Explain Defense to Me.

[Fista]

I was in another thread today and they were talking about 45% defense and even level MOBs only having a 5% chance to hit you. Something like that. Also the difference between To Hit and Accuracy. How does it all work?

[Sarrate]

Short summary from ParagonWiki:

 

The master hit chance formula is:

HitChance = Clamp( AccMods × Clamp( BaseHitChance + ToHitMods – DefMods ) )

 

where

 

    BaseHitChance is what the attack's chance of hitting would be if there were no modifiers at all – no Enhancements, no buffs, no level differences, nothing

    ToHitMods is the sum of all ToHit buffs and debuffs (the debuffs will be negative)

    DefMods is the sum of all relevant Defense buffs and debuffs (ditto)

    AccMods is the product of all Accuracy multipliers, and

    Clamp(x) limits x to the range of 5% to 95%

 

 

ToHitMods and DefMods are 0 by default. AccMods defaults to 1.

 

The basic gist is that, against a +0 minion and you have no defense, the formula (for an NPC) would look like this:

 

HitChance = Clamp( 1.0 * Clamp(0.5 + 0 - 0) = 0.5 = 50%

 

If you're fighting a Boss, that would be:

 

HitChance = Clamp( 1.3 * Clamp(0.5 + 0 - 0) = 0.65 = 65%

 

Now, if you add 10% defense to both:

 

Minion: Clamp( 1.0 * Clamp(0.5 + 0 - 0.1) = 0.4 = 40%

Boss = Clamp( 1.3 * Clamp(0.5 + 0 - 0.1) = 0.52 = 52%

 

Let's go all the way up to 45%:

 

Minion: Clamp( 1.0 * Clamp(0.5 + 0 - 0.45) = 0.05 = 5%

Boss = Clamp( 1.3 * Clamp(0.5 + 0 - 0.45) = 0.065 = 6.5%

 

If you add any more defense on top of that (or add tohit debuffs to the mobs), they will still have a 5% and 6.5% chance to hit you, respectively. This is why people talk about the 45% defense soft cap, above that (in normal situations) it does not improve survivability.

 

 

Defense / ToHit are additive (within the clamp) while accuracy is multiplicative outside.

 

 

A few quirks:

- Accuracy will always help the final chance to hit. It may not be huge (the boss's +30% accuracy yielded +1.5% final to hit), but it's there. This also raises the lowest chance to hit.

- ToHit / Defense can both have the largest impact, and the least. If you have 45% defense, and an enemy has +5% tohit, they basically doubled their final to hit. (A minion would go from 5% to 10%, an a boss would go from 6.5% to 13%.) On the other hand, if you have +100% defense, their +5 tohit wouldn't be enough to raise the clamp above 5%, leaving their final to hit chance unchanged.

 

 

What helps me is to play with numbers and see what happens when I start changing things. Maybe create an Excel spreadsheet or something with the formula and just start changing values and observe what happens.

[Fista]

If I understand this correctly then +0 MOBs only have a 50/50 chance to hit unless there are mitigating factors, right?

[PaxArcana]

Right.

 

Hence why +45% Defense will effectively soft-cap your pets against them.

 

OTOH, mobs that are +0 to you, are as much as +2 to your pets.

 

For example, with your Tier 1 pets:

• Level 1-5: you have one pet, it is -0 to you - a +0 enemy is +0 to the pet; 45% Defense soft-caps them.
  
• Levels 6-11: you have two pets, they are -1 to you - a +0 enemy is +1 to the pets; 50% Defense soft-caps them.
  
• Levels12+: you have three 1 pets, they are -2 to you - a +0 enemy is +2 to the pets; 55% Defense soft-caps them.

 

:)

 

And remember, a Lieutenant counts as +1 more than their actual level.  A Boss counts as +2 more than their actual level.  And so on.

 

So there will be times you want even more defense than the list above suggests.

[Konru]

Not quite, from what I read of that article on Paragon Wiki.  From even level to level +5, critters have a base 50% chance to hit which defense subtracts from and +to-hit skills adds to.  (Enemies that use +to-hit skills like Tactics are extremely rare, however.)  That means a Mastermind's minions will be capped with 45% defense as long as they are fighting critters between even and +3 levels to the Mastermind.  Minions level-2 with critter level+4 means the gap is 6 levels, with starts adding accuracy.

 

Instead there is an accuracy multiplier that is added to lieutenants, bosses, and greater from a base X1.0, a 0.1 gets added each level up until it hits X1.5 at level+5.  Since this multiplier is applied as the last step in the calculation, the 45% cap rule still holds.  For example a level+4 (relative to its target) minion attacking a defense capped you or your pet has a base 50%, - 45% defense leaving it at 5%, then multiplied by 1.4 for a final to-hit chance of 7%.  Lieutenants and bosses also aren't really levels above minions, but get an additional multiplier based on their status of lieutenant (1.15) or boss (1.3).  So in worst case that level+4 boss would only have a 8.5% chance to hit.  A Giant Monster which effectively ignores level differences and has a 1.5 accuracy would have that cap at 7.5%.  If I am reading that correctly.

 

Also do be careful that there are some critter attacks that can debuff defense.  So going beyond 45% will give you some extra room to stay capped when an enemy does land one of these attacks on you.