Diablo® III

Toughness: What it really means

DISCLAIMER: I am not saying toughness is wrong, or vit/hp are bad. I'm just trying to show you it may mean something other than you think, and not take the toughness value as gospel for allowing people into games.

I posted this in the crusader forum for a reason. Certain "glass-cannon" classes need more HP because of how their defenses work and the reality of their playstyle (like a rift boss that hits hard and has vortex). Crusader has to be "in the thick of it" and generally speaking can take a few more hits due to innately higher armor (thanks to shields).

This is important for melee on higher torments, but higher burst classes like Wizards and Demon Hunters will probably still favor HP due to being able to burst down packs within their HP pool + potion.


I see a lot of people throwing around their character sheet damage and toughness numbers on this forum. I won't go into why looking into damage is silly (that's kind of obvious since there's +elemental damage, cooldown reduction, etc), but I would like to give you guys a heads up about why toughness is misleading.

Toughness is the game's calculation of how much "raw" damage you can take before dying, IGNORING HEALING. This is done by using your mitigation % (based on armor, dodge, resists, etc) and your HP. However, because it doesn't distinguish between raw mitigation and high HP, it can make you think you are a lot "tougher" than you really are.

Lets take a look at two players. For the purposes of this, we will lump all mitigation stats together (dodge, armor, resists). We will do the same for healing (life per second, life per kill, life per hit) into an average "healing per second" as well for simplicity's sake.

Player A:

    HP: 100,000
    Mitigation: 50%
    Healing per second: 10,000


Player B:

    HP: 50,000
    Mitigation: 75%
    Healing per second: 10,000


So to start, you can see both of these players would die at the same point: taking a hit for 200k. According to the game, they would both have the exact same toughness. But let's be honest, in this game you don't get 1-shot typically; you get hit very often by painful things like arcane, fire chains, poison enchanted, etc. And that is where Player B would have a MASSIVE advantage over player A.

Effective DPS survival threshold:

    Player A: 10,000 * 1/(1-.5) = 20,000
    Player B: 10,000 * 1/(1-.75) = 40,000


Player B's mitigation allows him to successfully survive TWICE the incoming damage indefinitely (the stand-in-poo scenario) because his healing is more effective relative to his HP. Additionally, this makes healing a better survival stat for player B than A.

Let's mix things up. Now lets get Player A an extra 5k healing per second, pushing him to 15k hps:

Effective DPS survival threshold:

    Player A: 15,000 * 1/(1-.5) = 30,000
    Player B: 10,000 * 1/(1-.75) = 40,000


Well look at that, player B *STILL* wins, even with less healing & hp. Now his character sheet stats are WORSE than player A, but he's still better off! This tells us that mitigation makes the healing stat more effective compared to more HP.

As such, if you are looking at an item and are trying to decide if you should reroll the vit or all resists/armor off for a damage stat, consider removing the vit if you are >300k hp. While the game sheet may show your overall toughness being lower, if you have ANY healing at all you will be (in relative terms) losing survivability by using vit/% life over mitigation stats.

Technically, blizzard could fix this by factoring healing into the toughness calculation.

Also remember block is NOT calculated in character sheet toughness, but is extremely powerful for any effect that hits quickly and can be blocked. When combined with renewal, you can actually HEAL yourself standing in certain affixes (like fire chains, Malthael's whirl attack).

TLDR: Character sheet toughness is misleading and often wrong. Vit and +% Life are not as effective as mitigation stats and healing in terms of long-term survival.

EDIT: Changed a few things based on feedback here and on reddit.
Edited by Xyrm#1598 on 4/3/2014 6:58 AM PDT
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This is a good explanation (did not actually check the math, sounds legit).
There was some similar talk earlier but focusing more on how misleading the damage is.

I think more constructive (and positive) posting like this will go a long way in stopping all the forum rage as people think more about gear choices.
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This is well written and I thank you for posting this. This information will help me greatly as I level my crusader.
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I still follow the 10:1 ratio rule of armor to all resists. It works well.

Example, if you have 10,000 armor you should ideally have 1,000 all resists. Try to keep that balance the best you can. Throw in some life regen/life per hit/life after kill and bonus globes to be unstoppable.
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Nice write-up, but it only really applies if your main sources of healing are static values. Things like potions and % max-life-per-second favor the one with the higher toughness value.

Still, it's a good thing to keep in mind if you have a choice between health and mitigation.
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04/02/2014 07:38 AMPosted by Xyrm
This tells us that mitigation makes the healing stat more effective compared to more HP.


You can quantify this effect by measuring healing in "toughness per second."

The math to do this is simple. Take Toughness and divide Life. This number, which could reasonably be something between 5 and 20, very roughly, scales up your healing. Call it mitigation ratio.

Take your Healing and multiply it by the Mitigation Ratio. Voila! You're now measuring healing in toughness per second. You could call this effective healing because it scales up with damage mitigation.

While removing vitality may hurt paper doll Toughness, trading vitality for mitigation will simply trade Toughness for Effective Healing instead. This makes the real tradeoff much clearer.
Edited by Muphrid#1168 on 4/2/2014 11:00 AM PDT
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04/02/2014 08:35 AMPosted by CptnCrunch
I still follow the 10:1 ratio rule of armor to all resists. It works well.

Is there any math laid out behind this? A Google spreadsheet or anything? I'd love to have some numbers to crunch.

04/02/2014 10:59 AMPosted by Muphrid
You can quantify this effect by measuring healing in "toughness per second."

The math to do this is simple. Take Toughness and divide Life. This number, which could reasonably be something between 5 and 20, very roughly, scales up your healing. Call it mitigation ratio.

Take your Healing and multiply it by the Mitigation Ratio. Voila! You're now measuring healing in toughness per second. You could call this effective healing because it scales up with damage mitigation.

Love this. "Effective Survivability per Second?" ;)
Edited by Mog#1733 on 4/2/2014 11:33 AM PDT
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very good post actually, i like it.
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very well written and informative will help a lot a lot of people prioritze gear more efficiently now . very good job sir.
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Great info
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04/02/2014 08:53 AMPosted by Stardrinker
Nice write-up, but it only really applies if your main sources of healing are static values. Things like potions and % max-life-per-second favor the one with the higher toughness value.


Unless I'm missing something, I'm pretty sure this is a misconception also. Percentage healing only levels the two, but doesn't favor the hp over the mitigation. The percentage healing gives you more hp back, but each point of health is worth less than for the player with more damage mitigation, which in the end equals up.

It's easily calculated with the above numbers. If we take the health regained from a 60% health pot:

(100 000 x 1.6) / (1 - 0.5) = 320 000 effective hp.
(50 000 x 1.6) / (1 - 0.75) = 320 000 effective hp.
Edited by Kadani#1218 on 4/2/2014 12:17 PM PDT
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04/02/2014 07:38 AMPosted by Xyrm
TLDR: Character sheet toughness is misleading and often wrong. Vit and +% Life are bad stats (past the point where you no longer get 1-shot); healing and mitigation (armor and resists) are vastly superior.


Don't trust ingame stats, use a spreadsheet.

The problem with the toughness stat is the impact difficulty level has on it. Monster damage scales up 4x at Torment 1 and 25x at Torment 6. At specific monster damage thresholds and difficulty levels 100 all res maybe be better than 500 Vitality, but that also means below that threshold the Vitality is better. The decision on whether an item is an upgrade is more than red or green text.
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04/02/2014 11:32 AMPosted by Mog
04/02/2014 08:35 AMPosted by CptnCrunch
I still follow the 10:1 ratio rule of armor to all resists. It works well.

Is there any math laid out behind this? A Google spreadsheet or anything? I'd love to have some numbers to crunch.


I was just doing some simple math.. and the results were actually pretty surprising.

Damage reduction from armor and resist all are calculated multiplicative.

if you were to take a raw 100,000 damage hit on a say 70% reduction from armor and 70% reduction from resist all would be 100,000 x 0.3 x 0.3 = 9,000 damage.

However, if you were to sacrifice 5% from armor, and increase 5% to resist all, you would take less damage than if they were 70/70. so let's look at 65/75.

100,000 x 0.25 x 0.35 = 8,750.

The conclusion to this is to really just focus on either armor, or resist all and try not to balance the two..?
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<span class="truncated">...</span>
Is there any math laid out behind this? A Google spreadsheet or anything? I'd love to have some numbers to crunch.


I was just doing some simple math.. and the results were actually pretty surprising.

Damage reduction from armor and resist all are calculated multiplicative.

if you were to take a raw 100,000 damage hit on a say 70% reduction from armor and 70% reduction from resist all would be 100,000 x 0.3 x 0.3 = 9,000 damage.

However, if you were to sacrifice 5% from armor, and increase 5% to resist all, you would take less damage than if they were 70/70. so let's look at 65/75.

100,000 x 0.25 x 0.35 = 8,750.

The conclusion to this is to really just focus on either armor, or resist all and try not to balance the two..?


In theory, yes, but you have to take the cost into consideration. Since each point invested in either Armor or All resist will provide less damage reduction than the previous point (percentage wise, there is no diminishing return), gaining an extra 5% of all resist will take more all resis than it's equivalent in armor (10x) that you will need to lose its 5%.

Since there is a maximum value of Armor/All res a piece of gear can provide, it's easier to balance the two to get the 70/70 in your example than it would be to get the 65/75.
Edited by Kadani#1218 on 4/2/2014 12:54 PM PDT
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04/02/2014 07:38 AMPosted by Xyrm
Technically, blizzard could fix this by factoring healing into the toughness calculation.


All of your assumptions are based on sustained damage intake over a long period of time, not heavy intake over a relatively short period of time. This is where you are wrong.

From loads of experience farming T1-T3 Rifts where the largest dangers are 2-3 elite packs pulled at one time, I estimate that usually I go from full to zero in about 10 seconds, often less. Generally speaking 10 seconds is enough time to escape, kill the pack, find some health globes, etc. I am NEVER at a risk of dying from sustained damage, as you are using to make your point.

So, while you are correct that trading Life for DR makes the healing you have more effective, you are incorrect in assuming that healing is a better stat than life.

Lets take an example. 3 players get 2 packs at once, uh oh, a jailer/arcane and a frozen/frozen pulse.

They each take 1m DPS at once (this is a realistic number). The survival time equation we will use is:

Health / (IncomingDPS*(1-Mitigation)-HealingPerSecond)

Player A
500,000 Health
95% Mitigation
0 Healing per Second
Survival Time: 500,000/(1,000,000*(1-.95)-0) = 10 seconds.

Player B
400,000 Health
95% Mitigation
5,000 Healing per Second
Survival Time: 400,000/(1,000,000*(1-.95)-5000) = 8.89 seconds.

Player C
300,000 Health
95% Mitigation
10,000 Healing per Second
Survival Time: 300,000/(1,000,000*(1-.95)-10000) = 7.5 seconds.

As you can see, even sacrificing life for healing, player C is going to die a lot sooner than player A. This isn't even considering that its easier to get life than healing. The ratio of choosing Vitality to Life per Second is about 750:2500 or in terms of life, 60000:2500 or 24:1. In my examples I was being generous in terms of healing by using a ratio of 20:1, which you won't typically see on gear besides rings.

In this example, which is far more typical than dying slowly over 15+ seconds, +Life is CLEARLY a better choice than Life per Second.
Edited by wrl#1505 on 4/2/2014 1:04 PM PDT
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04/02/2014 12:58 PMPosted by wrl
04/02/2014 07:38 AMPosted by Xyrm
Technically, blizzard could fix this by factoring healing into the toughness calculation.


All of your assumptions are based on sustained damage intake over a long period of time, not heavy intake over a relatively short period of time. This is where you are wrong.

From loads of experience farming T1-T3 Rifts where the largest dangers are 2-3 elite packs pulled at one time, I estimate that usually I go from full to zero in about 10 seconds, often less. Generally speaking 10 seconds is enough time to escape, kill the pack, find some health globes, etc. I am NEVER at a risk of dying from sustained damage, as you are using to make your point.

So, while you are correct that trading Life for DR makes the healing you have more effective, you are incorrect in assuming that healing is a better stat than life.

Lets take an example. 3 players get 2 packs at once, uh oh, a jailer/arcane and a frozen/frozen pulse.

They each take 1m DPS at once (this is a realistic number). The survival time equation we will use is:

Health / (IncomingDPS*(1-Mitigation)-HealingPerSecond)

Player A
500,000 Health
95% Mitigation
0 Healing per Second
Survival Time: 500,000/(1,000,000*(1-.95)-0) = 10 seconds.

Player B
400,000 Health
95% Mitigation
5,000 Healing per Second
Survival Time: 400,000/(1,000,000*(1-.95)-5000) = 8.89 seconds.

Player C
300,000 Health
95% Mitigation
10,000 Healing per Second
Survival Time: 300,000/(1,000,000*(1-.95)-10000) = 7.5 seconds.

As you can see, even sacrificing life for healing, player C is going to die a lot sooner than player A. This isn't even considering that its easier to get life than healing. The ratio of choosing Vitality to Life per Second is about 750:2500 or in terms of life, 60000:2500 or 24:1. In my examples I was being generous in terms of healing by using a ratio of 20:1, which you won't typically see on gear besides rings.

In this example, which is far more typical than dying slowly over 15+ seconds, +Life is CLEARLY a better choice than Life per Second.


Your example is bias.. let me fix the numbers for you.. Because you can't account for just healing and max health. The OP also talked about Max health vs Damage reduction.

Player A
500,000 Health
85% Mitigation <----
0 Healing per Second
Survival Time: 500,000/(1,000,000*(1-.85)-0) = 3.33 seconds.

Player B
400,000 Health
90% Mitigation <----
5,000 Healing per Second
Survival Time: 400,000/(1,000,000*(1-.90)-5000) = 4.21 seconds.

Player C
300,000 Health
95% Mitigation <-----
10,000 Healing per Second
Survival Time: 300,000/(1,000,000*(1-.95)-10000) = 7.5 seconds.
Edited by Concretefist#1327 on 4/2/2014 1:22 PM PDT
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Player A
500,000 Health
85% Mitigation <----
0 Healing per Second
Survival Time: 500,000/(1,000,000*(1-.85)-0) = 3.33 seconds.

Player B
400,000 Health
90% Mitigation <----
5,000 Healing per Second
Survival Time: 400,000/(1,000,000*(1-.90)-5000) = 4.21 seconds.

Player C
300,000 Health
95% Mitigation <-----
10,000 Healing per Second
Survival Time: 300,000/(1,000,000*(1-.95)-10000) = 7.5 seconds.


You are giving Player C WAY better gear than player A, and I specifically stated that I was talking about Life vs Healing, not Life vs Mitigation AND healing. I'd love to see you come up with a way for Player C to get 10% Mitigation and 10,000 Healing for the cost of only 200,000 life.
Edited by wrl#1505 on 4/2/2014 1:34 PM PDT
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...

I was just doing some simple math.. and the results were actually pretty surprising.

Damage reduction from armor and resist all are calculated multiplicative.

if you were to take a raw 100,000 damage hit on a say 70% reduction from armor and 70% reduction from resist all would be 100,000 x 0.3 x 0.3 = 9,000 damage.

However, if you were to sacrifice 5% from armor, and increase 5% to resist all, you would take less damage than if they were 70/70. so let's look at 65/75.

100,000 x 0.25 x 0.35 = 8,750.

The conclusion to this is to really just focus on either armor, or resist all and try not to balance the two..?


In theory, yes, but you have to take the cost into consideration. Since each point invested in either Armor or All resist will provide less damage reduction than the previous point (percentage wise, there is no diminishing return), gaining an extra 5% of all resist will take more all resis than it's equivalent in armor (10x) that you will need to lose its 5%.

Since there is a maximum value of Armor/All res a piece of gear can provide, it's easier to balance the two to get the 70/70 in your example than it would be to get the 65/75.


In general, for me as a Monk it's easier for me to get all resist than it is armor. If I'm understanding the only reason to balance 10:1 armor/AR is stat constraints on items? So as an OWE Monk, my balance is slightly different since I can roll higher resist as a single resist on secondary stat. Not only does this free up a primary, it is more effective at reducing damage to have AR > armor?
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By Muphrid's forumla, I'm at 122,268 "effective healing" . What's a good number to aim at? Because my sader is pretty terrible even in t1. Then again my main for the last 2 years has been a wizard....

Pre-post edit: Oddly, my wizard's "effective healing" is only 33,140 but he survives far better on Torment II than my crusader does in torment 1. By surviving, lets use that arcane beam example. My wizard can stand in those for almost a full second more. They both have the same amount of HP (give or take a few hundred), but I'm guessing the difference lies in the fact that my wizard has like 300 more AR? Is this evidence of AR still being far better than armor and even healing?

This isn't even factoring in crusader passives like Renewal or Wrathful , as Ive noticed they do not change the "Healing" value, but are insane sources of healing. But even with those he still dies noticeably faster than my wizard.

So I guess this formula doesn't really work since AR is just that much better but still not reliably calculated by "toughness". When comparing gear with one that has the same stats but no AR, losing 100 AR shows a 0.1% loss when I know for a fact the difference is far larger than that...
Edited by Kougeru#1706 on 4/2/2014 1:59 PM PDT
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