constructs?
    • Aegis could be better suited to those heroes that are deemed vulnerable to DOTs. Good for OE?
    • Similarly, less benefit could be gained by putting Aegis on constructs, those with impervious or those that already have high resistances
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  • Because of the calculation Attack divided by Defence .. adding to Defence is worth more if your Defense is much lower than your attacker, and is worth much less if your Defense is already much higher than attacker. The equation is not linear. (For Attack it IS linear). I think i have my calcs correct.

    eg attacker has 2000 attack (1000+1000), you have 1000 defense and add 100 via rune, you will mitigate extra 91 dmg.
    eg attacker has 2000 attack (1000+1000), you have 2000 defense and add 100 via rune, you will mitigate extra 24 dmg.
    eg attacker has 2000 attack (1000+1000), you have 3000 defense and add 100 via rune, you will mitigate extra 11 dmg.

    I think Strapping a couple of Defense runes on Icebloom is (comparatively) could give you good bang-for-buck for that rune slot.
    Maybe a few more pennies
  • FoozleFoozle Member
    edited September 2016
    @Kidhak. The damage formula has 3 basic components (plus other modifiers like armor, resistance, etc.): Attacker's base damage amount, Attacker's attack rating and Defender's defense rating. In your examples, how does the "2000 attack (1000+1000)" fit into those components?

    In any case, you are correct that putting a defense rune on a hero becomes less useful the higher the base defense is, as there are diminishing returns. But, the Attacker's attack rating doesn't impact that decision -- it affects life, defense and damage reduction in the same way. I've created an extreme example to demonstrate this. In the table below, I have two examples. In both, the base defense and life remain the same. My theory is that once you know the base life and health, you can calculate what would be equivalent defense and life runes. In this case, defense of 278 and life of 454 provide the exact same benefit, regardless of the attacker's attack level. The only difference is that the overall damage required to kill the hero decreases with the higher attack rating scenario.

    So in the low attack rating example below, if you add a 278 defense rune to your hero and if an enemy outputs 52,748 in base damage, you apply the attack/defense modifier to that and it results in your hero taking 6,343 real damage (500/4158*52748). In that same example, if you put a 454 life rune on instead, it results in your hero taking 6,797 real damage (500/3880*52748). You will take more damage without the defense rune, but your extra 454 life exactly covers the additional damage, basically showing that a 278 defense rune and a 454 life rune (at your present base defense/life levels) provides the same benefit.

    In the high attack rating example below, if you add a 278 defense rune to your hero and if an enemy outputs 2,930 in base damage, you apply the attack/defense modifier to that and it results in your hero taking 6,343 real damage (9000/4158*2930). In that same example, if you put a 454 life rune on instead, it results in your hero taking 6,797 real damage (9000/3880*2930). You will take more damage without the defense rune, but your extra 454 life exactly covers the additional damage, basically showing that a 278 defense rune and a 454 life rune (at your present base defense/life levels) provides the same benefit.

    So based on these examples, you can see that 278 defense and 454 life provide the exact same benefit, whether the attacker's attack rating is high or low. What matters is your hero's starting base defense and life. As you hero's defense increases, defense runes become less valuable and as you hero's life increases, life runes become less valuable.

    I actually struggled with this concept for a while, thinking that attack rating should impact rune decision, but after doing the math many times, it doesn't appear to - unless someone can show me where my math is wrong, which is always possible!

    Thanks for the comment!

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    Post edited by Foozle on
  • My take away from the OP was tanks with high defense should value hp over defense but your new chart shows all tanks want defense for at least their first rune and some of them for all slots, which surprised me. Optimal runing isn't intuitive at all.
  • ok what I meant is this ..

    My BD has
    - damage of 1187 for her Blade Storm.
    - Attack score of 2517

    If you have a defender with 1500 Defense, they are taking roughly 1187 * (2517/1500) = 4461 damage on a normal hit.
    If you have a defender with 2500 Defense, they are taking roughly 1187 * (2517/2500) = 3664 damage on a normal hit.

    If you add a rune with 100 defense on each the equation and result changes to:

    If you have a defender with 1600 Defense, they are taking roughly 1187 * (2517/1600) = 4336 damage on a normal hit.
    If you have a defender with 2600 Defense, they are taking roughly 1187 * (2517/2600) = 3433 damage on a normal hit.

    The difference between the two is
    - 1500->1600 defense = 124 less damage
    - 2500->2600 defense = 46 less damage.

    Putting that 100 defense rune on a low defense toon is worth about 3* more than on a high defense toon in terms of damage mitigation.

    Adding defense runes is not linear, its worth more to a low defense toon.

    I think that maths is correct based on our assumptions on the damage formula. Let me know if I have something incorrect?
    Maybe a few more pennies
  • @kidhak. Thanks for clarifying. Yes, I think we are saying the same thing. Adding defense to a low defense hero is worth more than adding to a high defense hero. The new charts show this as Yasmin, who has very low defense, benefits more from adding defense than executum would, as his base defense is much higher than Yasmin's.
  • I think what you would want to do is calculate an average attack of the main pvp heroes assuming a certain level of runes (Say greater heroic). Then using that attack, solving for the optimal defense point where it become better to switch to life.

    Of course none of this takes into consideration how certain stats get double dipping benefit from things like team synergies or epic weapons which would obviously change the "switch from defense to life" number.
  • 4tom4tom Member
    edited September 2016
    One concept that's important for considering def/hp/damage reduction is that the first two (def + hp) give diminishing returns (the more you stack the less the benefit), while the third gives exponential returns--each % of damage reduction gives an increased amount of effective health as you scale towards infinite health (or 100% damage reduction).

    You look at 3* rare runes, which give small dmg reduction (6%) and def (278), but if you have a rune twice as powerful (12%) or (556), which is achievable with legendary great runes, then they aren't both twice as good. The former is actually more than twice as good, the latter is less than twice as good. I actually have a 12% dmg red rune (greater legendary). With 4 of those (green/green/blue/yellow) and a purple rune with 2%, I could hit the cap of 50%.

    I think at that point, dmg reduction becomes really viable. Mix in a few def and life secondary stats with a 50% damage reduction and you should be better than anyone using just def/hp. Of course, that doesn't leave you any room for crit/att or other stats.

    Post edited by 4tom on
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  • FoozleFoozle Member
    edited October 2016
    Just a follow on to @4tom who makes excellent points about life/defense having diminishing returns while damage reduction has exponential returns. I put some data together to illustrate this.

    For purposes of this post I'm using a level 70, FA, 6* Hansuke, since he has a fairly high defense and also can benefit from the undead passives. In the first table below, you can see that if you were able to stack 5 Aegis runes (superior, legendary, 5 star), it would be significantly better than either Life or Defense (using runes with two damage reduction stats and either life or defense as the 3rd stat). I'm comparing 5 Aegis to 3 Bulwark/2 Life and 3 Life/2 Bulwark. For the Life runes, I'm assuming the runes have 2 life stats and 1 defense and for the Bulwark runes I'm assuming they have 2 defense and 1 life stat. Because of the exponential returns on damage reduction, they are twice as effective as life/defense at the 84% level. If they'd let you stack to 100%, then obviously they would be infinitely more beneficial. I'm assuming they cap it at 50% to not let the stat get out of hand.

    Table to the right is just showing the values I used for the greater and superior runes (from another post I made).

    In the second set of tables, I'm comparing results if you have to stay within the 50% damage reduction cap. You can see at the Greater, Legendary, 5 Star level the results are very close between all three scenarios. Once you start comparing using Superior runes, the damage reduction stat becomes more beneficial. I didn't run all the scenarios, but the turning point is likely somewhere either at the high end of Rare or low end of Heroic, just roughly guessing.

    So, at least for now, damage reduction probably isn't beneficial compared to life/defense, but once Superior runes start being more available, that may change. Also keep in mind that damage reduction also reduces damage over time effects like burn and poison, where defense does not -- so another factor in their favor when comparing to defense runes at least.

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    Post edited by Foozle on
  • 4tom4tom Member
    edited September 2016
    @Foozle Awesome stuff.

    I am running a Yorick with greater, mostly legendary/5* defensive runes. I went with the 1 bulwark + 3 aegis approach (last rune is crit and att). It's pretty insane damage reduction. When coupled with his Epic weapon proc at 30%, it makes him insanely hard to kill. I've been in a few fights where the rest of the team wipes and it's Yorick 1 v 4 and Yorick has come out on top (usually I'm running zomm/han/yorick/Ponti).

    Essentially, his total EHP is close to that of the 3 bulwark / 2 life, but his actual healing efficiency is through the roof because he has relatively low hp. This means he gets the most out of every 10% heal (from Zomm bonus) and also from his Epic heals (I added crit to take these heals even further).

    So it's a viable strategy in my opinion.

    The only caveat is that the comparable benefit of Aegis doesn't really seem to kick in until you are talking about high-quality Greaters or Superiors. Which your data illustrates perfectly.
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  • @4tom -- Sounds like a good setup. If your EHP is close to 3 bulwark/2 Life, then you are at least on par in mitigating direct damage. You also get the additional benefit of much lower damage over time on Burn/Poison -- and possibly indirect shock damage that spills over to you when your teammates get hit while shocked.

    I still haven't gotten up the energy to tackle the healing question yet -- maybe next week. I suspect Life stat might be the best in concert with healing as it would prevent heal loss from overhealing in some cases. Looking forward to working that all out.
  • I've been trying to figure out whether life runes are better for someone like willow who buffs 15% heath. Assuming it buffs after runes are applied.

    Or same for defense like William or yorick

  • kegman wrote: »
    I've been trying to figure out whether life runes are better for someone like willow who buffs 15% heath. Assuming it buffs after runes are applied.

    Or same for defense like William or yorick

    The buffs don't matter in the analysis because they affect the base stat and the rune stat by the same amount. You measure the relative benefit to defense by looking at the percentage the runes will increase the stat they modify. Since the buffs increase the base stat and rune stat the percentage increases aren't impacted by the buffs.
  • Foozle wrote: »
    I'm assuming the cap it at 50% to not let the stat get out of hand.

    Fantastic work work as usual Foozle. Minor point: your 50% cap assumption is correct - it's actually available on a hero's stats screen when you tap on "Damage Reduction:" it states "(Max: 50%)".
  • 4tom4tom Member
    I have to look this up a lot, so I'm giving it a bump.
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  • koz8208koz8208 Member
    Hi Foozle, I was wondering how you know that damage is calculated by the method you explained in your first post? (base damage of attacker * attack rating of attacker / defense rating of defender)?
  • FoozleFoozle Member
    koz8208 wrote: »
    Hi Foozle, I was wondering how you know that damage is calculated by the method you explained in your first post? (base damage of attacker * attack rating of attacker / defense rating of defender)?

    I determined this through testing by attacking same level enemies over and over using different rune setups. Also, I wasn't the first to come up with this -- it was established a while ago by others and I just did some of my own testing to verify. I think they are working on a revamp of the combat system, so this formula will likely change when that gets released.
  • bvs72bvs72 Member
    When @Foozle speaks, players should listen
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