Increased Physical Damage vs Global Critical Multiplier

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LBJames wrote:

All,

I have a question regarding these two mods. If I'm doing a crit phys build, which one of these two mods is more effective? For example, if I have 1000 phys damage, 300 cold damage from hatred, 1.0 attack speed, 90% crit chance, 200% increased global physical damage and 300% global crit multiplier, should I spend the next skill point/jewel mod on a 15% physical damage or 15% critical multiplier?

Thanks!

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Abdiel_Kavash wrote:

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TheBagman wrote:

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LBJames wrote:

All,

I have a question regarding these two mods. If I'm doing a crit phys build, which one of these two mods is more effective? For example, if I have 1000 phys damage, 300 cold damage from hatred, 1.0 attack speed, 90% crit chance, 200% increased global physical damage and 300% global crit multiplier, should I spend the next skill point/jewel mod on a 15% physical damage or 15% critical multiplier?

Thanks!

In this scenario, crit multi is better, but only because of the cold damage.

The crit multi only applies when you crit, so, when you crit 90% of the time, it's a total increase of 13.5%. However, that's to all damage, so it increases the 300 cold as well as the 1000 phys (1300 dmg * 1.135 = 1475 dmg). 15% increased phys applies 100% of the time, but ignores cold (1000 dmg * 1.15 = 1150 + 300 cold = 1450 dmg). The attack speed, current increased phys and current global crit multi are all irrelevant.

The lesson is that crit multi becomes more or less relevant depending on your crit chance. Were you at 50% crit, 15% increased phys would be a significantly better choice.

First, if the cold damage is provided by Hatred, it is actually "physical converted to cold", and thus will be affected by physical damage modifiers.

Second, the critical damage multiplier is not additive to increased damage. Critical strikes multiply the total damage of a single hit, therefore crit multi is multiplicative with increased damage multipliers.


In the first case (15% increased physical damage), the damage of a non-critical hit would be:

1,000 * (1 + 2 + 0.15) = 3,150 physical damage
300 * (1 + 2 + 0.15) = 945 cold damage

and the damage of a crit would be:

3,150 * 3 = 9,450 physical damage
945 * 3 = 2,835 cold damage

Since your crit chance is 90%, the average damage of a hit is

0.1 * (3,150 + 945) + 0.9 * (9,450 + 2,835) = 11,466 total damage.


In the second case (15% critical multiplier), the damage of a non-crit is:

1,000 * (1 + 2) = 3,000 physical damage
300 * (1 + 2) = 900 cold damage

the damage of a crit is:

3,000 * (3 + 0.15) = 9,450 physical
900 * (3 + 0.15) = 2,835 cold

and the average damage of a hit is:

0.1 * (3,000 + 900) + 0.9 * (9,450 + 2,835) = 11,446 total damage.


In this case, the physical damage increase is (very slightly) better than the added crit multiplier.

As for why this is, consider the following: Almost all your hits are crits, thus let's focus on the damage of a critical hit. The damage is roughly (base damage) * (increased damage multiplier) * (crit multi). As it happens with the numbers given, both your increased damage multiplier and your critical multiplier are 300%. Thus, since multiplication is commutative, it does not matter which value you increase by the same amount. The only difference between the two cases is the damage of non-critical hits, which are a small portion of all your hits.

However, in cases where your increased damage and crit multiplier are considerably different, boosting the smaller of the two will result in a higher increase of average damage. (Again only considering critical hits.) You could run the math yourself for 100% increased damage and 500% critical multiplier, or vice versa. In the first case adding damage increase is better; in the second case adding crit multi is better.