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Basic Theorycrafting: All About Toughness, Part 1

by - 10 years ago

Hello, everyone! My Name is Dannie “IAmDir23” Ray, and I’ll be here every Saturday explaining all things theorycrafting in an effort to allo everyone to better understand the finer aspects of Diablo 3. Lets hope you haven’t forgotten all the math you learned in school because we will finally have a chance to put it to good use.


When we first started this series, it was all about DPS. We found out that the DPS formula was made of a bunch of damage factors, and toughness is no different.

Armor, HP, Resistances, Melee Reduction, Ranged Reduction, Damage Reduced from Elites. They are all part of Toughness Factors, which multiply themselves to add to your toughness, or effective HP.

We’ve done a lot of calculations on armor, all resistance, and dodge lately, but those calculations would be a lot clearer and maybe even more accurate if we had a notion of what the toughness factors are.

Hit Points

Hit points or HP are perhaps the easiest factor to calculate, as you don’t need to calculate anything. Your Max HP is your Hit Point Factor.

Armor

Here’s where it starts getting a bit more complicated. There are 3 values related to Armor, your armor amount, your armor damage reduction, and finally your armor toughness factor. Those three values are all different, and you can only access two of them from your character sheet.

Damage Reduction from Armor = Armor / (Armor +3500)

You likely known and understand the first two, but what is the armor toughness factor? In simple words, it is how many extra hits you can take before dying.

Lets say you are facing a monster that kills you in 5 attacks, lets say hitting you for 100 each time while you have 500 hp. If you had 50% armor reduction, the same monster would now hit you for 50 each time and kill you on 10 attacks. Since you went from lasting 5 attacks, to lasting 10 attacks. You can say that your armor toughness factor was 2 = 10/5. Your Armor Toughness factor is Two, because you can take Twice as many hits.

Now that’s a pretty easy and simple example, if you want to calculate it for any specific gear level. This the formula.

Armor Toughness Factor = 1/(1-Armor Reduction)

So lets say you have 75%, or 3/4 damage reduction. Plugging that into the formula you have:

1/(1-0,75) = 1/0,25 = 1/(1/4)= 4.

So you armor allows you to take 4 times as many hits. But,more importantly; if you have 500,000 HP, then your armor factor makes it so it would be equivalent to have 2,000,000 HP.

Resistances

Resistances work exactly like armor, the only interesting thing to add about them is how they interact with Armor. Take the 2,000,000 Effective HP of the above example, and now lets say you have 50% Resistance Reduction. We know that 50% reduction is equal to a 2 toughness factor. So Resistance allows you to take twice as many hits.

2,000,000 EHP * 2 = 4,000,000 EHP.

As you notices, these factors multiply with each other. So when you have a toughness upgrade, all you need to do is see how much your factor would be increasing. That will be the defining factor.

Dodge

So dodge is not a straight damage reduction, but given enough attacks, on average it works just like one. But the thing that Dodge is less like armor and resistances, and more Melee, Ranged, or Elites reductions. Dodge only applies to certain attacks, which reduces its effectiveness by a lot. Still, here’s the formula.

Dodge Toughness Factor = 1/(1-Dodge Chance)

Other Factors

There are a lot of things that provide tougness, but most of them are damage reductions. All of them work the same way mathematically.

Toughness Factor = 1/(1-damage reduction)

The thing with toughness is that there are a lot of factors that are mutually exclusive. Like you can’t benefit from Fire Resist and Cold Resist against the same attack, and likeways you can’t benefit from Melee reduction and Ranged Reduction. So you basically have different toughness levels against different types of attack.

Formula Crafting

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Lets say you want to calculate your toughness against melee, physical attacks, executed by elites. Since that’s an attack you CAN dodge, the formula would be like the one below.

Toughness = MAX HP * Armor Toughness Factor * Physical Resistance Toughness Factor * Dodge Toughness Factor * Melee Toughness Factor * Elites Toughness Factor

And just like that, the formula would change depending on the attacks you expect to take. But that’s enough for this week’s edition.

Next week we will take a look at graphs, diminishing returns, and how the different toughness stats can scale.

 


JR Cook

JR has been writing for fan sites since 2000 and has been involved with Blizzard Exclusive fansites since 2003. JR was also a co-host for 6 years on the Hearthstone podcast Well Met! He helped co-found BlizzPro in 2013.


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